university physics young and freedman 13th edition-Chapter Summary Chapter 9

university physics young and freedman 13th edition-Chapter Summary Chapter 9

Section 9.1 “Angular velocity,” of an object is its instantaneous … Read More...
Which statement regarding enzyme function is true? Excessive salt ions can cause an enzyme to denature. Enzymes cannot function at a pH lower than 6. Most coenzymes are inorganic substances such as ions of iron or potassium. Higher temperatures allow greater contact between enzymes and substrates; therefore, the higher the temperature the better the enzyme will function.

Which statement regarding enzyme function is true? Excessive salt ions can cause an enzyme to denature. Enzymes cannot function at a pH lower than 6. Most coenzymes are inorganic substances such as ions of iron or potassium. Higher temperatures allow greater contact between enzymes and substrates; therefore, the higher the temperature the better the enzyme will function.

Excessive salt ions can cause an enzyme to denature.
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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Name Tutorials in Introductory Physics ©Pearson Custom Publishing McDermott, Shaffer, & P.E.G., U. Wash. Updated Preliminary Second Edition, 2011 Mech HW–39 1. A block initially at rest is given a quick push by a hand. The block slides across the floor, gradually slows down, and comes to rest. a. In the spaces provided, draw and label separate free-body diagrams for the block at each of the three instants shown. A quick push by a hand… 1. (Initially at rest) the sliding block slows… 2. v and is finally at rest. 3. b. Rank the magnitudes of all the horizontal forces in the diagram for instant 1. Explain. c. Are any of the forces that you drew for instant 1 missing from your diagram for instant 2? If so, for each force that is missing, explain how you knew to include the force on the first diagram but not on the second. d. Are any of the forces that you drew for instant 1 missing from your diagram for instant 3? If so, for each force that is missing, explain how you knew to include the force on the first diagram but not on the third. NEWTON’S SECOND AND THIRD LAWS Newton’s second and third laws Tutorials in Introductory Physics ©Pearson Custom Publishing McDermott, Shaffer, & P.E.G., U. Wash. Updated Preliminary Second Edition, 2011 Mech HW–40 2. Two crates, A and B, are in an elevator as shown. The mass of crate A is greater than the mass of crate B. a. The elevator moves downward at constant speed. i. How does the acceleration of crate A compare to that of crate B? Explain. ii. In the spaces provided below, draw and label separate free-body diagrams for the crates. Free-body diagram for crate A Free-body diagram for crate B iii. Rank the forces on the crates according to magnitude, from largest to smallest. Explain your reasoning, including how you used Newton’s second and third laws. iv. In the spaces provided at right, draw arrows to indicate the direction of the net force on each crate. If the net force on either crate is zero, state so explicitly. Explain. Is the magnitude of the net force on crate A greater than, less than, or equal to that on crate B? Explain. Elevator (moving down at constant speed) A B Cable Crate A Crate B Direction of net force Newton’s second and third laws Name Tutorials in Introductory Physics ©Pearson Custom Publishing McDermott, Shaffer, & P.E.G., U. Wash. Updated Preliminary Second Edition, 2011 Mech HW–41 b. As the elevator approaches its destination, its speed decreases. (It continues to move downward.) i. How does the acceleration of crate A compare to that of crate B? Explain. ii. In the spaces provided below, draw and label separate free-body diagrams for the crates in this case. Free-body diagram for crate A Free-body diagram for crate B iii. Rank the forces on the crates according to magnitude, from largest to smallest. Explain your reasoning, including how you used Newton’s second and third laws. iv. In the spaces provided at right, draw arrows to indicate the direction of the net force on each crate. If the net force on either crate is zero, state so explicitly. Explain. Is the magnitude of the net force on crate A greater than, less than, or equal to that on crate B? Explain. Crate A Crate B Direction of net force Newton’s second and third laws Tutorials in Introductory Physics ©Pearson Custom Publishing McDermott, Shaffer, & P.E.G., U. Wash. Updated Preliminary Second Edition, 2011 Mech HW–42 3. A hand pushes three identical bricks as shown. The bricks are moving to the left and speeding up. System A consists of two bricks stacked together. System B consists of a single brick. System C consists of all three bricks. There is friction between the bricks and the table. a. In the spaces provided at right, draw and label separate free-body diagrams for systems A and B. b. The vector representing the acceleration of system A is shown at right. Draw the acceleration vectors for systems B and C using the same scale. Explain. c. The vector representing the net force on system A is shown at right. Draw the net force vectors for systems B and C using the same scale. Explain. d. The vector representing the frictional force on system A is shown below. Draw the remaining force vectors using the same scale. NBH NAB NBA fAT fBT Explain how you knew to draw the force vectors as you did. A B Free-body diagram for system A Free-body diagram for system B Acceleration of A Acceleration of B Acceleration of C Net force on A Net force on B Net force on C

Name Tutorials in Introductory Physics ©Pearson Custom Publishing McDermott, Shaffer, & P.E.G., U. Wash. Updated Preliminary Second Edition, 2011 Mech HW–39 1. A block initially at rest is given a quick push by a hand. The block slides across the floor, gradually slows down, and comes to rest. a. In the spaces provided, draw and label separate free-body diagrams for the block at each of the three instants shown. A quick push by a hand… 1. (Initially at rest) the sliding block slows… 2. v and is finally at rest. 3. b. Rank the magnitudes of all the horizontal forces in the diagram for instant 1. Explain. c. Are any of the forces that you drew for instant 1 missing from your diagram for instant 2? If so, for each force that is missing, explain how you knew to include the force on the first diagram but not on the second. d. Are any of the forces that you drew for instant 1 missing from your diagram for instant 3? If so, for each force that is missing, explain how you knew to include the force on the first diagram but not on the third. NEWTON’S SECOND AND THIRD LAWS Newton’s second and third laws Tutorials in Introductory Physics ©Pearson Custom Publishing McDermott, Shaffer, & P.E.G., U. Wash. Updated Preliminary Second Edition, 2011 Mech HW–40 2. Two crates, A and B, are in an elevator as shown. The mass of crate A is greater than the mass of crate B. a. The elevator moves downward at constant speed. i. How does the acceleration of crate A compare to that of crate B? Explain. ii. In the spaces provided below, draw and label separate free-body diagrams for the crates. Free-body diagram for crate A Free-body diagram for crate B iii. Rank the forces on the crates according to magnitude, from largest to smallest. Explain your reasoning, including how you used Newton’s second and third laws. iv. In the spaces provided at right, draw arrows to indicate the direction of the net force on each crate. If the net force on either crate is zero, state so explicitly. Explain. Is the magnitude of the net force on crate A greater than, less than, or equal to that on crate B? Explain. Elevator (moving down at constant speed) A B Cable Crate A Crate B Direction of net force Newton’s second and third laws Name Tutorials in Introductory Physics ©Pearson Custom Publishing McDermott, Shaffer, & P.E.G., U. Wash. Updated Preliminary Second Edition, 2011 Mech HW–41 b. As the elevator approaches its destination, its speed decreases. (It continues to move downward.) i. How does the acceleration of crate A compare to that of crate B? Explain. ii. In the spaces provided below, draw and label separate free-body diagrams for the crates in this case. Free-body diagram for crate A Free-body diagram for crate B iii. Rank the forces on the crates according to magnitude, from largest to smallest. Explain your reasoning, including how you used Newton’s second and third laws. iv. In the spaces provided at right, draw arrows to indicate the direction of the net force on each crate. If the net force on either crate is zero, state so explicitly. Explain. Is the magnitude of the net force on crate A greater than, less than, or equal to that on crate B? Explain. Crate A Crate B Direction of net force Newton’s second and third laws Tutorials in Introductory Physics ©Pearson Custom Publishing McDermott, Shaffer, & P.E.G., U. Wash. Updated Preliminary Second Edition, 2011 Mech HW–42 3. A hand pushes three identical bricks as shown. The bricks are moving to the left and speeding up. System A consists of two bricks stacked together. System B consists of a single brick. System C consists of all three bricks. There is friction between the bricks and the table. a. In the spaces provided at right, draw and label separate free-body diagrams for systems A and B. b. The vector representing the acceleration of system A is shown at right. Draw the acceleration vectors for systems B and C using the same scale. Explain. c. The vector representing the net force on system A is shown at right. Draw the net force vectors for systems B and C using the same scale. Explain. d. The vector representing the frictional force on system A is shown below. Draw the remaining force vectors using the same scale. NBH NAB NBA fAT fBT Explain how you knew to draw the force vectors as you did. A B Free-body diagram for system A Free-body diagram for system B Acceleration of A Acceleration of B Acceleration of C Net force on A Net force on B Net force on C

Researchers recently investigated whether or not coffee prevented the development of high blood sugar (hyperglycemia) in laboratory mice. The mice used in this experiment have a mutation that makes them become diabetic. Read about this research study in this article published on the Science Daily web-site New Evidence That Drinking Coffee May Reduce the Risk of Diabetes as well as the following summary: A group of 11 mice was given water, and another group of 10 mice was supplied with diluted black coffee (coffee:water 1:1) as drinking fluids for five weeks. The composition of the diets and living conditions were similar for both groups of mice. Blood glucose was monitored weekly for all mice. After five weeks, there was no change in average body weight between groups. Results indicated that blood glucose concentrations increased significantly in the mice that drank water compared with those that were supplied with coffee. Finally, blood glucose concentration in the coffee group exhibited a 30 percent decrease compared with that in the water group. In the original paper, the investigators acknowledged that the coffee for the experiment was supplied as a gift from a corporation. Then answer the following questions in your own words: 1. Identify and describe the steps of the scientific method. Which observations do you think the scientists made leading up to this research study? Given your understanding of the experimental design, formulate a specific hypothesis that is being tested in this experiment. Describe the experimental design including control and treatment group(s), and dependent and independent variables. Summarize the results and the conclusion (50 points) 2. Criticize the research described. Things to consider: Were the test subjects and treatments relevant and appropriate? Was the sample size large enough? Were the methods used appropriate? Can you think of a potential bias in a research study like this? What are the limitations of the conclusions made in this research study? Address at least two of these questions in your critique of the research study (20 points). 3. Discuss the relevance of this type of research, both for the world in general and for you personally (20 points). 4. Write answers in your own words with proper grammar and spelling (10 points)

Researchers recently investigated whether or not coffee prevented the development of high blood sugar (hyperglycemia) in laboratory mice. The mice used in this experiment have a mutation that makes them become diabetic. Read about this research study in this article published on the Science Daily web-site New Evidence That Drinking Coffee May Reduce the Risk of Diabetes as well as the following summary: A group of 11 mice was given water, and another group of 10 mice was supplied with diluted black coffee (coffee:water 1:1) as drinking fluids for five weeks. The composition of the diets and living conditions were similar for both groups of mice. Blood glucose was monitored weekly for all mice. After five weeks, there was no change in average body weight between groups. Results indicated that blood glucose concentrations increased significantly in the mice that drank water compared with those that were supplied with coffee. Finally, blood glucose concentration in the coffee group exhibited a 30 percent decrease compared with that in the water group. In the original paper, the investigators acknowledged that the coffee for the experiment was supplied as a gift from a corporation. Then answer the following questions in your own words: 1. Identify and describe the steps of the scientific method. Which observations do you think the scientists made leading up to this research study? Given your understanding of the experimental design, formulate a specific hypothesis that is being tested in this experiment. Describe the experimental design including control and treatment group(s), and dependent and independent variables. Summarize the results and the conclusion (50 points) 2. Criticize the research described. Things to consider: Were the test subjects and treatments relevant and appropriate? Was the sample size large enough? Were the methods used appropriate? Can you think of a potential bias in a research study like this? What are the limitations of the conclusions made in this research study? Address at least two of these questions in your critique of the research study (20 points). 3. Discuss the relevance of this type of research, both for the world in general and for you personally (20 points). 4. Write answers in your own words with proper grammar and spelling (10 points)

The steps of the scientific method used in this research … Read More...
Plato is very specific about Reality and Illusion in his allegory of the cave. Express your understanding of the metaphysical distinction. How does this relate to experiences in your own life where you have left the cave of illusion to a greater experience of reality?

Plato is very specific about Reality and Illusion in his allegory of the cave. Express your understanding of the metaphysical distinction. How does this relate to experiences in your own life where you have left the cave of illusion to a greater experience of reality?

In figurative script lettering, actions and surroundings are used as … Read More...
http://www.youtube.com/watch?v=UnKEFSVAiNQ Watch the video, and then answer the questions below. According to realism, which of the following represents something that states would NOT seek? A. security B. prestige C. autonomy D. wealth E. permanent cooperation Schweller suggests that realists are wary of interdependence. If that is true, which of the following might be the most acceptable to a realist? A. creating a permanent pact of nonviolence with all English-speaking countries B. establishing an alliance to defend the U.S. against an invading country C. turning North America into something similar to the European Union, with a unified currency D. permitting the United Nations to run a global military so that the U.S. can reduce its military spending E. entering into a global production agreement in which the U.S. only manufactures computers Based on the video, which of the following statements about realists would seem to be false? A. Realists see the world as perpetually violent and full of war. B. Realists see humans as basically self-interested. C. Realists believe that the absence of a threat means a country should retrench. D. Realists believe that intervening in other countries to spread democracy is dangerous. E. Realists believe that autonomy is better than interdependence. What does Schweller mean by his statement that “there is no 911”? A. There is no global authority that is guaranteed to help any state in trouble. B. The world needs a central government to provide a universal social safety net. C. States need to cooperate more with each other in order to provide greater security for all. D. The United Nations is terrible at dealing with international emergencies. E. Islamic terrorists were not responsible for the attacks of September 11, 2001. Which of the following would be the best way to convince a realist to go to war? A. argue that we signed a treaty to protect that country B. argue that the country we are helping to defend was an ally in a prior war C. argue that it will provide the world with a chance at long-term peace and stability D. argue that the other country is a direct threat to our interests E. argue that if we do not intervene, the United Nations will

http://www.youtube.com/watch?v=UnKEFSVAiNQ Watch the video, and then answer the questions below. According to realism, which of the following represents something that states would NOT seek? A. security B. prestige C. autonomy D. wealth E. permanent cooperation Schweller suggests that realists are wary of interdependence. If that is true, which of the following might be the most acceptable to a realist? A. creating a permanent pact of nonviolence with all English-speaking countries B. establishing an alliance to defend the U.S. against an invading country C. turning North America into something similar to the European Union, with a unified currency D. permitting the United Nations to run a global military so that the U.S. can reduce its military spending E. entering into a global production agreement in which the U.S. only manufactures computers Based on the video, which of the following statements about realists would seem to be false? A. Realists see the world as perpetually violent and full of war. B. Realists see humans as basically self-interested. C. Realists believe that the absence of a threat means a country should retrench. D. Realists believe that intervening in other countries to spread democracy is dangerous. E. Realists believe that autonomy is better than interdependence. What does Schweller mean by his statement that “there is no 911”? A. There is no global authority that is guaranteed to help any state in trouble. B. The world needs a central government to provide a universal social safety net. C. States need to cooperate more with each other in order to provide greater security for all. D. The United Nations is terrible at dealing with international emergencies. E. Islamic terrorists were not responsible for the attacks of September 11, 2001. Which of the following would be the best way to convince a realist to go to war? A. argue that we signed a treaty to protect that country B. argue that the country we are helping to defend was an ally in a prior war C. argue that it will provide the world with a chance at long-term peace and stability D. argue that the other country is a direct threat to our interests E. argue that if we do not intervene, the United Nations will

http://www.youtube.com/watch?v=UnKEFSVAiNQ   Watch the video, and then answer the questions … Read More...
Excel Review Assignment #1 – ISM3011 Ask before/after/during class or come into office/online hours if you have questions on any of this. Refer to the syllabus on Academic Dishonesty and group/individual work and allowable help for all projects – also remember it’s your responsibility to protect your work. Before you start — read this whole assignment and use your optional text and/or review the tutorials as necessary on Canvas or www.bwarner.org/tips. A project overview for each project is also available. Part 1 – Create / Download / Parts • Create a blank workbook. Name it using your Last name followed by your initials and _ 1EX (underscore then 1EX). For Example: WarnerBL_1EX .xlsx. Either extension is fine. • Download the Word file Ex1 Data1-F15.docx and copy/paste Word table from the file into the 2nd worksheet in your workbook. Name the tab ‘2014 Sales’. • Download the Word file Ex1 Data2-F15.docx and copy/paste Word table from the file into the 3rd worksheet in your workbook. Name the tab ‘2015 Sales’. • Adjust the column widths of both Sales worksheets so that no data is cut off. • Do not add any formulas or cells to the Sales worksheets Part 2 – Summary Worksheet • Create a summary sheet from the Sales worksheets. Name the worksheet ‘Summary’. Build two summaries on this worksheet. Summary 1: Comparison of Sales by Month and Summary 2: Comparison of Sales by Store ID. • Use the project overview as a guide for the format. Use colors, borders and backgrounds to make the worksheet look professional. o Include the following:  Month and Store ID headings that reference the 2014 Sales worksheet. This means if ‘January’ is changed to ‘Jan’ in the 2014 Sales worksheet, the summary worksheet heading will also change. Do the same with the Store ID and 2014 Sales worksheet.  Formulas that reference the 2014 and 2015 Sales worksheets. If the Sales worksheets change, the summary worksheet should also adjust automatically.  Correct format for all book totals (commas, no decimal places)  Correct % change formulas in both tables. This is how much the totals have changed compared to the 2014 totals.  Correct format for all % change (% sign, 1 decimal place).  Use borders and background colors on the column & row headings for both tables of data • On the summary worksheet, use conditional formatting to highlight any % change cell that greater than zero with a bright color background. If the % change is negative, display the value with a red font and no background color. o There should be only two conditional formats set on each cell. o **Note – to do the conditional formatting steps, you can set the conditional formatting for one cell and then use the format painter to apply to other appropriate cells. If the values are all changed, the conditional formatting should still work. Once you have it working, check by changing some values & see if the conditional formatting changes correctly. Return to the original values/formulas in the cell before you submit. If you don’t use the format painter for this be sure you still try it out & understand how it works. Part 3 – Chart • Create 2 column graphs displaying Totals by Month and Totals by Store ID. Include: • Titles on both chart as well as labeling on the x and the y axis. • Color fonts for the title and axis labels (not dark blue or black) • Large font for the title (at least 16 point) • Include a legend • Format the background (chart area/walls) of the graph with a texture – use one that is easy to see. • Be sure that if any headings or numbers in the worksheets change, these changes are automatically reflected in your chart. • Add a star or banner shape between the two charts and add your name. Be sure the text is part of the shape (not a shape and a separate text box). Part 4 – Finishing Up • Be sure your worksheet tabs are named correctly and if possible, make each worksheet tab a distinctly different color. If your version of Excel doesn’t allow this, don’t worry about it. But do delete any additional worksheets in the workbook. • Create a title in the first row of your summary worksheet. Use the merge and center feature (across all columns with data) and a larger font & different font color (not blue or black). Also add a background color. Add a comment with your email address and the date your spreadsheet was created. • Below the title, add a row with the current date (use the today or now formula) so it is updated whenever the spreadsheet is opened). • Check your formulas, be sure they are correct and make sense. For example, if you are subtracting 2 numbers don’t use the SUM formulas (sum is for adding). Excel may figure out what you mean, but we want the formulas to be used correctly (show that you understand how to use them). • Check your worksheet for errors! Potential errors in cells show up as small green triangles in the top left corner of each cell. Do a little Googling on error checking for your version of Excel and be sure you have error checking turned on and that you reconcile each error so they don’t display when we open your project for grading. Sample: Project Submission Instructions / Notes: • Office/online hours get busy as deadlines approach. If you procrastinate and wait until the last days to work on your project, you may not be able to get all the help you want. • The only way we can fairly grade the projects is if we check for each requirement. Please go through the instructions before you submit & be sure you have done each one correctly so you don’t miss out on points. Compare your solution to the project overview. • Submitting: o Remember to leave all of the internal file properties intact for your project, if they are modified or deleted, you project won’t be accepted (see syllabus for more on this). o Read and follow the instructions in the Assignments section of Canvas on uploading and checking your upload. If you follow these instructions you can ensure that your project is uploaded correctly (and is the correct project). Be sure that Access / Excel are closed before you try to upload your project files. o If your project doesn’t upload correctly before the due date, it will be considered late and be assessed the late penalty – even it was finished on time. This is the only way we can ensure that students check their Canvas submissions. • Technology problems relating to your home computer (Windows based or Mac), internet connection or slow Canvas access are not valid excuses for late/missing work, unless Canvas is down for 6+ hours on the due date. Computers at USF computer labs and the library are available; leave enough time to access them as needed. Also give yourself enough time that if a TA can’t answer a question, you’ll have time to contact me & I can either help you or make an allowance in your grade. If you wait until the last days, I may not be able to do either.

Excel Review Assignment #1 – ISM3011 Ask before/after/during class or come into office/online hours if you have questions on any of this. Refer to the syllabus on Academic Dishonesty and group/individual work and allowable help for all projects – also remember it’s your responsibility to protect your work. Before you start — read this whole assignment and use your optional text and/or review the tutorials as necessary on Canvas or www.bwarner.org/tips. A project overview for each project is also available. Part 1 – Create / Download / Parts • Create a blank workbook. Name it using your Last name followed by your initials and _ 1EX (underscore then 1EX). For Example: WarnerBL_1EX .xlsx. Either extension is fine. • Download the Word file Ex1 Data1-F15.docx and copy/paste Word table from the file into the 2nd worksheet in your workbook. Name the tab ‘2014 Sales’. • Download the Word file Ex1 Data2-F15.docx and copy/paste Word table from the file into the 3rd worksheet in your workbook. Name the tab ‘2015 Sales’. • Adjust the column widths of both Sales worksheets so that no data is cut off. • Do not add any formulas or cells to the Sales worksheets Part 2 – Summary Worksheet • Create a summary sheet from the Sales worksheets. Name the worksheet ‘Summary’. Build two summaries on this worksheet. Summary 1: Comparison of Sales by Month and Summary 2: Comparison of Sales by Store ID. • Use the project overview as a guide for the format. Use colors, borders and backgrounds to make the worksheet look professional. o Include the following:  Month and Store ID headings that reference the 2014 Sales worksheet. This means if ‘January’ is changed to ‘Jan’ in the 2014 Sales worksheet, the summary worksheet heading will also change. Do the same with the Store ID and 2014 Sales worksheet.  Formulas that reference the 2014 and 2015 Sales worksheets. If the Sales worksheets change, the summary worksheet should also adjust automatically.  Correct format for all book totals (commas, no decimal places)  Correct % change formulas in both tables. This is how much the totals have changed compared to the 2014 totals.  Correct format for all % change (% sign, 1 decimal place).  Use borders and background colors on the column & row headings for both tables of data • On the summary worksheet, use conditional formatting to highlight any % change cell that greater than zero with a bright color background. If the % change is negative, display the value with a red font and no background color. o There should be only two conditional formats set on each cell. o **Note – to do the conditional formatting steps, you can set the conditional formatting for one cell and then use the format painter to apply to other appropriate cells. If the values are all changed, the conditional formatting should still work. Once you have it working, check by changing some values & see if the conditional formatting changes correctly. Return to the original values/formulas in the cell before you submit. If you don’t use the format painter for this be sure you still try it out & understand how it works. Part 3 – Chart • Create 2 column graphs displaying Totals by Month and Totals by Store ID. Include: • Titles on both chart as well as labeling on the x and the y axis. • Color fonts for the title and axis labels (not dark blue or black) • Large font for the title (at least 16 point) • Include a legend • Format the background (chart area/walls) of the graph with a texture – use one that is easy to see. • Be sure that if any headings or numbers in the worksheets change, these changes are automatically reflected in your chart. • Add a star or banner shape between the two charts and add your name. Be sure the text is part of the shape (not a shape and a separate text box). Part 4 – Finishing Up • Be sure your worksheet tabs are named correctly and if possible, make each worksheet tab a distinctly different color. If your version of Excel doesn’t allow this, don’t worry about it. But do delete any additional worksheets in the workbook. • Create a title in the first row of your summary worksheet. Use the merge and center feature (across all columns with data) and a larger font & different font color (not blue or black). Also add a background color. Add a comment with your email address and the date your spreadsheet was created. • Below the title, add a row with the current date (use the today or now formula) so it is updated whenever the spreadsheet is opened). • Check your formulas, be sure they are correct and make sense. For example, if you are subtracting 2 numbers don’t use the SUM formulas (sum is for adding). Excel may figure out what you mean, but we want the formulas to be used correctly (show that you understand how to use them). • Check your worksheet for errors! Potential errors in cells show up as small green triangles in the top left corner of each cell. Do a little Googling on error checking for your version of Excel and be sure you have error checking turned on and that you reconcile each error so they don’t display when we open your project for grading. Sample: Project Submission Instructions / Notes: • Office/online hours get busy as deadlines approach. If you procrastinate and wait until the last days to work on your project, you may not be able to get all the help you want. • The only way we can fairly grade the projects is if we check for each requirement. Please go through the instructions before you submit & be sure you have done each one correctly so you don’t miss out on points. Compare your solution to the project overview. • Submitting: o Remember to leave all of the internal file properties intact for your project, if they are modified or deleted, you project won’t be accepted (see syllabus for more on this). o Read and follow the instructions in the Assignments section of Canvas on uploading and checking your upload. If you follow these instructions you can ensure that your project is uploaded correctly (and is the correct project). Be sure that Access / Excel are closed before you try to upload your project files. o If your project doesn’t upload correctly before the due date, it will be considered late and be assessed the late penalty – even it was finished on time. This is the only way we can ensure that students check their Canvas submissions. • Technology problems relating to your home computer (Windows based or Mac), internet connection or slow Canvas access are not valid excuses for late/missing work, unless Canvas is down for 6+ hours on the due date. Computers at USF computer labs and the library are available; leave enough time to access them as needed. Also give yourself enough time that if a TA can’t answer a question, you’ll have time to contact me & I can either help you or make an allowance in your grade. If you wait until the last days, I may not be able to do either.

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Sex, Gender, and Popular Culture Spring 2015 Look through popular magazines, and see if you can find advertisements that objectify women in order to sell a product. Alternately, you may use an advertisement on television (but make sure to provide a link to the ad so I can see it!). Study these images then write a paper about objectification that deals with all or some of the following: • What effect(s), if any, do you think the objectification of women’s bodies has on our culture? • Jean Kilbourne states “turning a human being into a thing is almost always the first step toward justifying violence against that person.” What do you think she means by this? Do you agree with her reasoning? Why or why not? • Some people would argue that depicting a woman’s body as an object is a form of art. What is your opinion of this point of view? Explain your reasoning. • Why do you think that women are objectified more often than men are? • How does sexualization and objectification play out differently across racial lines? • Kilbourne explains that the consequences of being objectified are different – and more serious – for women than for men. Do you agree? How is the world different for women than it is for men? How do objectified images of women interact with those in our culture differently from the way images of men do? Why is it important to look at images in the context of the culture? • What is the difference between sexual objectification and sexual subjectification? (Ros Gill ) • How do ads construct violent white masculinity and how does that vision of masculinity hurt both men and women? Throughout your written analysis, be sure to make clear and specific reference to the images you selected, and please submit these images with your paper. Make sure you engage with and reference to at least 4 of the following authors: Kilbourne, Bordo, Hunter & Soto, Rose, Durham, Gill, Katz, Schuchardt, Ono and Buescher. Guidelines:  Keep your content focused on structural, systemic, institutional factors rather than the individual: BE ANALYTICAL NOT ANECDOTAL.  Avoid using the first person or including personal stories/reactions. You must make sure to actively engage with your readings: these essays need to be informed and framed by the theoretical material you have been reading this semester.  Keep within the 4-6 page limit; use 12-point font, double spacing and 1-inch margins.  Use formal writing conventions (introduction/thesis statement, body, conclusion) and correct grammar. Resources may be cited within the text of your paper, i.e. (Walters, 2013).

Sex, Gender, and Popular Culture Spring 2015 Look through popular magazines, and see if you can find advertisements that objectify women in order to sell a product. Alternately, you may use an advertisement on television (but make sure to provide a link to the ad so I can see it!). Study these images then write a paper about objectification that deals with all or some of the following: • What effect(s), if any, do you think the objectification of women’s bodies has on our culture? • Jean Kilbourne states “turning a human being into a thing is almost always the first step toward justifying violence against that person.” What do you think she means by this? Do you agree with her reasoning? Why or why not? • Some people would argue that depicting a woman’s body as an object is a form of art. What is your opinion of this point of view? Explain your reasoning. • Why do you think that women are objectified more often than men are? • How does sexualization and objectification play out differently across racial lines? • Kilbourne explains that the consequences of being objectified are different – and more serious – for women than for men. Do you agree? How is the world different for women than it is for men? How do objectified images of women interact with those in our culture differently from the way images of men do? Why is it important to look at images in the context of the culture? • What is the difference between sexual objectification and sexual subjectification? (Ros Gill ) • How do ads construct violent white masculinity and how does that vision of masculinity hurt both men and women? Throughout your written analysis, be sure to make clear and specific reference to the images you selected, and please submit these images with your paper. Make sure you engage with and reference to at least 4 of the following authors: Kilbourne, Bordo, Hunter & Soto, Rose, Durham, Gill, Katz, Schuchardt, Ono and Buescher. Guidelines:  Keep your content focused on structural, systemic, institutional factors rather than the individual: BE ANALYTICAL NOT ANECDOTAL.  Avoid using the first person or including personal stories/reactions. You must make sure to actively engage with your readings: these essays need to be informed and framed by the theoretical material you have been reading this semester.  Keep within the 4-6 page limit; use 12-point font, double spacing and 1-inch margins.  Use formal writing conventions (introduction/thesis statement, body, conclusion) and correct grammar. Resources may be cited within the text of your paper, i.e. (Walters, 2013).

The objectification of women has been a very controversial topic … Read More...