PHSX 220 Homework 13 Paper – Due Online April 28 – 5:00 pm SHM and Wave the Equation Problem 1: A hanging mass system with a mass of 85 kg, spring constant of k= 490 N/m is realeased from rest from a distance of 10 meters below the systems equilibrium position (similar values to the bottom of a bungee jump). Calculate the following quantities in regards to this system after being released at t=0: a) The angular frequency of the system (radians/sec) b) The frequency of oscillations for the system (Hz) c) The period of oscillations for the system (seconds) d) The time it takes to get back to the equilibrium position of the system for the rst time Problem 2: A horizontal spring-mass system (mass of 2:21×10􀀀25 kg) with no friction has an ocsillation frequency of 9,192,631,770 cycles per second. (a second is de ned by 9,192,631,770 cycles of a Cs-133 atom)). Calculate the e ective spring constant of the system Problem 3: A swinging person, such as Tarzan, can be modeled after a simple pendulum with a mass of 85 kg and a length of 10 m. Consider the mass being released from rest at t=0 at an angle of +15 degrees from the vertical. Calculate the following quantities in regards to this system. You need to be in radians mode for this problem a) The angular frequency of the system (radians/sec) b) The frequency of oscillations for the system in (Hz) c) The period of oscillations of the system (seconds) d) Sketch plots of the angular position, angular velocity and angular acceleration of the system as a function of time. Hint: These will always help you with these time to it takes to a certain point in it’s cycle questions. e) The time it takes for the mass to get half way through its rst cycle (or to the other side of the swing if you were interested in timing say a rescue e ort or something along those lines) . f) The maximum angular velocity of the mass g) The maximum angular accleration of the mass h) The magnitude of the angular momentum of the mass at 3 seconds i) The magnitude of the torque acting on the mass at 3 seconds Problem 4: A wave has a wavenumber of 1 m-1, and an angular frequency of 2 radians per second, travels in the +x direction and has a maximum transverse amplitude of 0.1 m. At t=0, and x =0 the y position is equal to 0.0 m (y(0,0) = 0.0 m). a) Calculate the wavelength of the wave b) Calculate the period of oscillations for the wave c) Calculate the wave speed along the x axis d) Calculate the magnitude and direction of the transverse position of the wave at x=0.5 m and t = 8s e) Calculate the magnitude and direction of the transverse velocity of the wave at x=0.5 m and t = 8s f) Calculate the magnitude and direction of the transverse acceleration of the wave at x=0.5 m and t = 8s Problem 5-6: Chapter 16 Problem 10, 22 Additional Suggested Problems with Solutions Provided: Chapter 16 Problems 5, 9, 15, 45

PHSX 220 Homework 13 Paper – Due Online April 28 – 5:00 pm SHM and Wave the Equation Problem 1: A hanging mass system with a mass of 85 kg, spring constant of k= 490 N/m is realeased from rest from a distance of 10 meters below the systems equilibrium position (similar values to the bottom of a bungee jump). Calculate the following quantities in regards to this system after being released at t=0: a) The angular frequency of the system (radians/sec) b) The frequency of oscillations for the system (Hz) c) The period of oscillations for the system (seconds) d) The time it takes to get back to the equilibrium position of the system for the rst time Problem 2: A horizontal spring-mass system (mass of 2:21×10􀀀25 kg) with no friction has an ocsillation frequency of 9,192,631,770 cycles per second. (a second is de ned by 9,192,631,770 cycles of a Cs-133 atom)). Calculate the e ective spring constant of the system Problem 3: A swinging person, such as Tarzan, can be modeled after a simple pendulum with a mass of 85 kg and a length of 10 m. Consider the mass being released from rest at t=0 at an angle of +15 degrees from the vertical. Calculate the following quantities in regards to this system. You need to be in radians mode for this problem a) The angular frequency of the system (radians/sec) b) The frequency of oscillations for the system in (Hz) c) The period of oscillations of the system (seconds) d) Sketch plots of the angular position, angular velocity and angular acceleration of the system as a function of time. Hint: These will always help you with these time to it takes to a certain point in it’s cycle questions. e) The time it takes for the mass to get half way through its rst cycle (or to the other side of the swing if you were interested in timing say a rescue e ort or something along those lines) . f) The maximum angular velocity of the mass g) The maximum angular accleration of the mass h) The magnitude of the angular momentum of the mass at 3 seconds i) The magnitude of the torque acting on the mass at 3 seconds Problem 4: A wave has a wavenumber of 1 m-1, and an angular frequency of 2 radians per second, travels in the +x direction and has a maximum transverse amplitude of 0.1 m. At t=0, and x =0 the y position is equal to 0.0 m (y(0,0) = 0.0 m). a) Calculate the wavelength of the wave b) Calculate the period of oscillations for the wave c) Calculate the wave speed along the x axis d) Calculate the magnitude and direction of the transverse position of the wave at x=0.5 m and t = 8s e) Calculate the magnitude and direction of the transverse velocity of the wave at x=0.5 m and t = 8s f) Calculate the magnitude and direction of the transverse acceleration of the wave at x=0.5 m and t = 8s Problem 5-6: Chapter 16 Problem 10, 22 Additional Suggested Problems with Solutions Provided: Chapter 16 Problems 5, 9, 15, 45

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Homework 1 (Homework) Vanessa Amador Introduction to General Physics II – PHYS 1022, section 001, Fall 2013 Instructor: Nikolaos Sparveris Current Score : – / 16 Due : Saturday, September 28 2013 06:00 PM EDT 1. –/1 points SerCP9 15.P.001. A 7.10 nC charge is located 1.64 m from a 3.94 nC point charge. (a) Find the magnitude of the electrostatic force that one charge exerts on the other. N (b) Is the force attractive or repulsive? attractive repulsive 2. –/2 points SerCP9 15.P.026. Three point charges are located on a circular arc as shown in the figure below. (Let r = 4.32 cm. Let to the right be the +x direction and up along the screen be the +y direction.) (a) What is the total electric field at P, the center of the arc? = + (b) Find the electric force that would be exerted on a point charge placed at P. = + WebAssign −5.2 nC Homework 1 http://www.webassign.net/web/Student/Assignment-Responses/last?dep… 1 of 6 9/27/2013 8:41 PM 3. –/2 points SerCP9 15.P.044. A charge q = +3.53 μC is located at the center of a regular tetrahedron (a four-sided surface) as in figure below. (a) Find the total electric flux through the tetrahedron. N · m 2 /C (b) Find the electric flux through one face of the tetrahedron. N · m2/C Homework 1 http://www.webassign.net/web/Student/Assignment-Responses/last?dep… 2 of 6 9/27/2013 8:41 PM 4. –/1 points SerCP9 15.P.051.WI. Three point charges are aligned along the x-axis as shown in the figure below. Find the electric field at the position x = +2.2 m, y = 0. magnitude N/C direction: The field is in the +y direction. The field is in the −x direction. The field is in the −y direction. The field is in the +x direction. There is no field at the position x = +2.2 m, y = 0. 5. –/3 points SerCP9 16.P.002. A proton is released from rest in a uniform electric field of magnitude 397 N/C. (a) Find the electric force on the proton. magnitude N direction (b) Find the acceleration of the proton. magnitude m/s 2 direction (c) Find the distance it travels in 2.04 μs. cm Homework 1 http://www.webassign.net/web/Student/Assignment-Responses/last?dep… 3 of 6 9/27/2013 8:41 PM 6. –/1 points SerCP9 16.P.005.soln. The potential difference between the accelerating plates of a TV set is about 30 kV. If the distance between the plates is 1.9 cm, find the magnitude of the uniform electric field in the region between the plates. N/C 7. –/2 points SerCP9 16.P.013.soln. Consider the following figure. (a) Find the electric potential, taking zero at infinity, at the upper right corner (the corner without a charge) of the rectangle in the figure. (Let y = 3.5 cm and x = 5.8 cm.) J/C (b) Repeat if the 2.00-μC charge is replaced with a charge of −2.00 μC. J/C Homework 1 http://www.webassign.net/web/Student/Assignment-Responses/last?dep… 4 of 6 9/27/2013 8:41 PM 8. –/1 points SerCP9 16.P.023.WI. In Rutherford’s famous scattering experiments that led to the planetary model of the atom, alpha particles (having charges of +2e and masses of 6.64 × 10−27 kg) were fired toward a gold nucleus with charge +79e. An alpha particle, initially very far from the gold nucleus, is fired at 2.0 10 7 m/s directly toward the nucleus, as in the figure below. How close does the alpha particle get to the gold nucleus before turning around? Assume the gold nucleus remains stationary. m Homework 1 http://www.webassign.net/web/Student/Assignment-Responses/last?dep… 5 of 6 9/27/2013 8:41 PM 9. –/3 points SerCP9 16.P.037. For the system of capacitors shown in the figure below, find the following. (Let C 1 = 4.00 μF and C 2 = 8.00 μF.) (a) the equivalent capacitance of the system μF (b) the charge on each capacitor on C 1 μC on C 2 μC on the 6.00 μF capacitor μC on the 2.00 μF capacitor μC (c) the potential difference across each capacitor across C 1 V across C 2 V across the 6.00 μF capacitor V across the 2.00 μF capacitor V Homework 1 http://www.webassign.net/web/Student/Assignment-Responses/last?dep… 6 of 6 9/27/2013 8:41 PM

Homework 1 (Homework) Vanessa Amador Introduction to General Physics II – PHYS 1022, section 001, Fall 2013 Instructor: Nikolaos Sparveris Current Score : – / 16 Due : Saturday, September 28 2013 06:00 PM EDT 1. –/1 points SerCP9 15.P.001. A 7.10 nC charge is located 1.64 m from a 3.94 nC point charge. (a) Find the magnitude of the electrostatic force that one charge exerts on the other. N (b) Is the force attractive or repulsive? attractive repulsive 2. –/2 points SerCP9 15.P.026. Three point charges are located on a circular arc as shown in the figure below. (Let r = 4.32 cm. Let to the right be the +x direction and up along the screen be the +y direction.) (a) What is the total electric field at P, the center of the arc? = + (b) Find the electric force that would be exerted on a point charge placed at P. = + WebAssign −5.2 nC Homework 1 http://www.webassign.net/web/Student/Assignment-Responses/last?dep… 1 of 6 9/27/2013 8:41 PM 3. –/2 points SerCP9 15.P.044. A charge q = +3.53 μC is located at the center of a regular tetrahedron (a four-sided surface) as in figure below. (a) Find the total electric flux through the tetrahedron. N · m 2 /C (b) Find the electric flux through one face of the tetrahedron. N · m2/C Homework 1 http://www.webassign.net/web/Student/Assignment-Responses/last?dep… 2 of 6 9/27/2013 8:41 PM 4. –/1 points SerCP9 15.P.051.WI. Three point charges are aligned along the x-axis as shown in the figure below. Find the electric field at the position x = +2.2 m, y = 0. magnitude N/C direction: The field is in the +y direction. The field is in the −x direction. The field is in the −y direction. The field is in the +x direction. There is no field at the position x = +2.2 m, y = 0. 5. –/3 points SerCP9 16.P.002. A proton is released from rest in a uniform electric field of magnitude 397 N/C. (a) Find the electric force on the proton. magnitude N direction (b) Find the acceleration of the proton. magnitude m/s 2 direction (c) Find the distance it travels in 2.04 μs. cm Homework 1 http://www.webassign.net/web/Student/Assignment-Responses/last?dep… 3 of 6 9/27/2013 8:41 PM 6. –/1 points SerCP9 16.P.005.soln. The potential difference between the accelerating plates of a TV set is about 30 kV. If the distance between the plates is 1.9 cm, find the magnitude of the uniform electric field in the region between the plates. N/C 7. –/2 points SerCP9 16.P.013.soln. Consider the following figure. (a) Find the electric potential, taking zero at infinity, at the upper right corner (the corner without a charge) of the rectangle in the figure. (Let y = 3.5 cm and x = 5.8 cm.) J/C (b) Repeat if the 2.00-μC charge is replaced with a charge of −2.00 μC. J/C Homework 1 http://www.webassign.net/web/Student/Assignment-Responses/last?dep… 4 of 6 9/27/2013 8:41 PM 8. –/1 points SerCP9 16.P.023.WI. In Rutherford’s famous scattering experiments that led to the planetary model of the atom, alpha particles (having charges of +2e and masses of 6.64 × 10−27 kg) were fired toward a gold nucleus with charge +79e. An alpha particle, initially very far from the gold nucleus, is fired at 2.0 10 7 m/s directly toward the nucleus, as in the figure below. How close does the alpha particle get to the gold nucleus before turning around? Assume the gold nucleus remains stationary. m Homework 1 http://www.webassign.net/web/Student/Assignment-Responses/last?dep… 5 of 6 9/27/2013 8:41 PM 9. –/3 points SerCP9 16.P.037. For the system of capacitors shown in the figure below, find the following. (Let C 1 = 4.00 μF and C 2 = 8.00 μF.) (a) the equivalent capacitance of the system μF (b) the charge on each capacitor on C 1 μC on C 2 μC on the 6.00 μF capacitor μC on the 2.00 μF capacitor μC (c) the potential difference across each capacitor across C 1 V across C 2 V across the 6.00 μF capacitor V across the 2.00 μF capacitor V Homework 1 http://www.webassign.net/web/Student/Assignment-Responses/last?dep… 6 of 6 9/27/2013 8:41 PM

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PHSX 220 Homework 13 D2L – Friday April 28 – 5:00 pm SHM and Pendula Problem 1: Shown below are 6 identical masses attached to springs and hung vertically. The masses are pulled down various distances and then released. The spring constant (k), spring sti ness, and the distance (d) that the mass is pulled down from its equilibrium position are given for each situation. The expression relating k and m to the angular frequency of the system is the same for both a horizontal and vertical spring-block system. Rank the situations based on the time it takes the mass to get from its maximum height to its minimum height from greatest to least. Problem 2: Shown below are systems containing a block resting on a frictionless surface and attached to the end of a spring. The springs are displaced to the right by a distance given in each gure and then released from rest. The blocks oscillate back and forth. The mass and spring constant are given for each system. Rank the cases based on the frequency of oscillation from greatest to least. Problem 3: Shown below are six masses hung on the ends of strings forming a pendulum. The masses have been pulled to the side and released so that they are swinging back and forth. For each pendulum the diagrams give the mass of the swinging object, the frequency of the swing, and how far, in terms of the angle from the vertical, that the masses were initially pulled to the side. Rank the six cases based on the length of the string from greatest to least. Problem 4: Shown below are four spring-cart systsems that consist of a spring connected to a cart. All systems are shown with the cart located at the equilibrium position. The cart is resting on a horizontal frictionless surface. If the cart is pulled to the right a small distance and released, the mass will oscillate back and forth. The amplitude of oscillation, mass of the cart and spring constants for the four cases are provided in the gure. Rank the cases shown based on their frequency of oscillation from greatest to least.

PHSX 220 Homework 13 D2L – Friday April 28 – 5:00 pm SHM and Pendula Problem 1: Shown below are 6 identical masses attached to springs and hung vertically. The masses are pulled down various distances and then released. The spring constant (k), spring sti ness, and the distance (d) that the mass is pulled down from its equilibrium position are given for each situation. The expression relating k and m to the angular frequency of the system is the same for both a horizontal and vertical spring-block system. Rank the situations based on the time it takes the mass to get from its maximum height to its minimum height from greatest to least. Problem 2: Shown below are systems containing a block resting on a frictionless surface and attached to the end of a spring. The springs are displaced to the right by a distance given in each gure and then released from rest. The blocks oscillate back and forth. The mass and spring constant are given for each system. Rank the cases based on the frequency of oscillation from greatest to least. Problem 3: Shown below are six masses hung on the ends of strings forming a pendulum. The masses have been pulled to the side and released so that they are swinging back and forth. For each pendulum the diagrams give the mass of the swinging object, the frequency of the swing, and how far, in terms of the angle from the vertical, that the masses were initially pulled to the side. Rank the six cases based on the length of the string from greatest to least. Problem 4: Shown below are four spring-cart systsems that consist of a spring connected to a cart. All systems are shown with the cart located at the equilibrium position. The cart is resting on a horizontal frictionless surface. If the cart is pulled to the right a small distance and released, the mass will oscillate back and forth. The amplitude of oscillation, mass of the cart and spring constants for the four cases are provided in the gure. Rank the cases shown based on their frequency of oscillation from greatest to least.

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Assignment 10 Due: 11:59pm on Wednesday, April 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 12.3 Part A The figure shows three rotating disks, all of equal mass. Rank in order, from largest to smallest, their rotational kinetic energies to . Rank from largest to smallest. To rank items as equivalent, overlap them. ANSWER: Ka Kc Correct Conceptual Question 12.6 You have two steel solid spheres. Sphere 2 has twice the radius of sphere 1. Part A By what factor does the moment of inertia of sphere 2 exceed the moment of inertia of sphere 1? ANSWER: I2 I1 Correct Problem 12.2 A high-speed drill reaches 2500 in 0.59 . Part A What is the drill’s angular acceleration? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B Through how many revolutions does it turn during this first 0.59 ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct I2/I1 = 32 rpm s  = 440 rad s2 s  = 12 rev Constant Angular Acceleration in the Kitchen Dario, a prep cook at an Italian restaurant, spins a salad spinner and observes that it rotates 20.0 times in 5.00 seconds and then stops spinning it. The salad spinner rotates 6.00 more times before it comes to rest. Assume that the spinner slows down with constant angular acceleration. Part A What is the angular acceleration of the salad spinner as it slows down? Express your answer numerically in degrees per second per second. Hint 1. How to approach the problem Recall from your study of kinematics the three equations of motion derived for systems undergoing constant linear acceleration. You are now studying systems undergoing constant angular acceleration and will need to work with the three analogous equations of motion. Collect your known quantities and then determine which of the angular kinematic equations is appropriate to find the angular acceleration . Hint 2. Find the angular velocity of the salad spinner while Dario is spinning it What is the angular velocity of the salad spinner as Dario is spinning it? Express your answer numerically in degrees per second. Hint 1. Converting rotations to degrees When the salad spinner spins through one revolution, it turns through 360 degrees. ANSWER: Hint 3. Find the angular distance the salad spinner travels as it comes to rest Through how many degrees does the salad spinner rotate as it comes to rest? Express your answer numerically in degrees. Hint 1. Converting rotations to degrees  0 = 1440 degrees/s  =  − 0 One revolution is equivalent to 360 degrees. ANSWER: Hint 4. Determine which equation to use You know the initial and final velocities of the system and the angular distance through which the spinner rotates as it comes to a stop. Which equation should be used to solve for the unknown constant angular acceleration ? ANSWER: ANSWER: Correct Part B How long does it take for the salad spinner to come to rest? Express your answer numerically in seconds.  = 2160 degrees   = 0 + 0t+  1 2 t2  = 0 + t = + 2( − ) 2 20 0  = -480 degrees/s2 Hint 1. How to approach the problem Again, you will need the equations of rotational kinematics that apply to situations of constant angular acceleration. Collect your known quantities and then determine which of the angular kinematic equations is appropriate to find . Hint 2. Determine which equation to use You have the initial and final velocities of the system and the angular acceleration, which you found in the previous part. Which is the best equation to use to solve for the unknown time ? ANSWER: ANSWER: Correct ± A Spinning Electric Fan An electric fan is turned off, and its angular velocity decreases uniformly from 540 to 250 in a time interval of length 4.40 . Part A Find the angular acceleration in revolutions per second per second. Hint 1. Average acceleration Recall that if the angular velocity decreases uniformly, the angular acceleration will remain constant. Therefore, the angular acceleration is just the total change in angular velocity divided by t t  = 0 + 0t+  1 2 t2  = 0 + t = + 2( − ) 2 20 0 t = 3.00 s rev/min rev/min s  the total change in time. Be careful of the sign of the angular acceleration. ANSWER: Correct Part B Find the number of revolutions made by the fan blades during the time that they are slowing down in Part A. Hint 1. Determine the correct kinematic equation Which of the following kinematic equations is best suited to this problem? Here and are the initial and final angular velocities, is the elapsed time, is the constant angular acceleration, and and are the initial and final angular displacements. Hint 1. How to chose the right equation Notice that you were given in the problem introduction the initial and final speeds, as well as the length of time between them. In this problem, you are asked to find the number of revolutions (which here is the change in angular displacement, ). If you already found the angular acceleration in Part A, you could use that as well, but you would end up using a more complex equation. Also, in general, it is somewhat favorable to use given quantities instead of quantities that you have calculated. ANSWER:  = -1.10 rev/s2 0  t  0   − 0  = 0 + t  = 0 + t+  1 2 t2 = + 2( − ) 2 20 0 − 0 = (+ )t 1 2 0 ANSWER: Correct Part C How many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in Part A? Hint 1. Finding the total time for spin down To find the total time for spin down, just calculate when the velocity will equal zero. This is accomplished by setting the initial velocity plus the acceleration multipled by the time equal to zero and then solving for the time. One can then just subtract the time it took to reach 250 from the total time. Be careful of your signs when you set up the equation. ANSWER: Correct Problem 12.8 A 100 ball and a 230 ball are connected by a 34- -long, massless, rigid rod. The balls rotate about their center of mass at 130 . Part A What is the speed of the 100 ball? Express your answer to two significant figures and include the appropriate units. ANSWER: 29.0 rev rev/min 3.79 s g g cm rpm g Correct Problem 12.10 A thin, 60.0 disk with a diameter of 9.00 rotates about an axis through its center with 0.200 of kinetic energy. Part A What is the speed of a point on the rim? Express your answer with the appropriate units. ANSWER: Correct Problem 12.12 A drum major twirls a 95- -long, 470 baton about its center of mass at 150 . Part A What is the baton’s rotational kinetic energy? Express your answer to two significant figures and include the appropriate units. ANSWER: v = 3.2 ms g cm J 3.65 ms cm g rpm K = 4.4 J Correct Net Torque on a Pulley The figure below shows two blocks suspended by a cord over a pulley. The mass of block B is twice the mass of block A, while the mass of the pulley is equal to the mass of block A. The blocks are let free to move and the cord moves on the pulley without slipping or stretching. There is no friction in the pulley axle, and the cord’s weight can be ignored. Part A Which of the following statements correctly describes the system shown in the figure? Check all that apply. Hint 1. Conditions for equilibrium If the blocks had the same mass, the system would be in equilibrium. The blocks would have zero acceleration and the tension in each part of the cord would equal the weight of each block. Both parts of the cord would then pull with equal force on the pulley, resulting in a zero net torque and no rotation of the pulley. Is this still the case in the current situation where block B has twice the mass of block A? Hint 2. Rotational analogue of Newton’s second law The net torque of all the forces acting on a rigid body is proportional to the angular acceleration of the body net  and is given by , where is the moment of inertia of the body. Hint 3. Relation between linear and angular acceleration A particle that rotates with angular acceleration has linear acceleration equal to , where is the distance of the particle from the axis of rotation. In the present case, where there is no slipping or stretching of the cord, the cord and the pulley must move together at the same speed. Therefore, if the cord moves with linear acceleration , the pulley must rotate with angular acceleration , where is the radius of the pulley. ANSWER: Correct Part B What happens when block B moves downward? Hint 1. How to approach the problem To determine whether the tensions in both parts of the cord are equal, it is convenient to write a mathematical expression for the net torque on the pulley. This will allow you to relate the tensions in the cord to the pulley’s angular acceleration. Hint 2. Find the net torque on the pulley Let’s assume that the tensions in both parts of the cord are different. Let be the tension in the right cord and the tension in the left cord. If is the radius of the pulley, what is the net torque acting on the pulley? Take the positive sense of rotation to be counterclockwise. Express your answer in terms of , , and . net = I I  a a = R R a  = a R R The acceleration of the blocks is zero. The net torque on the pulley is zero. The angular acceleration of the pulley is nonzero. T1 T2 R net T1 T2 R Hint 1. Torque The torque of a force with respect to a point is defined as the product of the magnitude times the perpendicular distance between the line of action of and the point . In other words, . ANSWER: ANSWER: Correct Note that if the pulley were stationary (as in many systems where only linear motion is studied), then the tensions in both parts of the cord would be equal. However, if the pulley rotates with a certain angular acceleration, as in the present situation, the tensions must be different. If they were equal, the pulley could not have an angular acceleration. Problem 12.18 Part A In the figure , what is the magnitude of net torque about the axle? Express your answer to two significant figures and include the appropriate units.  F  O F l F  O  = Fl net = R(T2 − T1 ) The left cord pulls on the pulley with greater force than the right cord. The left and right cord pull with equal force on the pulley. The right cord pulls on the pulley with greater force than the left cord. ANSWER: Correct Part B What is the direction of net torque about the axle? ANSWER: Correct Problem 12.22 An athlete at the gym holds a 3.5 steel ball in his hand. His arm is 78 long and has a mass of 3.6 . Assume the center of mass of the arm is at the geometrical center of the arm. Part A What is the magnitude of the torque about his shoulder if he holds his arm straight out to his side, parallel to the floor? Express your answer to two significant figures and include the appropriate units.  = 0.20 Nm Clockwise Counterclockwise kg cm kg ANSWER: Correct Part B What is the magnitude of the torque about his shoulder if he holds his arm straight, but below horizontal? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Parallel Axis Theorem The parallel axis theorem relates , the moment of inertia of an object about an axis passing through its center of mass, to , the moment of inertia of the same object about a parallel axis passing through point p. The mathematical statement of the theorem is , where is the perpendicular distance from the center of mass to the axis that passes through point p, and is the mass of the object. Part A Suppose a uniform slender rod has length and mass . The moment of inertia of the rod about about an axis that is perpendicular to the rod and that passes through its center of mass is given by . Find , the moment of inertia of the rod with respect to a parallel axis through one end of the rod. Express in terms of and . Use fractions rather than decimal numbers in your answer. Hint 1. Find the distance from the axis to the center of mass Find the distance appropriate to this problem. That is, find the perpendicular distance from the center of mass of the rod to the axis passing through one end of the rod.  = 41 Nm 45  = 29 Nm Icm Ip Ip = Icm + Md2 d M L m Icm = m 1 12 L2 Iend Iend m L d ANSWER: ANSWER: Correct Part B Now consider a cube of mass with edges of length . The moment of inertia of the cube about an axis through its center of mass and perpendicular to one of its faces is given by . Find , the moment of inertia about an axis p through one of the edges of the cube Express in terms of and . Use fractions rather than decimal numbers in your answer. Hint 1. Find the distance from the axis to the axis Find the perpendicular distance from the center of mass axis to the new edge axis (axis labeled p in the figure). ANSWER: d = L 2 Iend = mL2 3 m a Icm Icm = m 1 6 a2 Iedge Iedge m a o p d ANSWER: Correct Problem 12.26 Starting from rest, a 12- -diameter compact disk takes 2.9 to reach its operating angular velocity of 2000 . Assume that the angular acceleration is constant. The disk’s moment of inertia is . Part A How much torque is applied to the disk? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How many revolutions does it make before reaching full speed? Express your answer using two significant figures. ANSWER: d = a 2 Iedge = 2ma2 3 cm s rpm 2.5 × 10−5 kg m2 = 1.8×10−3  Nm Correct Problem 12.23 An object’s moment of inertia is 2.20 . Its angular velocity is increasing at the rate of 3.70 . Part A What is the total torque on the object? ANSWER: Correct Problem 12.31 A 5.1 cat and a 2.5 bowl of tuna fish are at opposite ends of the 4.0- -long seesaw. N = 48 rev kgm2 rad/s2 8.14 N  m kg kg m Part A How far to the left of the pivot must a 3.8 cat stand to keep the seesaw balanced? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Static Equilibrium of the Arm You are able to hold out your arm in an outstretched horizontal position because of the action of the deltoid muscle. Assume the humerus bone has a mass , length and its center of mass is a distance from the scapula. (For this problem ignore the rest of the arm.) The deltoid muscle attaches to the humerus a distance from the scapula. The deltoid muscle makes an angle of with the horizontal, as shown. Use throughout the problem. Part A kg d = 1.4 m M1 = 3.6 kg L = 0.66 m L1 = 0.33 m L2 = 0.15 m  = 17 g = 9.8 m/s2 Find the tension in the deltoid muscle. Express the tension in newtons, to the nearest integer. Hint 1. Nature of the problem Remember that this is a statics problem, so all forces and torques are balanced (their sums equal zero). Hint 2. Origin of torque Calculate the torque about the point at which the arm attaches to the rest of the body. This allows one to balance the torques without having to worry about the undefined forces at this point. Hint 3. Adding up the torques Add up the torques about the point in which the humerus attaches to the body. Answer in terms of , , , , , and . Remember that counterclockwise torque is positive. ANSWER: ANSWER: Correct Part B Using the conditions for static equilibrium, find the magnitude of the vertical component of the force exerted by the scapula on the humerus (where the humerus attaches to the rest of the body). Express your answer in newtons, to the nearest integer. T L1 L2 M1 g T  total = 0 = L1M1g − Tsin()L2 T = 265 N Fy Hint 1. Total forces involved Recall that there are three vertical forces in this problem: the force of gravity acting on the bone, the force from the vertical component of the muscle tension, and the force exerted by the scapula on the humerus (where it attaches to the rest of the body). ANSWER: Correct Part C Now find the magnitude of the horizontal component of the force exerted by the scapula on the humerus. Express your answer in newtons, to the nearest integer. ANSWER: Correct ± Moments around a Rod A rod is bent into an L shape and attached at one point to a pivot. The rod sits on a frictionless table and the diagram is a view from above. This means that gravity can be ignored for this problem. There are three forces that are applied to the rod at different points and angles: , , and . Note that the dimensions of the bent rod are in centimeters in the figure, although the answers are requested in SI units (kilograms, meters, seconds). |Fy| = 42 N Fx |Fx| = 254 N F 1 F  2 F  3 Part A If and , what does the magnitude of have to be for there to be rotational equilibrium? Answer numerically in newtons to two significant figures. Hint 1. Finding torque about pivot from What is the magnitude of the torque | | provided by around the pivot point? Give your answer numerically in newton-meters to two significant figures. ANSWER: ANSWER: Correct Part B If the L-shaped rod has a moment of inertia , , , and again , how long a time would it take for the object to move through ( /4 radians)? Assume that as the object starts to move, each force moves with the object so as to retain its initial angle relative to the object. Express the time in seconds to two significant figures. F3 = 0 F1 = 12 N F 2 F 1   1 F  1 |  1 | = 0.36 N  m F2 = 4.5 N I = 9 kg m2 F1 = 12 N F2 = 27 N F3 = 0 t 45  Hint 1. Find the net torque about the pivot What is the magnitude of the total torque around the pivot point? Answer numerically in newton-meters to two significant figures. ANSWER: Hint 2. Calculate Given the total torque around the pivot point, what is , the magnitude of the angular acceleration? Express your answer numerically in radians per second squared to two significant figures. Hint 1. Equation for If you know the magnitude of the total torque ( ) and the rotational inertia ( ), you can then find the rotational acceleration ( ) from ANSWER: Hint 3. Description of angular kinematics Now that you know the angular acceleration, this is a problem in rotational kinematics; find the time needed to go through a given angle . For constant acceleration ( ) and starting with (where is angular speed) the relation is given by which is analogous to the expression for linear displacement ( ) with constant acceleration ( ) starting from rest, | p ivot| | p ivot| = 1.8 N  m    vot Ivot  pivot = Ipivot.  = 0.20 radians/s2    = 0   = 1  , 2 t2 x a . ANSWER: Correct Part C Now consider the situation in which and , but now a force with nonzero magnitude is acting on the rod. What does have to be to obtain equilibrium? Give a numerical answer, without trigonometric functions, in newtons, to two significant figures. Hint 1. Find the required component of Only the tangential (perpendicular) component of (call it ) provides a torque. What is ? Answer in terms of . You will need to evaluate any trigonometric functions. ANSWER: ANSWER: Correct x = 1 a 2 t2 t = 2.8 s F1 = 12 N F2 = 0 F3 F3 F 3 F  3 F3t F3t F3 F3t = 1 2 F3 F3 = 9.0 N Problem 12.32 A car tire is 55.0 in diameter. The car is traveling at a speed of 24.0 . Part A What is the tire’s rotation frequency, in rpm? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part B What is the speed of a point at the top edge of the tire? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part C What is the speed of a point at the bottom edge of the tire? Express your answer as an integer and include the appropriate units. ANSWER: cm m/s 833 rpm 48.0 ms 0 ms Correct Problem 12.33 A 460 , 8.00-cm-diameter solid cylinder rolls across the floor at 1.30 . Part A What is the can’s kinetic energy? Express your answer with the appropriate units. ANSWER: Correct Problem 12.45 Part A What is the magnitude of the angular momentum of the 780 rotating bar in the figure ? g m/s 0.583 J g ANSWER: Correct Part B What is the direction of the angular momentum of the bar ? ANSWER: Correct Problem 12.46 Part A What is the magnitude of the angular momentum of the 2.20 , 4.60-cm-diameter rotating disk in the figure ? 3.27 kgm2/s into the page out of the page kg ANSWER: Correct Part B What is its direction? ANSWER: Correct Problem 12.60 A 3.0- -long ladder, as shown in the following figure, leans against a frictionless wall. The coefficient of static friction between the ladder and the floor is 0.46. 3.66×10−2 kgm /s 2 x direction -x direction y direction -y direction z direction -z direction m Part A What is the minimum angle the ladder can make with the floor without slipping? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 12.61 The 3.0- -long, 90 rigid beam in the following figure is supported at each end. An 70 student stands 2.0 from support 1.  = 47 m kg kg m Part A How much upward force does the support 1 exert on the beam? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How much upward force does the support 2 exert on the beam? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 12.63 A 44 , 5.5- -long beam is supported, but not attached to, the two posts in the figure . A 22 boy starts walking along the beam. You may want to review ( pages 330 – 334) . For help with math skills, you may want to review: F1 = 670 N F2 = 900 N kg m kg The Vector Cross Product Part A How close can he get to the right end of the beam without it falling over? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Draw a picture of the four forces acting on the beam, indicating both their direction and the place on the beam that the forces are acting. Choose a coordinate system with a direction for the axis along the beam, and indicate the position of the boy. What is the net force on the beam if it is stationary? Just before the beam tips, the force of the left support on the beam is zero. Using the zero net force condition, what is the force due to the right support just before the beam tips? For the beam to remain stationary, what must be zero besides the net force on the beam? Choose a point on the beam, and compute the net torque on the beam about that point. Be sure to choose a positive direction for the rotation axis and therefore the torques. Using the zero torque condition, what is the position of the boy on the beam just prior to tipping? How far is this position from the right edge of the beam? ANSWER: Correct d = 2.0 m Problem 12.68 Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel’s energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.6 diameter and a mass of 270 . Its maximum angular velocity is 1500 . Part A A motor spins up the flywheel with a constant torque of 54 . How long does it take the flywheel to reach top speed? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How much energy is stored in the flywheel? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C The flywheel is disconnected from the motor and connected to a machine to which it will deliver energy. Half the energy stored in the flywheel is delivered in 2.2 . What is the average power delivered to the machine? Express your answer to two significant figures and include the appropriate units. ANSWER: m kg rpm N  m t = 250 s = 1.1×106 E J s Correct Part D How much torque does the flywheel exert on the machine? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 12.71 The 3.30 , 40.0-cm-diameter disk in the figure is spinning at 350 . Part A How much friction force must the brake apply to the rim to bring the disk to a halt in 2.10 ? P = 2.4×105 W  = 1800 Nm kg rpm s Express your answer with the appropriate units. ANSWER: Correct Problem 12.74 A 5.0 , 60- -diameter cylinder rotates on an axle passing through one edge. The axle is parallel to the floor. The cylinder is held with the center of mass at the same height as the axle, then released. Part A What is the magnitude of the cylinder’s initial angular acceleration? Express your answer to two significant figures and include the appropriate units. ANSWER: 5.76 N kg cm  = 22 rad s2 Correct Part B What is the magnitude of the cylinder’s angular velocity when it is directly below the axle? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 12.82 A 45 figure skater is spinning on the toes of her skates at 0.90 . Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (40 , 20 average diameter, 160 tall) plus two rod-like arms (2.5 each, 67 long) attached to the outside of the torso. The skater then raises her arms straight above her head, where she appears to be a 45 , 20- -diameter, 200- -tall cylinder. Part A What is her new rotation frequency, in revolutions per second? Express your answer to two significant figures and include the appropriate units. ANSWER: Incorrect; Try Again Score Summary:  = 6.6 rad s kg rev/s kg cm cm kg cm kg cm cm 2 = Your score on this assignment is 95.7%. You received 189.42 out of a possible total of 198 points.

Assignment 10 Due: 11:59pm on Wednesday, April 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 12.3 Part A The figure shows three rotating disks, all of equal mass. Rank in order, from largest to smallest, their rotational kinetic energies to . Rank from largest to smallest. To rank items as equivalent, overlap them. ANSWER: Ka Kc Correct Conceptual Question 12.6 You have two steel solid spheres. Sphere 2 has twice the radius of sphere 1. Part A By what factor does the moment of inertia of sphere 2 exceed the moment of inertia of sphere 1? ANSWER: I2 I1 Correct Problem 12.2 A high-speed drill reaches 2500 in 0.59 . Part A What is the drill’s angular acceleration? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B Through how many revolutions does it turn during this first 0.59 ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct I2/I1 = 32 rpm s  = 440 rad s2 s  = 12 rev Constant Angular Acceleration in the Kitchen Dario, a prep cook at an Italian restaurant, spins a salad spinner and observes that it rotates 20.0 times in 5.00 seconds and then stops spinning it. The salad spinner rotates 6.00 more times before it comes to rest. Assume that the spinner slows down with constant angular acceleration. Part A What is the angular acceleration of the salad spinner as it slows down? Express your answer numerically in degrees per second per second. Hint 1. How to approach the problem Recall from your study of kinematics the three equations of motion derived for systems undergoing constant linear acceleration. You are now studying systems undergoing constant angular acceleration and will need to work with the three analogous equations of motion. Collect your known quantities and then determine which of the angular kinematic equations is appropriate to find the angular acceleration . Hint 2. Find the angular velocity of the salad spinner while Dario is spinning it What is the angular velocity of the salad spinner as Dario is spinning it? Express your answer numerically in degrees per second. Hint 1. Converting rotations to degrees When the salad spinner spins through one revolution, it turns through 360 degrees. ANSWER: Hint 3. Find the angular distance the salad spinner travels as it comes to rest Through how many degrees does the salad spinner rotate as it comes to rest? Express your answer numerically in degrees. Hint 1. Converting rotations to degrees  0 = 1440 degrees/s  =  − 0 One revolution is equivalent to 360 degrees. ANSWER: Hint 4. Determine which equation to use You know the initial and final velocities of the system and the angular distance through which the spinner rotates as it comes to a stop. Which equation should be used to solve for the unknown constant angular acceleration ? ANSWER: ANSWER: Correct Part B How long does it take for the salad spinner to come to rest? Express your answer numerically in seconds.  = 2160 degrees   = 0 + 0t+  1 2 t2  = 0 + t = + 2( − ) 2 20 0  = -480 degrees/s2 Hint 1. How to approach the problem Again, you will need the equations of rotational kinematics that apply to situations of constant angular acceleration. Collect your known quantities and then determine which of the angular kinematic equations is appropriate to find . Hint 2. Determine which equation to use You have the initial and final velocities of the system and the angular acceleration, which you found in the previous part. Which is the best equation to use to solve for the unknown time ? ANSWER: ANSWER: Correct ± A Spinning Electric Fan An electric fan is turned off, and its angular velocity decreases uniformly from 540 to 250 in a time interval of length 4.40 . Part A Find the angular acceleration in revolutions per second per second. Hint 1. Average acceleration Recall that if the angular velocity decreases uniformly, the angular acceleration will remain constant. Therefore, the angular acceleration is just the total change in angular velocity divided by t t  = 0 + 0t+  1 2 t2  = 0 + t = + 2( − ) 2 20 0 t = 3.00 s rev/min rev/min s  the total change in time. Be careful of the sign of the angular acceleration. ANSWER: Correct Part B Find the number of revolutions made by the fan blades during the time that they are slowing down in Part A. Hint 1. Determine the correct kinematic equation Which of the following kinematic equations is best suited to this problem? Here and are the initial and final angular velocities, is the elapsed time, is the constant angular acceleration, and and are the initial and final angular displacements. Hint 1. How to chose the right equation Notice that you were given in the problem introduction the initial and final speeds, as well as the length of time between them. In this problem, you are asked to find the number of revolutions (which here is the change in angular displacement, ). If you already found the angular acceleration in Part A, you could use that as well, but you would end up using a more complex equation. Also, in general, it is somewhat favorable to use given quantities instead of quantities that you have calculated. ANSWER:  = -1.10 rev/s2 0  t  0   − 0  = 0 + t  = 0 + t+  1 2 t2 = + 2( − ) 2 20 0 − 0 = (+ )t 1 2 0 ANSWER: Correct Part C How many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in Part A? Hint 1. Finding the total time for spin down To find the total time for spin down, just calculate when the velocity will equal zero. This is accomplished by setting the initial velocity plus the acceleration multipled by the time equal to zero and then solving for the time. One can then just subtract the time it took to reach 250 from the total time. Be careful of your signs when you set up the equation. ANSWER: Correct Problem 12.8 A 100 ball and a 230 ball are connected by a 34- -long, massless, rigid rod. The balls rotate about their center of mass at 130 . Part A What is the speed of the 100 ball? Express your answer to two significant figures and include the appropriate units. ANSWER: 29.0 rev rev/min 3.79 s g g cm rpm g Correct Problem 12.10 A thin, 60.0 disk with a diameter of 9.00 rotates about an axis through its center with 0.200 of kinetic energy. Part A What is the speed of a point on the rim? Express your answer with the appropriate units. ANSWER: Correct Problem 12.12 A drum major twirls a 95- -long, 470 baton about its center of mass at 150 . Part A What is the baton’s rotational kinetic energy? Express your answer to two significant figures and include the appropriate units. ANSWER: v = 3.2 ms g cm J 3.65 ms cm g rpm K = 4.4 J Correct Net Torque on a Pulley The figure below shows two blocks suspended by a cord over a pulley. The mass of block B is twice the mass of block A, while the mass of the pulley is equal to the mass of block A. The blocks are let free to move and the cord moves on the pulley without slipping or stretching. There is no friction in the pulley axle, and the cord’s weight can be ignored. Part A Which of the following statements correctly describes the system shown in the figure? Check all that apply. Hint 1. Conditions for equilibrium If the blocks had the same mass, the system would be in equilibrium. The blocks would have zero acceleration and the tension in each part of the cord would equal the weight of each block. Both parts of the cord would then pull with equal force on the pulley, resulting in a zero net torque and no rotation of the pulley. Is this still the case in the current situation where block B has twice the mass of block A? Hint 2. Rotational analogue of Newton’s second law The net torque of all the forces acting on a rigid body is proportional to the angular acceleration of the body net  and is given by , where is the moment of inertia of the body. Hint 3. Relation between linear and angular acceleration A particle that rotates with angular acceleration has linear acceleration equal to , where is the distance of the particle from the axis of rotation. In the present case, where there is no slipping or stretching of the cord, the cord and the pulley must move together at the same speed. Therefore, if the cord moves with linear acceleration , the pulley must rotate with angular acceleration , where is the radius of the pulley. ANSWER: Correct Part B What happens when block B moves downward? Hint 1. How to approach the problem To determine whether the tensions in both parts of the cord are equal, it is convenient to write a mathematical expression for the net torque on the pulley. This will allow you to relate the tensions in the cord to the pulley’s angular acceleration. Hint 2. Find the net torque on the pulley Let’s assume that the tensions in both parts of the cord are different. Let be the tension in the right cord and the tension in the left cord. If is the radius of the pulley, what is the net torque acting on the pulley? Take the positive sense of rotation to be counterclockwise. Express your answer in terms of , , and . net = I I  a a = R R a  = a R R The acceleration of the blocks is zero. The net torque on the pulley is zero. The angular acceleration of the pulley is nonzero. T1 T2 R net T1 T2 R Hint 1. Torque The torque of a force with respect to a point is defined as the product of the magnitude times the perpendicular distance between the line of action of and the point . In other words, . ANSWER: ANSWER: Correct Note that if the pulley were stationary (as in many systems where only linear motion is studied), then the tensions in both parts of the cord would be equal. However, if the pulley rotates with a certain angular acceleration, as in the present situation, the tensions must be different. If they were equal, the pulley could not have an angular acceleration. Problem 12.18 Part A In the figure , what is the magnitude of net torque about the axle? Express your answer to two significant figures and include the appropriate units.  F  O F l F  O  = Fl net = R(T2 − T1 ) The left cord pulls on the pulley with greater force than the right cord. The left and right cord pull with equal force on the pulley. The right cord pulls on the pulley with greater force than the left cord. ANSWER: Correct Part B What is the direction of net torque about the axle? ANSWER: Correct Problem 12.22 An athlete at the gym holds a 3.5 steel ball in his hand. His arm is 78 long and has a mass of 3.6 . Assume the center of mass of the arm is at the geometrical center of the arm. Part A What is the magnitude of the torque about his shoulder if he holds his arm straight out to his side, parallel to the floor? Express your answer to two significant figures and include the appropriate units.  = 0.20 Nm Clockwise Counterclockwise kg cm kg ANSWER: Correct Part B What is the magnitude of the torque about his shoulder if he holds his arm straight, but below horizontal? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Parallel Axis Theorem The parallel axis theorem relates , the moment of inertia of an object about an axis passing through its center of mass, to , the moment of inertia of the same object about a parallel axis passing through point p. The mathematical statement of the theorem is , where is the perpendicular distance from the center of mass to the axis that passes through point p, and is the mass of the object. Part A Suppose a uniform slender rod has length and mass . The moment of inertia of the rod about about an axis that is perpendicular to the rod and that passes through its center of mass is given by . Find , the moment of inertia of the rod with respect to a parallel axis through one end of the rod. Express in terms of and . Use fractions rather than decimal numbers in your answer. Hint 1. Find the distance from the axis to the center of mass Find the distance appropriate to this problem. That is, find the perpendicular distance from the center of mass of the rod to the axis passing through one end of the rod.  = 41 Nm 45  = 29 Nm Icm Ip Ip = Icm + Md2 d M L m Icm = m 1 12 L2 Iend Iend m L d ANSWER: ANSWER: Correct Part B Now consider a cube of mass with edges of length . The moment of inertia of the cube about an axis through its center of mass and perpendicular to one of its faces is given by . Find , the moment of inertia about an axis p through one of the edges of the cube Express in terms of and . Use fractions rather than decimal numbers in your answer. Hint 1. Find the distance from the axis to the axis Find the perpendicular distance from the center of mass axis to the new edge axis (axis labeled p in the figure). ANSWER: d = L 2 Iend = mL2 3 m a Icm Icm = m 1 6 a2 Iedge Iedge m a o p d ANSWER: Correct Problem 12.26 Starting from rest, a 12- -diameter compact disk takes 2.9 to reach its operating angular velocity of 2000 . Assume that the angular acceleration is constant. The disk’s moment of inertia is . Part A How much torque is applied to the disk? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How many revolutions does it make before reaching full speed? Express your answer using two significant figures. ANSWER: d = a 2 Iedge = 2ma2 3 cm s rpm 2.5 × 10−5 kg m2 = 1.8×10−3  Nm Correct Problem 12.23 An object’s moment of inertia is 2.20 . Its angular velocity is increasing at the rate of 3.70 . Part A What is the total torque on the object? ANSWER: Correct Problem 12.31 A 5.1 cat and a 2.5 bowl of tuna fish are at opposite ends of the 4.0- -long seesaw. N = 48 rev kgm2 rad/s2 8.14 N  m kg kg m Part A How far to the left of the pivot must a 3.8 cat stand to keep the seesaw balanced? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Static Equilibrium of the Arm You are able to hold out your arm in an outstretched horizontal position because of the action of the deltoid muscle. Assume the humerus bone has a mass , length and its center of mass is a distance from the scapula. (For this problem ignore the rest of the arm.) The deltoid muscle attaches to the humerus a distance from the scapula. The deltoid muscle makes an angle of with the horizontal, as shown. Use throughout the problem. Part A kg d = 1.4 m M1 = 3.6 kg L = 0.66 m L1 = 0.33 m L2 = 0.15 m  = 17 g = 9.8 m/s2 Find the tension in the deltoid muscle. Express the tension in newtons, to the nearest integer. Hint 1. Nature of the problem Remember that this is a statics problem, so all forces and torques are balanced (their sums equal zero). Hint 2. Origin of torque Calculate the torque about the point at which the arm attaches to the rest of the body. This allows one to balance the torques without having to worry about the undefined forces at this point. Hint 3. Adding up the torques Add up the torques about the point in which the humerus attaches to the body. Answer in terms of , , , , , and . Remember that counterclockwise torque is positive. ANSWER: ANSWER: Correct Part B Using the conditions for static equilibrium, find the magnitude of the vertical component of the force exerted by the scapula on the humerus (where the humerus attaches to the rest of the body). Express your answer in newtons, to the nearest integer. T L1 L2 M1 g T  total = 0 = L1M1g − Tsin()L2 T = 265 N Fy Hint 1. Total forces involved Recall that there are three vertical forces in this problem: the force of gravity acting on the bone, the force from the vertical component of the muscle tension, and the force exerted by the scapula on the humerus (where it attaches to the rest of the body). ANSWER: Correct Part C Now find the magnitude of the horizontal component of the force exerted by the scapula on the humerus. Express your answer in newtons, to the nearest integer. ANSWER: Correct ± Moments around a Rod A rod is bent into an L shape and attached at one point to a pivot. The rod sits on a frictionless table and the diagram is a view from above. This means that gravity can be ignored for this problem. There are three forces that are applied to the rod at different points and angles: , , and . Note that the dimensions of the bent rod are in centimeters in the figure, although the answers are requested in SI units (kilograms, meters, seconds). |Fy| = 42 N Fx |Fx| = 254 N F 1 F  2 F  3 Part A If and , what does the magnitude of have to be for there to be rotational equilibrium? Answer numerically in newtons to two significant figures. Hint 1. Finding torque about pivot from What is the magnitude of the torque | | provided by around the pivot point? Give your answer numerically in newton-meters to two significant figures. ANSWER: ANSWER: Correct Part B If the L-shaped rod has a moment of inertia , , , and again , how long a time would it take for the object to move through ( /4 radians)? Assume that as the object starts to move, each force moves with the object so as to retain its initial angle relative to the object. Express the time in seconds to two significant figures. F3 = 0 F1 = 12 N F 2 F 1   1 F  1 |  1 | = 0.36 N  m F2 = 4.5 N I = 9 kg m2 F1 = 12 N F2 = 27 N F3 = 0 t 45  Hint 1. Find the net torque about the pivot What is the magnitude of the total torque around the pivot point? Answer numerically in newton-meters to two significant figures. ANSWER: Hint 2. Calculate Given the total torque around the pivot point, what is , the magnitude of the angular acceleration? Express your answer numerically in radians per second squared to two significant figures. Hint 1. Equation for If you know the magnitude of the total torque ( ) and the rotational inertia ( ), you can then find the rotational acceleration ( ) from ANSWER: Hint 3. Description of angular kinematics Now that you know the angular acceleration, this is a problem in rotational kinematics; find the time needed to go through a given angle . For constant acceleration ( ) and starting with (where is angular speed) the relation is given by which is analogous to the expression for linear displacement ( ) with constant acceleration ( ) starting from rest, | p ivot| | p ivot| = 1.8 N  m    vot Ivot  pivot = Ipivot.  = 0.20 radians/s2    = 0   = 1  , 2 t2 x a . ANSWER: Correct Part C Now consider the situation in which and , but now a force with nonzero magnitude is acting on the rod. What does have to be to obtain equilibrium? Give a numerical answer, without trigonometric functions, in newtons, to two significant figures. Hint 1. Find the required component of Only the tangential (perpendicular) component of (call it ) provides a torque. What is ? Answer in terms of . You will need to evaluate any trigonometric functions. ANSWER: ANSWER: Correct x = 1 a 2 t2 t = 2.8 s F1 = 12 N F2 = 0 F3 F3 F 3 F  3 F3t F3t F3 F3t = 1 2 F3 F3 = 9.0 N Problem 12.32 A car tire is 55.0 in diameter. The car is traveling at a speed of 24.0 . Part A What is the tire’s rotation frequency, in rpm? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part B What is the speed of a point at the top edge of the tire? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part C What is the speed of a point at the bottom edge of the tire? Express your answer as an integer and include the appropriate units. ANSWER: cm m/s 833 rpm 48.0 ms 0 ms Correct Problem 12.33 A 460 , 8.00-cm-diameter solid cylinder rolls across the floor at 1.30 . Part A What is the can’s kinetic energy? Express your answer with the appropriate units. ANSWER: Correct Problem 12.45 Part A What is the magnitude of the angular momentum of the 780 rotating bar in the figure ? g m/s 0.583 J g ANSWER: Correct Part B What is the direction of the angular momentum of the bar ? ANSWER: Correct Problem 12.46 Part A What is the magnitude of the angular momentum of the 2.20 , 4.60-cm-diameter rotating disk in the figure ? 3.27 kgm2/s into the page out of the page kg ANSWER: Correct Part B What is its direction? ANSWER: Correct Problem 12.60 A 3.0- -long ladder, as shown in the following figure, leans against a frictionless wall. The coefficient of static friction between the ladder and the floor is 0.46. 3.66×10−2 kgm /s 2 x direction -x direction y direction -y direction z direction -z direction m Part A What is the minimum angle the ladder can make with the floor without slipping? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 12.61 The 3.0- -long, 90 rigid beam in the following figure is supported at each end. An 70 student stands 2.0 from support 1.  = 47 m kg kg m Part A How much upward force does the support 1 exert on the beam? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How much upward force does the support 2 exert on the beam? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 12.63 A 44 , 5.5- -long beam is supported, but not attached to, the two posts in the figure . A 22 boy starts walking along the beam. You may want to review ( pages 330 – 334) . For help with math skills, you may want to review: F1 = 670 N F2 = 900 N kg m kg The Vector Cross Product Part A How close can he get to the right end of the beam without it falling over? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Draw a picture of the four forces acting on the beam, indicating both their direction and the place on the beam that the forces are acting. Choose a coordinate system with a direction for the axis along the beam, and indicate the position of the boy. What is the net force on the beam if it is stationary? Just before the beam tips, the force of the left support on the beam is zero. Using the zero net force condition, what is the force due to the right support just before the beam tips? For the beam to remain stationary, what must be zero besides the net force on the beam? Choose a point on the beam, and compute the net torque on the beam about that point. Be sure to choose a positive direction for the rotation axis and therefore the torques. Using the zero torque condition, what is the position of the boy on the beam just prior to tipping? How far is this position from the right edge of the beam? ANSWER: Correct d = 2.0 m Problem 12.68 Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel’s energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.6 diameter and a mass of 270 . Its maximum angular velocity is 1500 . Part A A motor spins up the flywheel with a constant torque of 54 . How long does it take the flywheel to reach top speed? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How much energy is stored in the flywheel? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C The flywheel is disconnected from the motor and connected to a machine to which it will deliver energy. Half the energy stored in the flywheel is delivered in 2.2 . What is the average power delivered to the machine? Express your answer to two significant figures and include the appropriate units. ANSWER: m kg rpm N  m t = 250 s = 1.1×106 E J s Correct Part D How much torque does the flywheel exert on the machine? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 12.71 The 3.30 , 40.0-cm-diameter disk in the figure is spinning at 350 . Part A How much friction force must the brake apply to the rim to bring the disk to a halt in 2.10 ? P = 2.4×105 W  = 1800 Nm kg rpm s Express your answer with the appropriate units. ANSWER: Correct Problem 12.74 A 5.0 , 60- -diameter cylinder rotates on an axle passing through one edge. The axle is parallel to the floor. The cylinder is held with the center of mass at the same height as the axle, then released. Part A What is the magnitude of the cylinder’s initial angular acceleration? Express your answer to two significant figures and include the appropriate units. ANSWER: 5.76 N kg cm  = 22 rad s2 Correct Part B What is the magnitude of the cylinder’s angular velocity when it is directly below the axle? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 12.82 A 45 figure skater is spinning on the toes of her skates at 0.90 . Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (40 , 20 average diameter, 160 tall) plus two rod-like arms (2.5 each, 67 long) attached to the outside of the torso. The skater then raises her arms straight above her head, where she appears to be a 45 , 20- -diameter, 200- -tall cylinder. Part A What is her new rotation frequency, in revolutions per second? Express your answer to two significant figures and include the appropriate units. ANSWER: Incorrect; Try Again Score Summary:  = 6.6 rad s kg rev/s kg cm cm kg cm kg cm cm 2 = Your score on this assignment is 95.7%. You received 189.42 out of a possible total of 198 points.

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• Question 1 10 out of 10 points The composition of the Alexander Mosaic is designed to convey: • Question 2 10 out of 10 points What is so revolutionary about Walking Man? • Question 3 10 out of 10 points What does the Justinian mosaic in the Church of San Vitale in Ravenna demonstrate? • Question 4 10 out of 10 points Who is the artist of Brillo Box? • Question 5 10 out of 10 points What is Shiva Nataraja responsible for doing? • Question 6 0 out of 10 points Willard Wigan created a lifesize replica of the Statue of Liberty for the people of France. • Question 7 10 out of 10 points Who is the artist of The Nightmare? • Question 8 10 out of 10 points Astrolabes were used by Muslims to determine the direction of Mecca. • Question 9 10 out of 10 points Who is the artist of the painting Woman Holding a Balance? • Question 10 10 out of 10 points The lyre from the Royal Cemetery of Ur (4.14) cannot be appreciated by viewers today in the same way that it was by the ancient Sumerians who made it. • Question 11 10 out of 10 points Which part of René Magritte’s The Human Condition is painted? • Question 12 10 out of 10 points The sarcophagus lid from the tomb of Lord Pacal shows him ________. • Question 13 10 out of 10 points Which artist created a three-dimensional sculpture of his own face? • Question 14 10 out of 10 points Salvador Dalí’s painting Persistence of Memory shows warped clocks, ants, and a distorted face, all of which are symbols of his mother, who died the month before this was painted. • Question 15 10 out of 10 points Muqarnas are ________. • Question 16 10 out of 10 points Synesthesia is when stimulation of one sense triggers an experience in another, for example visualizing color when one hears music. • Question 17 10 out of 10 points Mary Richardson, the attacker of the Rokeby Venus in 1914, did so because: • Question 18 10 out of 10 points Which of the following is emphasized in Lewis Wickes Hine’s Power House Mechanic Working on Steam Pump? • Question 19 10 out of 10 points Artemisia Gentileschi made ________ paintings of the biblical story of Judith and Holofernes. • Question 20 10 out of 10 points Which artist was investigated by the U.S. Treasury Department for counterfeiting because his painting of a dollar bill looked so incredibly real? • Question 21 10 out of 10 points Ancient Egyptian pyramids were only positioned according to geographical coordinates. • Question 22 10 out of 10 points The form of the goddess’s figure in The Birth of Venus was based on ________. • Question 23 10 out of 10 points Dorothea Lange’s Migrant Mother shows ________. • Question 24 0 out of 10 points Which of the following artworks does not address social class: • Question 25 10 out of 10 points How are the dual genders of the Hermaphrodite with a Dog made visible? • Question 26 10 out of 10 points The ziggurat at Ur was dedicated to: • Question 27 10 out of 10 points The sculpture of a head, which probably represents a king of Ife (4.134), was made using which medium? • Question 28 10 out of 10 points What is the subject matter of Myron’s Discus Thrower? • Question 29 10 out of 10 points Nick Ut’s photographs of the Vietnam War are brutally truthful, but he was not an impartial photographer. • Question 30 10 out of 10 points J. M. W. Turner’s painting Slave Ship uses pale colors and smooth brushstrokes to depict the serenity of life at sea. • Question 31 0 out of 10 points A lyre is used for what purpose? • Question 32 10 out of 10 points The Hopi of the southwestern United States are responsible for making which of the following sculptures? • Question 33 10 out of 10 points What is the medium of Yves Klein’s Anthropométries de l’époque bleue? • Question 34 10 out of 10 points Artists have often been influenced by scientific discoveries. • Question 35 10 out of 10 points Rituals that connect with ancestors and nature spirits are as important as the tasks of daily life for African peoples like the Kongo. • Question 36 10 out of 10 points As described in the article, Linda Bengalis made headlines when she strapped dead eagle around her waist and posed in Art Forum • Question 37 10 out of 10 points Shepard Fairey sued Barak Obama for using his original image. • Question 38 10 out of 10 points Hennessey Youngman made the Spiral Jetty • Question 39 10 out of 10 points According to the video, Mary Mattingly’s greatest concern coincides with that of the Guerrilla Girls.

• Question 1 10 out of 10 points The composition of the Alexander Mosaic is designed to convey: • Question 2 10 out of 10 points What is so revolutionary about Walking Man? • Question 3 10 out of 10 points What does the Justinian mosaic in the Church of San Vitale in Ravenna demonstrate? • Question 4 10 out of 10 points Who is the artist of Brillo Box? • Question 5 10 out of 10 points What is Shiva Nataraja responsible for doing? • Question 6 0 out of 10 points Willard Wigan created a lifesize replica of the Statue of Liberty for the people of France. • Question 7 10 out of 10 points Who is the artist of The Nightmare? • Question 8 10 out of 10 points Astrolabes were used by Muslims to determine the direction of Mecca. • Question 9 10 out of 10 points Who is the artist of the painting Woman Holding a Balance? • Question 10 10 out of 10 points The lyre from the Royal Cemetery of Ur (4.14) cannot be appreciated by viewers today in the same way that it was by the ancient Sumerians who made it. • Question 11 10 out of 10 points Which part of René Magritte’s The Human Condition is painted? • Question 12 10 out of 10 points The sarcophagus lid from the tomb of Lord Pacal shows him ________. • Question 13 10 out of 10 points Which artist created a three-dimensional sculpture of his own face? • Question 14 10 out of 10 points Salvador Dalí’s painting Persistence of Memory shows warped clocks, ants, and a distorted face, all of which are symbols of his mother, who died the month before this was painted. • Question 15 10 out of 10 points Muqarnas are ________. • Question 16 10 out of 10 points Synesthesia is when stimulation of one sense triggers an experience in another, for example visualizing color when one hears music. • Question 17 10 out of 10 points Mary Richardson, the attacker of the Rokeby Venus in 1914, did so because: • Question 18 10 out of 10 points Which of the following is emphasized in Lewis Wickes Hine’s Power House Mechanic Working on Steam Pump? • Question 19 10 out of 10 points Artemisia Gentileschi made ________ paintings of the biblical story of Judith and Holofernes. • Question 20 10 out of 10 points Which artist was investigated by the U.S. Treasury Department for counterfeiting because his painting of a dollar bill looked so incredibly real? • Question 21 10 out of 10 points Ancient Egyptian pyramids were only positioned according to geographical coordinates. • Question 22 10 out of 10 points The form of the goddess’s figure in The Birth of Venus was based on ________. • Question 23 10 out of 10 points Dorothea Lange’s Migrant Mother shows ________. • Question 24 0 out of 10 points Which of the following artworks does not address social class: • Question 25 10 out of 10 points How are the dual genders of the Hermaphrodite with a Dog made visible? • Question 26 10 out of 10 points The ziggurat at Ur was dedicated to: • Question 27 10 out of 10 points The sculpture of a head, which probably represents a king of Ife (4.134), was made using which medium? • Question 28 10 out of 10 points What is the subject matter of Myron’s Discus Thrower? • Question 29 10 out of 10 points Nick Ut’s photographs of the Vietnam War are brutally truthful, but he was not an impartial photographer. • Question 30 10 out of 10 points J. M. W. Turner’s painting Slave Ship uses pale colors and smooth brushstrokes to depict the serenity of life at sea. • Question 31 0 out of 10 points A lyre is used for what purpose? • Question 32 10 out of 10 points The Hopi of the southwestern United States are responsible for making which of the following sculptures? • Question 33 10 out of 10 points What is the medium of Yves Klein’s Anthropométries de l’époque bleue? • Question 34 10 out of 10 points Artists have often been influenced by scientific discoveries. • Question 35 10 out of 10 points Rituals that connect with ancestors and nature spirits are as important as the tasks of daily life for African peoples like the Kongo. • Question 36 10 out of 10 points As described in the article, Linda Bengalis made headlines when she strapped dead eagle around her waist and posed in Art Forum • Question 37 10 out of 10 points Shepard Fairey sued Barak Obama for using his original image. • Question 38 10 out of 10 points Hennessey Youngman made the Spiral Jetty • Question 39 10 out of 10 points According to the video, Mary Mattingly’s greatest concern coincides with that of the Guerrilla Girls.

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Ch 2 Questions that might be on the test. If you cannot answer them, check your class notes or the textbook. 1. A mineral is a naturally occurring substance formed through geological processes that has: a) a characteristic chemical composition, b) a highly ordered atomic structure c) specific physical properties d) all of the above 2. There are currently more than ______ known minerals, according to the International Mineralogical Association, a) 40 b) 400 c) 4000 d) 40 000 3. Some minerals, like quartz, mica or feldspar are: a) rare b) common c) valuable d) priceless 4. Rocks from which minerals are mined for economic purposes are referred to as: a) gangue b) tailings c) ores d) granite 5. Electrons, which have a _____ charge, a size which is so small as to be currently unmeasurable, and which are the least massive of the three types of basic particles. a) positive b) negative c) neutral 6. Both protons and neutrons are themselves now thought to be composed of even more elementary particles called: a) quarks b) quakes c) parsons d) megans 7. In processes which change the number of protons in a nucleus, the atom becomes an atom of a different chemical: a) isotope b) compound c) element d) planet 8. Atoms which have either a deficit or a surplus of electrons are called: a) elements b) isotopes c) ions d) molecules 9. In the Bohr model of the atom, electrons can only orbit the nucleus in particular circular orbits with fixed angular momentum and energy, their distances from the nucleus being proportional to their respective energies. They can only make _____ leaps between the fixed energy levels. a) tiny b) quantum c) gradual 10. It is impossible to simultaneously derive precise values for both the position and momentum of a particle for any given point in time; this became known as the ______ principle. a) Bohr b) Einstein c) uncertainty d) quantum 11. The modern model of the atom describes the positions of electrons in an atom in terms of: a) quantum levels b) orbital paths c) probabilities d) GPS 12. Isotopes of an element have nuclei with the same number of protons (the same atomic number) but different numbers of: a) electrons b) neutrons c) ions d) photons 13. In helium-3 (or 3He), how many protons are present? a) 1 b) 2 c) 3 d) 4 14. In helium-3 (or 3He), how many neutrons are present? a) 1 b) 2 c) 3 d) 4 15. The relative abundance of an isotope is strongly correlated with its tendency toward nuclear _____, short-lived nuclides quickly go away, while their long-lived counterparts endure. a) fission b) fusion c) decay d) bombardment 16. The isotopic composition of elements is different on different planets. a) True b) False 17. As a general rule, the fewer electrons in an atom’s valence shell, the ____ reactive it is. Lithium, sodium, and potassium have one electron in their outer shells. a) more b) less 18. Every atom is much more stable, or less reactive, with a ____ valence shell. a) partly full b) completely full 19. A positively-charged ion, which has fewer electrons than protons, is known as a: a) anion b) cation c) fermion d) bation 20. Bonds vary widely in their strength. Generally covalent and ionic bonds are often described as “strong”, whereas ______ bonds are generally considered to be “weak”. a) van der Waals b) Faradays c) van Neumans 21. This bonding involves sharing of electrons in which the positively charged nuclei of two or more atoms simultaneously attract the negatively charged electrons that are being shared a) ionic b) covalent c) van der Waals d) metallic 22. This bond results from electrostatic attraction between atoms: a) ionic b) covalent c) van der Waals d) metallic 23. A sea of delocalized electrons causes this bonding: a) ionic b) covalent c) van der Waals d) metallic 24. The chemical composition of minerals may vary between end members of a mineral system. For example the ______ feldspars comprise a continuous series from sodiumrich albite to calcium-rich anorthite. a) plagioclase b) orthoclase c) alkaline d) acidic 25. Crystal structure is based on ____ internal atomic arrangement. a) irregular b) regular c) random d) curvilinear 26. Pyrite and marcasite are both _______, but their arrangement of atoms differs. a) iron sulfide b) lead sulfide c) copper silfide d) silver sulfide 27. The carbon atoms in ______ are arranged into sheets which can slide easily past each other, while the carbon atoms in diamond form a strong, interlocking three-dimensional network. a) sapphire b) graphite c) aluminum d) carbonate 28. TGCFAOQTCD a) Crystal habit b) Hardness scale c) Luster scale 29. Dull to metallic, submetallic, adamantine, vitreous, pearly, resinous, or silky. a) Crystal habit b) Hardness scale c) Luster scale d) Heft scale 30. The color of the powder a mineral leaves after rubbing it on unglazed porcelain. a) color b) streak c) lustre d) iridescense 31. Describes the way a mineral may split apart along various planes. a) fracture b) streak c) lustre d) cleavage 32. In modern physics, the position of electrons about a nucleus are defined in terms of: a) probabilities b) circles c) ellipses d) chromodomes 33. The symbol H+ suggests a: a) hydrogen atom b) hydrogen isotope c) hydrogen cation d) hydrogen anion 34. The tabulated atomic mass of natural carbon is not exactly 12 because carbon in nature always has multiple ________ present. a) electrons b) isotopes c) quarks d) protons 35. This type of bonding due to delocalized electrons leads to malleability, ductility, and high melting points: a) covalent b) ionic c) van der Waals d) metallic 36. The mineral ___________ is 3 on Mohs Scale whereas the mineral ___________ is 9. a) calcite, corundum b) corundum, calcite c) caliche, calcite d) chalcedony, quartz 37. In hand specimens, geologists identify most minerals based on: a) physical properties b) chemical analyses c) xray diffraction 38. This type of chemical bonding is the weakest but occurs in all substances. a) covalent b) ionic c) metallic d) none of the above 39. Quartz, feldspar, mica, chlorite, kaolin, calcite, epidote, olivine, augite, hornblende, magnetite, hematite, limonite: these minerals are: a) common in rocks b) occasionally found c) rare d) extremely rare 40. Characteristics of a mineral do NOT include: a) naturally occurring b) characteristic chemical formula c) crystalline d) organic e) all of the above 41. The chemical composition of a particular mineral may vary between end members. For example, the common mineral plagioclase feldspar varies from being _______-rich to being _________-rich. a) sodium, calcium b) potassium, sodium c) iron, magnesium d) carbon, oxygen 42. Sharing of electrons typifies the __________ bond whereas electrostatic attraction typifies the _______ bond. a) ionic, covalent b) ionic, triclinic c) covalent, ionic d) triclinic, covalent 43. If number of protons does not equal the number of electrons, the atom is a(n) : a) isotope b) ion c) quark d) simplex e) google 44. Atoms generally consist of: a) electrons b) protons c) neutrons d) all of the above 45. Not counting rare minerals, about how many mineral species are at least occasionally encountered in rocks? a) 20 b) 200 c) 2000 46. Carbon is atomic number 6. Carbon-13 has _______ protons and _______ neutrons. a) thirteen, six b) six, seven c) twelve, twenty-five d) twelve, twelve 47. Which of these particles are not nucleons? a) electrons b) neutrons c) protons 48. A mineral with visibly recognizable crystals is said to have good crystal habit; otherwise the mineral is said to be: a) massive b) granular c) compact d) any of the above 49. In chemical bonding, two atoms become linked by moving or sharing __________. a) neutrons b) protons c) electrons 50. The name of an element is determined by the number of ______ present in the ______ of an atom. a) electrons, nucleus b) neutrons, nucleus c) protons, nucleus d) protons, electron cloud e) neutrons, electron cloud 51. Generally ________ and ____________ bonds are strong whereas the ______________ bond is weak. a) covalent, ionic, van der Waals b) van der Waals, covalent, ionic c) ionic, van der Waals, covalent 52. Which of the following are held together by chemical bonds? a) molecules b) crystals c) diatomic gases 53. An ion with fewer electrons than protons is called an ______ and it carries a _________ electric charge. a) cation, positive b) anion, negative c) cation, negative d) anion, positive 54. Two or more minerals may have the same _________ composition but different _______ structure. These are called polymorphs. a) crystal, chemical b) chemical, crystal 55. Industrial minerals are: a) gem quality b) commercially valuable c) tailings d) worthless 56. All minerals are crystalline. If the crystals are too small to see, they can be detected by: a) x-ray diffraction b) cosmic rays c) sound waves d) odor 57. If two atomes have the same number of protons but different numbers of neutrons, the atoms are _______ of the same _________. a) elements, mineral b) atoms, isotope c) elements, isotope d) isotopes, element 58. Modern physics recognizes that electrons show both particle and ______ behavior. a) wave b) emotional c) thermal d) revolting 59. Sodium and potassium have one ______ electron in their outer shells and are extremely ________. a) valence, stable b) inverted, reactive c) valence, reactive d) contaminated, inactive 60. The luster of _______ would be described as ________. a) glass, vitreous b) diamond, dull c) pyrite, silky d) graphite, resinous 61. The minerals ________ and __________ are polymorphs of carbon. a) diamond, graphite b) calcite, silicate c) bonite, bronzite 62. In the ______ atom based on _______ physics, electrons were restricted to circular orbits of fixed energy levels. a) Bohr , quantum b) Rutherford, classical c) Bohr, classical d) Rutherford, quantum 63. Virtually all elements other than ______ and _______ were formed in stars and supernovae long after the Big Bang. a) hydrogen, helium b) carbon, phosphorus c) carbon, oxygen d) silica, carbon 64. Physicist Werner _________ developed the ___________ principle which means that it is impossible to know exactly the position and momentum of a particle. a) Heisenberg, certainty b) Heisenberg, uncertainty c) Bohr, uncertainty d) Bohr, certainty

Ch 2 Questions that might be on the test. If you cannot answer them, check your class notes or the textbook. 1. A mineral is a naturally occurring substance formed through geological processes that has: a) a characteristic chemical composition, b) a highly ordered atomic structure c) specific physical properties d) all of the above 2. There are currently more than ______ known minerals, according to the International Mineralogical Association, a) 40 b) 400 c) 4000 d) 40 000 3. Some minerals, like quartz, mica or feldspar are: a) rare b) common c) valuable d) priceless 4. Rocks from which minerals are mined for economic purposes are referred to as: a) gangue b) tailings c) ores d) granite 5. Electrons, which have a _____ charge, a size which is so small as to be currently unmeasurable, and which are the least massive of the three types of basic particles. a) positive b) negative c) neutral 6. Both protons and neutrons are themselves now thought to be composed of even more elementary particles called: a) quarks b) quakes c) parsons d) megans 7. In processes which change the number of protons in a nucleus, the atom becomes an atom of a different chemical: a) isotope b) compound c) element d) planet 8. Atoms which have either a deficit or a surplus of electrons are called: a) elements b) isotopes c) ions d) molecules 9. In the Bohr model of the atom, electrons can only orbit the nucleus in particular circular orbits with fixed angular momentum and energy, their distances from the nucleus being proportional to their respective energies. They can only make _____ leaps between the fixed energy levels. a) tiny b) quantum c) gradual 10. It is impossible to simultaneously derive precise values for both the position and momentum of a particle for any given point in time; this became known as the ______ principle. a) Bohr b) Einstein c) uncertainty d) quantum 11. The modern model of the atom describes the positions of electrons in an atom in terms of: a) quantum levels b) orbital paths c) probabilities d) GPS 12. Isotopes of an element have nuclei with the same number of protons (the same atomic number) but different numbers of: a) electrons b) neutrons c) ions d) photons 13. In helium-3 (or 3He), how many protons are present? a) 1 b) 2 c) 3 d) 4 14. In helium-3 (or 3He), how many neutrons are present? a) 1 b) 2 c) 3 d) 4 15. The relative abundance of an isotope is strongly correlated with its tendency toward nuclear _____, short-lived nuclides quickly go away, while their long-lived counterparts endure. a) fission b) fusion c) decay d) bombardment 16. The isotopic composition of elements is different on different planets. a) True b) False 17. As a general rule, the fewer electrons in an atom’s valence shell, the ____ reactive it is. Lithium, sodium, and potassium have one electron in their outer shells. a) more b) less 18. Every atom is much more stable, or less reactive, with a ____ valence shell. a) partly full b) completely full 19. A positively-charged ion, which has fewer electrons than protons, is known as a: a) anion b) cation c) fermion d) bation 20. Bonds vary widely in their strength. Generally covalent and ionic bonds are often described as “strong”, whereas ______ bonds are generally considered to be “weak”. a) van der Waals b) Faradays c) van Neumans 21. This bonding involves sharing of electrons in which the positively charged nuclei of two or more atoms simultaneously attract the negatively charged electrons that are being shared a) ionic b) covalent c) van der Waals d) metallic 22. This bond results from electrostatic attraction between atoms: a) ionic b) covalent c) van der Waals d) metallic 23. A sea of delocalized electrons causes this bonding: a) ionic b) covalent c) van der Waals d) metallic 24. The chemical composition of minerals may vary between end members of a mineral system. For example the ______ feldspars comprise a continuous series from sodiumrich albite to calcium-rich anorthite. a) plagioclase b) orthoclase c) alkaline d) acidic 25. Crystal structure is based on ____ internal atomic arrangement. a) irregular b) regular c) random d) curvilinear 26. Pyrite and marcasite are both _______, but their arrangement of atoms differs. a) iron sulfide b) lead sulfide c) copper silfide d) silver sulfide 27. The carbon atoms in ______ are arranged into sheets which can slide easily past each other, while the carbon atoms in diamond form a strong, interlocking three-dimensional network. a) sapphire b) graphite c) aluminum d) carbonate 28. TGCFAOQTCD a) Crystal habit b) Hardness scale c) Luster scale 29. Dull to metallic, submetallic, adamantine, vitreous, pearly, resinous, or silky. a) Crystal habit b) Hardness scale c) Luster scale d) Heft scale 30. The color of the powder a mineral leaves after rubbing it on unglazed porcelain. a) color b) streak c) lustre d) iridescense 31. Describes the way a mineral may split apart along various planes. a) fracture b) streak c) lustre d) cleavage 32. In modern physics, the position of electrons about a nucleus are defined in terms of: a) probabilities b) circles c) ellipses d) chromodomes 33. The symbol H+ suggests a: a) hydrogen atom b) hydrogen isotope c) hydrogen cation d) hydrogen anion 34. The tabulated atomic mass of natural carbon is not exactly 12 because carbon in nature always has multiple ________ present. a) electrons b) isotopes c) quarks d) protons 35. This type of bonding due to delocalized electrons leads to malleability, ductility, and high melting points: a) covalent b) ionic c) van der Waals d) metallic 36. The mineral ___________ is 3 on Mohs Scale whereas the mineral ___________ is 9. a) calcite, corundum b) corundum, calcite c) caliche, calcite d) chalcedony, quartz 37. In hand specimens, geologists identify most minerals based on: a) physical properties b) chemical analyses c) xray diffraction 38. This type of chemical bonding is the weakest but occurs in all substances. a) covalent b) ionic c) metallic d) none of the above 39. Quartz, feldspar, mica, chlorite, kaolin, calcite, epidote, olivine, augite, hornblende, magnetite, hematite, limonite: these minerals are: a) common in rocks b) occasionally found c) rare d) extremely rare 40. Characteristics of a mineral do NOT include: a) naturally occurring b) characteristic chemical formula c) crystalline d) organic e) all of the above 41. The chemical composition of a particular mineral may vary between end members. For example, the common mineral plagioclase feldspar varies from being _______-rich to being _________-rich. a) sodium, calcium b) potassium, sodium c) iron, magnesium d) carbon, oxygen 42. Sharing of electrons typifies the __________ bond whereas electrostatic attraction typifies the _______ bond. a) ionic, covalent b) ionic, triclinic c) covalent, ionic d) triclinic, covalent 43. If number of protons does not equal the number of electrons, the atom is a(n) : a) isotope b) ion c) quark d) simplex e) google 44. Atoms generally consist of: a) electrons b) protons c) neutrons d) all of the above 45. Not counting rare minerals, about how many mineral species are at least occasionally encountered in rocks? a) 20 b) 200 c) 2000 46. Carbon is atomic number 6. Carbon-13 has _______ protons and _______ neutrons. a) thirteen, six b) six, seven c) twelve, twenty-five d) twelve, twelve 47. Which of these particles are not nucleons? a) electrons b) neutrons c) protons 48. A mineral with visibly recognizable crystals is said to have good crystal habit; otherwise the mineral is said to be: a) massive b) granular c) compact d) any of the above 49. In chemical bonding, two atoms become linked by moving or sharing __________. a) neutrons b) protons c) electrons 50. The name of an element is determined by the number of ______ present in the ______ of an atom. a) electrons, nucleus b) neutrons, nucleus c) protons, nucleus d) protons, electron cloud e) neutrons, electron cloud 51. Generally ________ and ____________ bonds are strong whereas the ______________ bond is weak. a) covalent, ionic, van der Waals b) van der Waals, covalent, ionic c) ionic, van der Waals, covalent 52. Which of the following are held together by chemical bonds? a) molecules b) crystals c) diatomic gases 53. An ion with fewer electrons than protons is called an ______ and it carries a _________ electric charge. a) cation, positive b) anion, negative c) cation, negative d) anion, positive 54. Two or more minerals may have the same _________ composition but different _______ structure. These are called polymorphs. a) crystal, chemical b) chemical, crystal 55. Industrial minerals are: a) gem quality b) commercially valuable c) tailings d) worthless 56. All minerals are crystalline. If the crystals are too small to see, they can be detected by: a) x-ray diffraction b) cosmic rays c) sound waves d) odor 57. If two atomes have the same number of protons but different numbers of neutrons, the atoms are _______ of the same _________. a) elements, mineral b) atoms, isotope c) elements, isotope d) isotopes, element 58. Modern physics recognizes that electrons show both particle and ______ behavior. a) wave b) emotional c) thermal d) revolting 59. Sodium and potassium have one ______ electron in their outer shells and are extremely ________. a) valence, stable b) inverted, reactive c) valence, reactive d) contaminated, inactive 60. The luster of _______ would be described as ________. a) glass, vitreous b) diamond, dull c) pyrite, silky d) graphite, resinous 61. The minerals ________ and __________ are polymorphs of carbon. a) diamond, graphite b) calcite, silicate c) bonite, bronzite 62. In the ______ atom based on _______ physics, electrons were restricted to circular orbits of fixed energy levels. a) Bohr , quantum b) Rutherford, classical c) Bohr, classical d) Rutherford, quantum 63. Virtually all elements other than ______ and _______ were formed in stars and supernovae long after the Big Bang. a) hydrogen, helium b) carbon, phosphorus c) carbon, oxygen d) silica, carbon 64. Physicist Werner _________ developed the ___________ principle which means that it is impossible to know exactly the position and momentum of a particle. a) Heisenberg, certainty b) Heisenberg, uncertainty c) Bohr, uncertainty d) Bohr, certainty

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Chapter 04 Homework Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Activity: Investigating Survivorship Curves Click here to complete this activity. Then answer the questions. Part A Which of these species typically has a mortality rate that remains fairly constant over an individual’s life span? ANSWER: Correct The mortality rate of robins remains relatively constant throughout their life span. Part B Oyster populations are primarily, if not exclusively, composed of _____. ANSWER: Correct Young oysters have a very high mortality rate; older oysters have a much lower mortality rate. Thus, most oyster populations consist primarily of older individuals. Part C Which of these organisms has a survivorship curve similar to that of oysters? ANSWER: grasses oysters elephants robins humans juveniles adults prereproductive oysters larval and juvenile oysters larvae Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 13 5/21/2014 7:59 PM Correct Grasses, like oysters, have a relatively high mortality rate early in their life span, after which the mortality rate decreases. Part D Which of these organisms has a survivorship curve similar to that of humans? ANSWER: Correct The mortality rate of elephants, like that of humans, remains relatively low for much of their life span and then dramatically increases for older individuals. BioFlix Quiz: Population Ecology Watch the animation at left before answering the questions below. cats robins elephants grasses humans cats oysters grasses robins elephants Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 13 5/21/2014 7:59 PM Part A An ideal habitat with unlimited resources is associated with Hint 1. Review the animation or your Study Sheet for Population Ecology ANSWER: Correct Populations grow exponentially with unlimited resources. Part B The maximum population a habitat can support is its Hint 1. Review the animation or your Study Sheet for Population Ecology ANSWER: Correct Part C Logistic growth involves Hint 1. Review the animation or your Study Sheet for Population Ecology ANSWER: Both exponential growth and logistic growth. Population crashes. Exponential growth. Logistic growth. Neither exponential growth nor logistic growth. Logistic growth. Death rate. Birth rate. Carrying capacity. Exponential growth. A population crash. Population growth continuing forever. Population growth reaching carrying capacity and then speeding up. Population size decreasing to zero. Population growth slowing down as the population approaches carrying capacity. Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 13 5/21/2014 7:59 PM Correct Part D In exponential growth Hint 1. Review the animation or your Study Sheet for Population Ecology ANSWER: Correct Part E Which of the following would NOT cause population size to decrease? Hint 1. Review the animation. ANSWER: Correct An increased birth rate would cause population size to increase. BioFlix Activity: Photosynthesis — Inputs and Outputs Can you fill in the photosynthesis equation? To review photosynthesis, watch this BioFlix animation: Photosynthesis. Part A – Photosynthesis equation Drag the labels onto the equation to identify the inputs and outputs of photosynthesis. ANSWER: Population size grows more and more slowly as the population gets bigger. Population size grows faster and faster as the population gets bigger. Population size stays constant. Population growth slows as the population gets close to its carrying capacity. None of these are correct. Increased death rate A exponentially growing population outgrowing its food supply and crashing Poor weather, resulting in less food being available Increase in the number of predators Increased birth rate Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 13 5/21/2014 7:59 PM BioFlix Activity: Cellular Respiration and Photosynthesis — Energy Flow Can you identify how energy flows through an ecosystem? To review energy flow in cellular respiration and photosynthesis, watch these BioFlix animations: Cellular Respiration and Photosynthesis. Part A – Energy flow through an ecosystem Drag the labels onto the diagram to identify how energy flows through an ecosystem. ANSWER: BioFlix Activity: Cellular Respiration and Photosynthesis — Chemical Cycling Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 13 5/21/2014 7:59 PM Can you identify how chemicals cycle in an ecosystem? To review the chemical inputs and outputs of cellular respiration and photosynthesis, watch these BioFlix animations: Cellular Respiration and Photosynthesis. Part A – Chemical cycling in an ecosystem Drag the labels onto the diagram to identify how chemicals cycle in an ecosystem. ANSWER: BioFlix Activity: Cellular Respiration — Inputs and Outputs Can you fill in the cellular respiration equation? To review cellular respiration, watch this BioFlix animation: Cellular Respiration. Part A – Cellular respiration equation Drag the labels onto the equation to identify the inputs and outputs of cellular respiration. ANSWER: Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 13 5/21/2014 7:59 PM BioFlix Activity: Population Ecology — Types of Population Growth Can you identify the different ways in which populations grow? To review types of population growth, watch this BioFlix animation: Population Ecology. Part A – Types of population growth Drag the correct label under each graph to identify the type of population growth shown. ANSWER: Concept Review: Calculating Doubling Time Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 7 of 13 5/21/2014 7:59 PM Can you calculate doubling times and growth rates for exponentially growing populations? Remember that the doubling time (in years) for an exponentially growing population is estimated by dividing 70 by the growth rate of the population (as a percentage): Doubling time (in years) = 70 / annual growth rate (%) Part A Drag the values on the left to the appropriate blanks on the right to complete the sentences. Not all values will be used. ANSWER: Concept Review: Calculating Population Growth Rates Populations grow larger from births and immigration and grow smaller from deaths and emigration. The growth rate for a population is determined by adding the birth rate and the immigration rate, and then subtracting the death rate and the emigration rate (all rates expressed as the number per 1,000 individuals per year): (birth rate + immigration rate) (death rate + emigration rate) = growth rate Positive population growth rates lead to population increases, and negative population growth rates lead to population declines. Part A Suppose you are studying a population with the following characteristics: Birth rate = 14 per 1,000/year Death rate = 6 per 1,000/year Immigration rate = 5 per 1,000/year Emigration rate = 1 per 1,000/year What is the growth rate for this population? ANSWER: Part B Suppose you are studying a population with the following characteristics: 4 per 1,000/year 12 per 1,000/year 14 per 1,000/year 26 per 1,000/year Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 8 of 13 5/21/2014 7:59 PM Birth rate = 11 per 1,000/year Death rate = 10 per 1,000/year Immigration rate = 4 per 1,000/year Emigration rate = 3 per 1,000/year What is the growth rate for this population? ANSWER: Part C Suppose you are studying a population with the following characteristics: Birth rate = 10 per 1,000/year Death rate = 12 per 1,000/year Immigration rate = 2 per 1,000/year Emigration rate = 3 per 1,000/year What is the growth rate for this population? ANSWER: Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). Concept Review: Levels of Ecological Organization Can you identify the example that corresponds to each level of ecological organization? Part A Drag the labels to the appropriate targets in the table. ANSWER: 0 per 1,000/year 2 per 1,000/year 14 per 1,000/year 28 per 1,000/year 3 per 1,000/year 1 per 1,000/year 17 per 1,000/year 27 per 1,000/year Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 9 of 13 5/21/2014 7:59 PM BioFlix Activity: Mechanisms of Evolution — Natural Selection: Pesticides Can you identify the process by which natural selection acts on an insect population exposed to pesticides? To review the process of natural selection, watch this BioFlix animation: Mechanisms of Evolution: Natural Selection. Part A – Natural selection: Pesticides Drag the labels onto the flowchart to place them in the correct sequence. ANSWER: Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 10 of 13 5/21/2014 7:59 PM ABC News Video: Protecting the Galapagos Islands Watch the ABC News video (2:07 minutes). Then answer the questions below. Part A Where are the Galapagos Islands located? ANSWER: Part B Which of the following sets of animals are likely to be found on the Galapagos Islands? ANSWER: near the tip of South Africa northeast of Australia along the Great Barrier Reef 600 miles west of Ecuador, near the equator in the Mediterranean Sea, as part of the Greek Islands frogs, lungfish, mountain goats tortoises, finches, blue-footed boobies ostriches, cougars, porcupines beaver, snakes, armadillos Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 11 of 13 5/21/2014 7:59 PM Part C Which species is threatening the natural wildlife on the Galapagos Islands? ANSWER: Part D The Galapagos Islands were the first place on Earth to _____. ANSWER: Part E Tourism on the Galapagos Islands is being restricted by requiring tourists to _____. ANSWER: Current Events: A Surplus Washington Could Do Without: A Capital Park’s Rapacious Deer (New York Times, 2/28/2012) Read this New York Times article and then answer the questions. A Surplus Washington Could Do Without: A Capital Park’s Rapacious Deer (2/28/2012) Registration with The New York Times provides instant access to breaking news on NYTimes.com. To register, go to http://www.nytimes.com/register. Visit http://www.nytimes.com/content/help/rights/terms/terms-of-service.html to review the current NYT Terms of Service. Part A Which of the following is true? ANSWER: Part B What predator currently feeds on deer in Rock Creek Park? humans zebra mussels Asian carp mountain lions suffer the complete extinction of all native species be declared off-limits to all humans be declared a world heritage site be invaded by human-introduced species visit each island in groups of only ten individuals at a time view the islands only from the water be escorted by trained guides at all times stay at least 100 feet away from all animals on the islands Deer have always been a problem in Rock Creek Park. Deer are not a problem in Rock Creek Park. Deer are not native to Rock Creek Park, and have been a problem since they were introduced in 1952. Deer were once absent from Rock Creek Park, and have only become a problem in the last 20 years. Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 12 of 13 5/21/2014 7:59 PM ANSWER: Part C Why isn’t the deer population controlled by hunting in Rock Creek Park? ANSWER: Part D It is hoped that the deer herd can be reduced by how much? ANSWER: Part E Which of the following is true? ANSWER: Part F Because the park is changing in response to the increasing deer population, this is an example of ______________. ANSWER: Score Summary: Your score on this assignment is 21.2%. You received 9.1 out of a possible total of 43 points. There are no predators of deer in Rock Creek Park. mountain lion coyote wolf Hunting has been attempted in the park, but the trees are too thick. Hunting is prohibited in the park. There is no public interest in hunting in the park. Deer are a protected species. one-quarter one-half three-quarters the entire herd Animals cannot be killed on federally managed public lands. Only Congress can decide to have animals killed on federally managed public lands. The federal agency in charge of management of the land in question decides if animals should be killed. Only the National Park Service can decide to have animals killed on federally managed public lands. succession artificial selection recession progression Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 13 of 13 5/21/2014 7:59 PM

Chapter 04 Homework Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Activity: Investigating Survivorship Curves Click here to complete this activity. Then answer the questions. Part A Which of these species typically has a mortality rate that remains fairly constant over an individual’s life span? ANSWER: Correct The mortality rate of robins remains relatively constant throughout their life span. Part B Oyster populations are primarily, if not exclusively, composed of _____. ANSWER: Correct Young oysters have a very high mortality rate; older oysters have a much lower mortality rate. Thus, most oyster populations consist primarily of older individuals. Part C Which of these organisms has a survivorship curve similar to that of oysters? ANSWER: grasses oysters elephants robins humans juveniles adults prereproductive oysters larval and juvenile oysters larvae Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 13 5/21/2014 7:59 PM Correct Grasses, like oysters, have a relatively high mortality rate early in their life span, after which the mortality rate decreases. Part D Which of these organisms has a survivorship curve similar to that of humans? ANSWER: Correct The mortality rate of elephants, like that of humans, remains relatively low for much of their life span and then dramatically increases for older individuals. BioFlix Quiz: Population Ecology Watch the animation at left before answering the questions below. cats robins elephants grasses humans cats oysters grasses robins elephants Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 13 5/21/2014 7:59 PM Part A An ideal habitat with unlimited resources is associated with Hint 1. Review the animation or your Study Sheet for Population Ecology ANSWER: Correct Populations grow exponentially with unlimited resources. Part B The maximum population a habitat can support is its Hint 1. Review the animation or your Study Sheet for Population Ecology ANSWER: Correct Part C Logistic growth involves Hint 1. Review the animation or your Study Sheet for Population Ecology ANSWER: Both exponential growth and logistic growth. Population crashes. Exponential growth. Logistic growth. Neither exponential growth nor logistic growth. Logistic growth. Death rate. Birth rate. Carrying capacity. Exponential growth. A population crash. Population growth continuing forever. Population growth reaching carrying capacity and then speeding up. Population size decreasing to zero. Population growth slowing down as the population approaches carrying capacity. Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 13 5/21/2014 7:59 PM Correct Part D In exponential growth Hint 1. Review the animation or your Study Sheet for Population Ecology ANSWER: Correct Part E Which of the following would NOT cause population size to decrease? Hint 1. Review the animation. ANSWER: Correct An increased birth rate would cause population size to increase. BioFlix Activity: Photosynthesis — Inputs and Outputs Can you fill in the photosynthesis equation? To review photosynthesis, watch this BioFlix animation: Photosynthesis. Part A – Photosynthesis equation Drag the labels onto the equation to identify the inputs and outputs of photosynthesis. ANSWER: Population size grows more and more slowly as the population gets bigger. Population size grows faster and faster as the population gets bigger. Population size stays constant. Population growth slows as the population gets close to its carrying capacity. None of these are correct. Increased death rate A exponentially growing population outgrowing its food supply and crashing Poor weather, resulting in less food being available Increase in the number of predators Increased birth rate Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 13 5/21/2014 7:59 PM BioFlix Activity: Cellular Respiration and Photosynthesis — Energy Flow Can you identify how energy flows through an ecosystem? To review energy flow in cellular respiration and photosynthesis, watch these BioFlix animations: Cellular Respiration and Photosynthesis. Part A – Energy flow through an ecosystem Drag the labels onto the diagram to identify how energy flows through an ecosystem. ANSWER: BioFlix Activity: Cellular Respiration and Photosynthesis — Chemical Cycling Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 13 5/21/2014 7:59 PM Can you identify how chemicals cycle in an ecosystem? To review the chemical inputs and outputs of cellular respiration and photosynthesis, watch these BioFlix animations: Cellular Respiration and Photosynthesis. Part A – Chemical cycling in an ecosystem Drag the labels onto the diagram to identify how chemicals cycle in an ecosystem. ANSWER: BioFlix Activity: Cellular Respiration — Inputs and Outputs Can you fill in the cellular respiration equation? To review cellular respiration, watch this BioFlix animation: Cellular Respiration. Part A – Cellular respiration equation Drag the labels onto the equation to identify the inputs and outputs of cellular respiration. ANSWER: Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 13 5/21/2014 7:59 PM BioFlix Activity: Population Ecology — Types of Population Growth Can you identify the different ways in which populations grow? To review types of population growth, watch this BioFlix animation: Population Ecology. Part A – Types of population growth Drag the correct label under each graph to identify the type of population growth shown. ANSWER: Concept Review: Calculating Doubling Time Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 7 of 13 5/21/2014 7:59 PM Can you calculate doubling times and growth rates for exponentially growing populations? Remember that the doubling time (in years) for an exponentially growing population is estimated by dividing 70 by the growth rate of the population (as a percentage): Doubling time (in years) = 70 / annual growth rate (%) Part A Drag the values on the left to the appropriate blanks on the right to complete the sentences. Not all values will be used. ANSWER: Concept Review: Calculating Population Growth Rates Populations grow larger from births and immigration and grow smaller from deaths and emigration. The growth rate for a population is determined by adding the birth rate and the immigration rate, and then subtracting the death rate and the emigration rate (all rates expressed as the number per 1,000 individuals per year): (birth rate + immigration rate) (death rate + emigration rate) = growth rate Positive population growth rates lead to population increases, and negative population growth rates lead to population declines. Part A Suppose you are studying a population with the following characteristics: Birth rate = 14 per 1,000/year Death rate = 6 per 1,000/year Immigration rate = 5 per 1,000/year Emigration rate = 1 per 1,000/year What is the growth rate for this population? ANSWER: Part B Suppose you are studying a population with the following characteristics: 4 per 1,000/year 12 per 1,000/year 14 per 1,000/year 26 per 1,000/year Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 8 of 13 5/21/2014 7:59 PM Birth rate = 11 per 1,000/year Death rate = 10 per 1,000/year Immigration rate = 4 per 1,000/year Emigration rate = 3 per 1,000/year What is the growth rate for this population? ANSWER: Part C Suppose you are studying a population with the following characteristics: Birth rate = 10 per 1,000/year Death rate = 12 per 1,000/year Immigration rate = 2 per 1,000/year Emigration rate = 3 per 1,000/year What is the growth rate for this population? ANSWER: Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). Concept Review: Levels of Ecological Organization Can you identify the example that corresponds to each level of ecological organization? Part A Drag the labels to the appropriate targets in the table. ANSWER: 0 per 1,000/year 2 per 1,000/year 14 per 1,000/year 28 per 1,000/year 3 per 1,000/year 1 per 1,000/year 17 per 1,000/year 27 per 1,000/year Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 9 of 13 5/21/2014 7:59 PM BioFlix Activity: Mechanisms of Evolution — Natural Selection: Pesticides Can you identify the process by which natural selection acts on an insect population exposed to pesticides? To review the process of natural selection, watch this BioFlix animation: Mechanisms of Evolution: Natural Selection. Part A – Natural selection: Pesticides Drag the labels onto the flowchart to place them in the correct sequence. ANSWER: Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 10 of 13 5/21/2014 7:59 PM ABC News Video: Protecting the Galapagos Islands Watch the ABC News video (2:07 minutes). Then answer the questions below. Part A Where are the Galapagos Islands located? ANSWER: Part B Which of the following sets of animals are likely to be found on the Galapagos Islands? ANSWER: near the tip of South Africa northeast of Australia along the Great Barrier Reef 600 miles west of Ecuador, near the equator in the Mediterranean Sea, as part of the Greek Islands frogs, lungfish, mountain goats tortoises, finches, blue-footed boobies ostriches, cougars, porcupines beaver, snakes, armadillos Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 11 of 13 5/21/2014 7:59 PM Part C Which species is threatening the natural wildlife on the Galapagos Islands? ANSWER: Part D The Galapagos Islands were the first place on Earth to _____. ANSWER: Part E Tourism on the Galapagos Islands is being restricted by requiring tourists to _____. ANSWER: Current Events: A Surplus Washington Could Do Without: A Capital Park’s Rapacious Deer (New York Times, 2/28/2012) Read this New York Times article and then answer the questions. A Surplus Washington Could Do Without: A Capital Park’s Rapacious Deer (2/28/2012) Registration with The New York Times provides instant access to breaking news on NYTimes.com. To register, go to http://www.nytimes.com/register. Visit http://www.nytimes.com/content/help/rights/terms/terms-of-service.html to review the current NYT Terms of Service. Part A Which of the following is true? ANSWER: Part B What predator currently feeds on deer in Rock Creek Park? humans zebra mussels Asian carp mountain lions suffer the complete extinction of all native species be declared off-limits to all humans be declared a world heritage site be invaded by human-introduced species visit each island in groups of only ten individuals at a time view the islands only from the water be escorted by trained guides at all times stay at least 100 feet away from all animals on the islands Deer have always been a problem in Rock Creek Park. Deer are not a problem in Rock Creek Park. Deer are not native to Rock Creek Park, and have been a problem since they were introduced in 1952. Deer were once absent from Rock Creek Park, and have only become a problem in the last 20 years. Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 12 of 13 5/21/2014 7:59 PM ANSWER: Part C Why isn’t the deer population controlled by hunting in Rock Creek Park? ANSWER: Part D It is hoped that the deer herd can be reduced by how much? ANSWER: Part E Which of the following is true? ANSWER: Part F Because the park is changing in response to the increasing deer population, this is an example of ______________. ANSWER: Score Summary: Your score on this assignment is 21.2%. You received 9.1 out of a possible total of 43 points. There are no predators of deer in Rock Creek Park. mountain lion coyote wolf Hunting has been attempted in the park, but the trees are too thick. Hunting is prohibited in the park. There is no public interest in hunting in the park. Deer are a protected species. one-quarter one-half three-quarters the entire herd Animals cannot be killed on federally managed public lands. Only Congress can decide to have animals killed on federally managed public lands. The federal agency in charge of management of the land in question decides if animals should be killed. Only the National Park Service can decide to have animals killed on federally managed public lands. succession artificial selection recession progression Chapter 04 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 13 of 13 5/21/2014 7:59 PM

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Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 Assignment 4 – Noise and Correlation 1. If a signal is measured as 2.5 V and the noise is 28 mV (28 × 10−3 V), what is the SNR in dB? 2. A single sinusoidal signal is found with some noise. If the RMS value of the noise is 0.5 V and the SNR is 10 dB, what is the RMS amplitude of the sinusoid? 3. The file signal_noise.mat contains a variable x that consists of a 1.0-V peak sinusoidal signal buried in noise. What is the SNR for this signal and noise? Assume that the noise RMS is much greater than the signal RMS. Note: “signal_noise.mat” and other files used in these assignments can be downloaded from the content area of Brightspace, within the “Data Files for Exercises” folder. These files can be opened in Matlab by copying into the active folder and double-clicking on the file or using the Matlab load command using the format: load(‘signal_noise.mat’). To discover the variables within the files use the Matlab who command. 4. An 8-bit ADC converter that has an input range of ±5 V is used to convert a signal that ranges between ±2 V. What is the SNR of the input if the input noise equals the quantization noise of the converter? Hint: Refer to Equation below to find the quantization noise: 5. The file filter1.mat contains the spectrum of a fourth-order lowpass filter as variable x in dB. The file also contains the corresponding frequencies of x in variable freq. Plot the spectrum of this filter both as dB versus log frequency and as linear amplitude versus linear frequency. The frequency axis should range between 10 and 400 Hz in both plots. Hint: Use Equation below to convert: Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 6. Generate one cycle of the square wave similar to the one shown below in a 500-point MATLAB array. Determine the RMS value of this waveform. [Hint: When you take the square of the data array, be sure to use a period before the up arrow so that MATLAB does the squaring point-by-point (i.e., x.^2).]. 7. A resistor produces 10 μV noise (i.e., 10 × 10−6 V noise) when the room temperature is 310 K and the bandwidth is 1 kHz (i.e., 1000 Hz). What current noise would be produced by this resistor? 8. A 3-ma current flows through both a diode (i.e., a semiconductor) and a 20,000-Ω (i.e., 20-kΩ) resistor. What is the net current noise, in? Assume a bandwidth of 1 kHz (i.e., 1 × 103 Hz). Which of the two components is responsible for producing the most noise? 9. Determine if the two signals, x and y, in file correl1.mat are correlated by checking the angle between them. 10. Modify the approach used in Practice Problem 3 to find the angle between short signals: Do not attempt to plot these vectors as it would require a 6-dimensional plot!

Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 Assignment 4 – Noise and Correlation 1. If a signal is measured as 2.5 V and the noise is 28 mV (28 × 10−3 V), what is the SNR in dB? 2. A single sinusoidal signal is found with some noise. If the RMS value of the noise is 0.5 V and the SNR is 10 dB, what is the RMS amplitude of the sinusoid? 3. The file signal_noise.mat contains a variable x that consists of a 1.0-V peak sinusoidal signal buried in noise. What is the SNR for this signal and noise? Assume that the noise RMS is much greater than the signal RMS. Note: “signal_noise.mat” and other files used in these assignments can be downloaded from the content area of Brightspace, within the “Data Files for Exercises” folder. These files can be opened in Matlab by copying into the active folder and double-clicking on the file or using the Matlab load command using the format: load(‘signal_noise.mat’). To discover the variables within the files use the Matlab who command. 4. An 8-bit ADC converter that has an input range of ±5 V is used to convert a signal that ranges between ±2 V. What is the SNR of the input if the input noise equals the quantization noise of the converter? Hint: Refer to Equation below to find the quantization noise: 5. The file filter1.mat contains the spectrum of a fourth-order lowpass filter as variable x in dB. The file also contains the corresponding frequencies of x in variable freq. Plot the spectrum of this filter both as dB versus log frequency and as linear amplitude versus linear frequency. The frequency axis should range between 10 and 400 Hz in both plots. Hint: Use Equation below to convert: Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 6. Generate one cycle of the square wave similar to the one shown below in a 500-point MATLAB array. Determine the RMS value of this waveform. [Hint: When you take the square of the data array, be sure to use a period before the up arrow so that MATLAB does the squaring point-by-point (i.e., x.^2).]. 7. A resistor produces 10 μV noise (i.e., 10 × 10−6 V noise) when the room temperature is 310 K and the bandwidth is 1 kHz (i.e., 1000 Hz). What current noise would be produced by this resistor? 8. A 3-ma current flows through both a diode (i.e., a semiconductor) and a 20,000-Ω (i.e., 20-kΩ) resistor. What is the net current noise, in? Assume a bandwidth of 1 kHz (i.e., 1 × 103 Hz). Which of the two components is responsible for producing the most noise? 9. Determine if the two signals, x and y, in file correl1.mat are correlated by checking the angle between them. 10. Modify the approach used in Practice Problem 3 to find the angle between short signals: Do not attempt to plot these vectors as it would require a 6-dimensional plot!

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