What is meant by the term viscoelasticity

What is meant by the term viscoelasticity

In actuality all materials depart from Hooke’s law in numerous … Read More...
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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Before brain surgery, Elliott was a good father and held a responsible job. After removal of portions of his frontal lobe, what prediction about Elliott’s personality is likely to come true? He will experience visual hallucinations. He will experience auditory hallucinations. His emotional reactions and decision-making abilities will be impaired. He will be even more driven and focused on his work.

Before brain surgery, Elliott was a good father and held a responsible job. After removal of portions of his frontal lobe, what prediction about Elliott’s personality is likely to come true? He will experience visual hallucinations. He will experience auditory hallucinations. His emotional reactions and decision-making abilities will be impaired. He will be even more driven and focused on his work.

Before brain surgery, Elliott was a good father and held … Read More...
Other things held constant, which of the following actions would increase the amount of cash on a company’s balance sheet? The company repurchases common stock. The company pays a dividend. The company issues new common stock. The company gives customers more time to pay their bills. The company purchases a new piece of equipment.

Other things held constant, which of the following actions would increase the amount of cash on a company’s balance sheet? The company repurchases common stock. The company pays a dividend. The company issues new common stock. The company gives customers more time to pay their bills. The company purchases a new piece of equipment.

  Other things held constant, which of the following actions … Read More...
1 Lab Assignment Q1) The PIC16F1937 Memory Banks i) The Special Function Registers within the PIC16F1937 microcontroller are held within a number of memory banks. How many memory banks are there within the PIC16F1937 microcontroller? ii) Explain two methods to show how a special function register within a particular memory bank can be selected. Q1) The TRIS Registers The PIC16F61937 microcontroller has five TRIS registers, TRISA, TRISB, TRISC, TRISD, and TRISE situated in bank 1 in the special function register memory map. i) What is the function of the TRIS registers? ii) How can the TRIS registers in bank 1 be accessed? Write a short program to configure PORTA of the microcontroller as inputs and PORTB of the microcontroller as outputs. For the remaining exercises assume that PORTA is connected to switches and PORTB is connected to LEDs in common cathode configuration (i.e. output a 1 to illuminate). Q2) Key Press Accumulator It is required to produce a system incorporating a microcontroller that keeps count (in binary) of the number of times that a key has been pressed. The key is connected to bit RA0 of PORTA and when pressed should increment the binary value displayed on LEDs connected to PORTB. Write a program to meet the above specification, simulate the program to ensure correct operation, program a microcontroller and test. (Marks allocated for correct program demonstration). 2 Q3) Software Delays The PIC16F1937 assembly language program listed below is a software time delay incorporating two nested loops. value1 equ 0x20 value2 equ 0x21 org 0x00 delay movlw .65 movwf value1 outer movlw .255 movwf value2 inner decfsz value2 goto inner decfsz value1 goto outer wait goto wait By incorporating breakpoints and using the stopwatch determine the amount of time elapsed in the software delay assuming the microcontroller is operating from a 4 MHz crystal oscillator. Compare the value obtained above with that obtained by calculation. Are the time values equal? Q4) Travelling LED program It is required to produce a system incorporating a PIC16F1937 to produce the following sequence on LEDs (travelling LED). And repeat The LEDs are connected to PORTB and the sequence should only start after the key connected to RA0 has been asserted. Should key RA1 be pressed then all of the LEDs should be switched off. The sequence can be set off again by reasserting key RA0. Incorporate a 100ms delay between changes of state of the sequence. Write a program to carry out the above specification, simulate, program a microcontroller and test. (Marks allocated for correct program demonstration). 3 Lab Assignment Checklist Marks allocation: Q1) The PIC16F1937 memory banks Qi) 2% Qii) 2% Q1) TRIS Registers Qi) 2% Qii) 2% Configuration program 4% Q2) Key Press Accumulator Program Flowchart 8% Program 20% Explanation 5% Demonstration 5% Q3) Software Delays By stopwatch 6% By calculation 6% Q4) Travelling LED program Flowchart 8% Program 20% Explanation 5% Demonstration 5% TOTAL 100%

1 Lab Assignment Q1) The PIC16F1937 Memory Banks i) The Special Function Registers within the PIC16F1937 microcontroller are held within a number of memory banks. How many memory banks are there within the PIC16F1937 microcontroller? ii) Explain two methods to show how a special function register within a particular memory bank can be selected. Q1) The TRIS Registers The PIC16F61937 microcontroller has five TRIS registers, TRISA, TRISB, TRISC, TRISD, and TRISE situated in bank 1 in the special function register memory map. i) What is the function of the TRIS registers? ii) How can the TRIS registers in bank 1 be accessed? Write a short program to configure PORTA of the microcontroller as inputs and PORTB of the microcontroller as outputs. For the remaining exercises assume that PORTA is connected to switches and PORTB is connected to LEDs in common cathode configuration (i.e. output a 1 to illuminate). Q2) Key Press Accumulator It is required to produce a system incorporating a microcontroller that keeps count (in binary) of the number of times that a key has been pressed. The key is connected to bit RA0 of PORTA and when pressed should increment the binary value displayed on LEDs connected to PORTB. Write a program to meet the above specification, simulate the program to ensure correct operation, program a microcontroller and test. (Marks allocated for correct program demonstration). 2 Q3) Software Delays The PIC16F1937 assembly language program listed below is a software time delay incorporating two nested loops. value1 equ 0x20 value2 equ 0x21 org 0x00 delay movlw .65 movwf value1 outer movlw .255 movwf value2 inner decfsz value2 goto inner decfsz value1 goto outer wait goto wait By incorporating breakpoints and using the stopwatch determine the amount of time elapsed in the software delay assuming the microcontroller is operating from a 4 MHz crystal oscillator. Compare the value obtained above with that obtained by calculation. Are the time values equal? Q4) Travelling LED program It is required to produce a system incorporating a PIC16F1937 to produce the following sequence on LEDs (travelling LED). And repeat The LEDs are connected to PORTB and the sequence should only start after the key connected to RA0 has been asserted. Should key RA1 be pressed then all of the LEDs should be switched off. The sequence can be set off again by reasserting key RA0. Incorporate a 100ms delay between changes of state of the sequence. Write a program to carry out the above specification, simulate, program a microcontroller and test. (Marks allocated for correct program demonstration). 3 Lab Assignment Checklist Marks allocation: Q1) The PIC16F1937 memory banks Qi) 2% Qii) 2% Q1) TRIS Registers Qi) 2% Qii) 2% Configuration program 4% Q2) Key Press Accumulator Program Flowchart 8% Program 20% Explanation 5% Demonstration 5% Q3) Software Delays By stopwatch 6% By calculation 6% Q4) Travelling LED program Flowchart 8% Program 20% Explanation 5% Demonstration 5% TOTAL 100%

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Assignment 10 Due: 11:59pm on Friday, April 18, 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: Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 1 of 21 4/11/2014 1:13 PM Incorrect; Try Again 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: 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: 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: Constant Angular Acceleration in the Kitchen = 32 = = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 2 of 21 4/11/2014 1:13 PM 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. You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). ± 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. You did not open hints for this part. ANSWER: Part B Find the number of revolutions made by the fan blades during the time that they are slowing down in Part A. = = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 3 of 21 4/11/2014 1:13 PM You did not open hints for this part. ANSWER: 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? You did not open hints for this part. ANSWER: 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: 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? = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 4 of 21 4/11/2014 1:13 PM Express your answer with the appropriate units. ANSWER: 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: 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. = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 5 of 21 4/11/2014 1:13 PM You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). 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. ANSWER: Part B What is the direction of net torque about the axle? ANSWER: The acceleration of the blocks is zero. The net torque on the pulley is zero. The angular acceleration of the pulley is nonzero. = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 6 of 21 4/11/2014 1:13 PM 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. ANSWER: 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: 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. Clockwise Counterclockwise = = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 7 of 21 4/11/2014 1:13 PM You did not open hints for this part. ANSWER: 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. You did not open hints for this part. ANSWER: 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. = = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 8 of 21 4/11/2014 1:13 PM ANSWER: Part B How many revolutions does it make before reaching full speed? Express your answer using two significant figures. ANSWER: 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: 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. = = rev Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 9 of 21 4/11/2014 1:13 PM 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: 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 Find the tension in the deltoid muscle. Express the tension in newtons, to the nearest integer. You did not open hints for this part. ANSWER: = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 10 of 21 4/11/2014 1:13 PM 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. You did not open hints for this part. ANSWER: 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: ± 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). = N = = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 11 of 21 4/11/2014 1:13 PM 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. You did not open hints for this part. ANSWER: 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. You did not open hints for this part. ANSWER: 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. You did not open hints for this part. ANSWER: = N = s = N Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 12 of 21 4/11/2014 1:13 PM 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: 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: 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: 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. Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 13 of 21 4/11/2014 1:13 PM ANSWER: Problem 12.45 Part A What is the magnitude of the angular momentum of the 780 rotating bar in the figure ? ANSWER: Part B What is the direction of the angular momentum of the bar ? ANSWER: Problem 12.46 into the page out of the page Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 14 of 21 4/11/2014 1:13 PM Part A What is the magnitude of the angular momentum of the 2.20 , 4.60-cm-diameter rotating disk in the figure ? ANSWER: Part B What is its direction? ANSWER: 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. x direction -x direction y direction -y direction z direction -z direction Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 15 of 21 4/11/2014 1:13 PM 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: 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. 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: = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 16 of 21 4/11/2014 1:13 PM 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: 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: 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. You did not open hints for this part. ANSWER: = = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 17 of 21 4/11/2014 1:13 PM 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: Part B How much energy is stored in the flywheel? Express your answer to two significant figures and include the appropriate units. ANSWER: 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: = = = = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 18 of 21 4/11/2014 1:13 PM 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: 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 ? Express your answer with the appropriate units. ANSWER: 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. = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 19 of 21 4/11/2014 1:13 PM 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: 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: 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: = = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 20 of 21 4/11/2014 1:13 PM Score Summary: Your score on this assignment is 4.0%. You received 7.84 out of a possible total of 198 points. = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?disp

Assignment 10 Due: 11:59pm on Friday, April 18, 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: Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 1 of 21 4/11/2014 1:13 PM Incorrect; Try Again 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: 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: 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: Constant Angular Acceleration in the Kitchen = 32 = = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 2 of 21 4/11/2014 1:13 PM 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. You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). ± 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. You did not open hints for this part. ANSWER: Part B Find the number of revolutions made by the fan blades during the time that they are slowing down in Part A. = = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 3 of 21 4/11/2014 1:13 PM You did not open hints for this part. ANSWER: 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? You did not open hints for this part. ANSWER: 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: 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? = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 4 of 21 4/11/2014 1:13 PM Express your answer with the appropriate units. ANSWER: 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: 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. = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 5 of 21 4/11/2014 1:13 PM You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). 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. ANSWER: Part B What is the direction of net torque about the axle? ANSWER: The acceleration of the blocks is zero. The net torque on the pulley is zero. The angular acceleration of the pulley is nonzero. = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 6 of 21 4/11/2014 1:13 PM 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. ANSWER: 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: 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. Clockwise Counterclockwise = = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 7 of 21 4/11/2014 1:13 PM You did not open hints for this part. ANSWER: 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. You did not open hints for this part. ANSWER: 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. = = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 8 of 21 4/11/2014 1:13 PM ANSWER: Part B How many revolutions does it make before reaching full speed? Express your answer using two significant figures. ANSWER: 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: 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. = = rev Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 9 of 21 4/11/2014 1:13 PM 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: 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 Find the tension in the deltoid muscle. Express the tension in newtons, to the nearest integer. You did not open hints for this part. ANSWER: = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 10 of 21 4/11/2014 1:13 PM 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. You did not open hints for this part. ANSWER: 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: ± 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). = N = = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 11 of 21 4/11/2014 1:13 PM 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. You did not open hints for this part. ANSWER: 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. You did not open hints for this part. ANSWER: 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. You did not open hints for this part. ANSWER: = N = s = N Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 12 of 21 4/11/2014 1:13 PM 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: 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: 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: 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. Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 13 of 21 4/11/2014 1:13 PM ANSWER: Problem 12.45 Part A What is the magnitude of the angular momentum of the 780 rotating bar in the figure ? ANSWER: Part B What is the direction of the angular momentum of the bar ? ANSWER: Problem 12.46 into the page out of the page Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 14 of 21 4/11/2014 1:13 PM Part A What is the magnitude of the angular momentum of the 2.20 , 4.60-cm-diameter rotating disk in the figure ? ANSWER: Part B What is its direction? ANSWER: 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. x direction -x direction y direction -y direction z direction -z direction Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 15 of 21 4/11/2014 1:13 PM 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: 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. 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: = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 16 of 21 4/11/2014 1:13 PM 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: 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: 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. You did not open hints for this part. ANSWER: = = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 17 of 21 4/11/2014 1:13 PM 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: Part B How much energy is stored in the flywheel? Express your answer to two significant figures and include the appropriate units. ANSWER: 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: = = = = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 18 of 21 4/11/2014 1:13 PM 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: 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 ? Express your answer with the appropriate units. ANSWER: 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. = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 19 of 21 4/11/2014 1:13 PM 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: 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: 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: = = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 20 of 21 4/11/2014 1:13 PM Score Summary: Your score on this assignment is 4.0%. You received 7.84 out of a possible total of 198 points. = Assignment 10 http://session.masteringphysics.com/myct/assignmentPrintView?disp

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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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