Part I Multiple Choice (4 points. ea.)

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1 Each Exam usually consists of 10 Multiple choice questions which are conceptual in nature. They are often based upon the assigned thought questions from the homework. There are also 4 problems in each exam, based upon the assigned homework problems. Partial credit may be awarded for the problems. Physical constants and equation sheets are provided for the exam. Part I Multiple Choice (4 points. ea.) Two objects have the same momentum. The object that has more mass (A) has greater kinetic energy and greater speed than the object that has less mass. (B) has the same kinetic energy but less speed than the object that has less mass. (C) has less kinetic energy but the same speed than the object that has less mass. (D) has less kinetic energy and less speed than the object that has less mass. (E) none of the above. Suppose an object is moving along at constant velocity, while a second identical object moves with half the first's speed, in the same direction. Compared to the first object, the second has (A) half the momentum of the first. (B) half the potential energy of the first. (C) half the kinetic energy of the first. (D) half the acceleration of the first. (E) all of the above Which of the following is/are CORRECT? (1) The momentum of a bowling must be larger than that of a ping-pong ball. (2) Dropping an egg to the ground is an example of inelastic collision. (3) Conservation of momentum can be used to investigate the speed of cars in car accidents. (A) (1) only (B) (2) and (3) only (C) (1) and (2) only (D) (1), (2) and (3) Which of the following is/are CORRECT for an elastic collision? (1) Two identical masses are moving towards each other at the same speed and are having a head on collision. After collision, the two masses will become stationary according to the conservation of momentum. (2) Two identical masses A and B, A is moving with uniform velocity u and B is stationary. After the collision, A will become stationary while B will move with uniform velocity u because of the conservation of momentum. (3) Two identical masses A and B, A is moving with uniform velocity u and B is moving with 0.5 u. After the collision, A moves with 2u and B moves with 0.5 u because of conservation of momentum. (A) (1) only (B) (2) only (C) (1) and (3) only (D) (1) and (2) only 1

2 Which of the following is/are CORRECT for a completely inelastic collision? (1) Two identical masses are moving towards each other at the same speed and are having a head on collision. After collision, the two masses will become stationary according to the conservation of momentum. (2) Two identical masses A and B, A is moving with uniform velocity u and B is stationary. After the collision, A will become stationary while B will move with uniform velocity u because of the conservation of momentum. (3) Two identical masses A and B, A is moving with uniform velocity u and B is moving with 3 u. B rear ends A, hitting A from behind. After the collision, A and B move 2u because of conservation of momentum. (A) (1) only (B) (2) only (C) (1) and (3) only (D) (1) and (2) only (E) none of the above. When the velocity of an object is halved, (A) its momentum is halved. (B) its potential energy is halved. (C) its kinetic energy is halved. (D) its acceleration is halved. (E) all of the above Two objects have the same mass. The object that has more momentum (A) has greater kinetic energy and greater speed than the object that has less mass. (B) has the same kinetic energy but less speed than the object that has less mass. (C) has less kinetic energy but the same speed than the object that has less mass. (D) has less kinetic energy and less speed than the object that has less mass. (E) none of the above. Two objects have the same kinetic energy. The object that has more mass (A) has greater momentum and greater speed than the object that has less mass. (B) has greater momentum but less speed than the object that has less mass. (C) has less momentum and less speed than the object that has less mass. (D) has less momentum but greater speed than the object that has less mass. (E) has greater momentum but the same speed as the object that has less mass.. A thrown bowling ball will present the least danger if it has (A) the same speed as a thrown baseball. (B) the same momentum as a thrown baseball. (C) the same kinetic energy as a thrown baseball. (D) all three of the above will be exactly the same! (E) none of the above.. A machine gun is fired at a steel plate. The average force on the plate is greatest if (A) the bullets bounce off of the plate. (B) the bullets are squashed and stick to the plate. (C) the bullets pierce the plate, slowing down somewhat in the process. (D) the machine gun is firing blanks. (E) the bullets miss the plate. 2

3 A machine gun is fired at a steel plate. Consider the following cases: (1) the bullets bounce off of the plate. (2) the bullets are squashed and stick to the plate. (3) the bullets pierce the plate, slowing down somewhat in the process. (4) the machine gun is firing blanks. (5) the bullets miss the plate. Rank these cases in terms of the magnitude of the average force on the plate (A) F 1 > F 2 > F 3 > F 4 > F 5 (B) F 1 > F 2 > F 3 > F 4 = F 5 (C) F 1 > F 2 > F 3 = F 4 = F 5 (D) F 2 > F 1 > F 3 = F 4 = F 5 (E) F 1 = F 2 = F 3 = F 4 = F 5 An object initially at rest "explodes" into two fragments (where the external forces can be taken to be zero), which move off in opposite directions. The one which moves off at the greatest speed is the one with (A) the least mass. (B) the most mass. (C) trick question, both fragments will have the same speed regardless of their mass. (D) trick question, more information is needed about the details of the "explosion". An object initially at rest "explodes" into two fragments (where the external forces can be taken to be zero), which move off in opposite directions. The one which moves off with the greatest magnitude of momentum is the one with 1. (A) the least mass. (B) the most mass. (C) trick question, both fragments will have the same magnitude of momentum regardless of their mass, since their momenta must add (as vectors) to zero. (D) trick question, more information is needed about the details of the "explosion". In a completely inelastic and head-on collision between two moving objects, when can the final kinetic energy of the system can be zero? (A) Always (it must be zero). (B) Only if both objects have the same mass and the same speed. (C) Only if one of the objects is at rest, and both objects have the same mass. (D) Only if both objects have the same magnitude of momentum. (E) Never! 3

4 A woman holding a large rock stands upon a frictionless horizontal surface (an ice ring, e.g.). Consider the system consisting of the woman and the rock. She throws the rock at an angle α above the horizontal. Then (A) Kinetic Energy and momentum are conserved in this system. (B) Kinetic Energy and the horizontal components of momentum are conserved. (C) Only the horizontal components of momentum are conserved. (D) Only the Kinetic Energy is conserved. (E) No physical quantities are conserved.. A large truck collides with a small car. How does the magnitude of the impulse experienced by the truck compare to that experienced by the car? (A) The truck experiences a greater magnitude impulse. (B) The car experiences a greater magnitude impulse. (C) They both experience the same magnitude impulse. (D) More information is needed to compare. A large mass collides elastically head on with a small mass which is initially at rest (as was seen in the cart collision laboratory). The small mass (A) is kicked forward at a higher speed than the original speed of the large mass, because energy and momentum are conserved. (B) is kicked forward at a much lower speed than the original speed of the large mass, because energy and momentum are conserved. (C) causes the large mass to rebound in the opposite direction, moving back towards its starting point. (D) sticks to the large mass, slowing it considerably because energy and momentum are conserved. (E) spontaneously bursts into flame, engulfing the large mass and two adjacent multiple choice questions in a spectacular pyrotechnics display. In an inelastic collision (A) momentum is conserved but KE is not. (B) KE is conserved but momentum is not. (C) both KE and momentum are conserved. (D) neither KE nor momentum are conserved. (E) none of the above is always true. In an elastic collision (A) momentum is conserved but KE is not. (B) both KE and momentum are conserved. (C) KE is conserved but momentum is not. (D) neither KE nor momentum are conserved. (E) none of the above is always true. In a completely inelastic collision (A) momentum is conserved but kinetic energy is not. (B) kinetic energy is conserved but momentum is not. (C) both kinetic energy and momentum are conserved. (D) neither kinetic energy nor momentum are conserved. (E) none of the above is always true. 4

5 Two children sit on a merry-go-round as it spins about. One child sits all the way out on the outer edge of the merry-go-round. The second one sits closer to the center, halfway between the axis of rotation and the outer edge. In meters per second, which child travels fastest? (A) Both travel at the same speed in m/s since their angular frequency is the same. (B) The speed is greater for the child on the outside edge. (C) The speed is greater for the child on the inner edge. (D) The speed of the child on the outside is half the speed of the child seated on the inside. (E) both (C) and (D). Which of the following rotational quantities are the same for all points on a solid rotating disk? (A) Angular velocity. (B) Tangential velocity. (C) Tangential acceleration. (D) Centripetal acceleration. (E) all of the above.. When would it be possible for a rotating object to have increasing angular speed and have negative angular acceleration? (A) when angular velocity and angular acceleration are both negative. (B) when angular velocity is positive and angular acceleration is negative. (C) when the angular velocity and the angular acceleration are perpendicular. (D) never. Torque (τ), is the (A) rotational analogue of Force (F) in linear motion. (B) rotational analogue of Momentum (p) in linear motion. (C) rotational analogue of Work (W) in linear motion.. (D) linear analogue of Angular Velocity (ω) in rotational motion. (E) linear analogue of Angular Momentum (L) in rotational motion. Angular momentum (L) (A) is the rotational analogue of momentum (m) in linear motion. (B) is conserved in the absence of external torques. (C) allows a skater or gymnast to change rotation rates by repositioning limbs. (D) all of the above. (E) none of the above The moment of inertia I is the rotational analogue of (A) mass, from linear motion. (B) force, from linear motion. (C) kinetic energy, from linear motion. (D) orbital period, from circular motion. (E) none of the above.. In rotational motion, the analog of mass in linear motion is (A) angular momentum. (B) moment of inertia. (C) torque. (D) radian. (E) weight. 5

6 . When a flywheel rotates with constant angular velocity, then a point on its rim will have (A) a constant magnitude tangential acceleration but no radial acceleration. (B) a constant magnitude radial acceleration but no tangential acceleration. (C) a constant magnitude tangential acceleration and constant magnitude tangential acceleration. (D) no acceleration. (E) impossible to tell since tangential and radial acceleration are not related to angular velocity.. For a point on the rim of a flywheel that rotates at constant angular velocity (A) The tangential acceleration and the radial acceleration are zero. (B) The tangential acceleration is zero and the radial acceleration is constant. (C) The radial acceleration is zero and the tangential acceleration is constant. (D) The tangential acceleration is zero and the radial acceleration is constant in magnitude but changing in direction. (E) The tangential and radial acceleration are both changing in both magnitude and direction. A force is applied to a to a wrench as shown. The distance which best indicates the moment arm l of the applied force as it creates a torque about the nut as shown is (A) distance (A) from the diagram. (B) distance (B) from the diagram. (C) distance (C) from the diagram. (D) 0, since the force does not act parallel to the radial line. (E) 0, since the force does not act perpendicular to the radial line. A B C F When a flywheel rotates with constant angular velocity, then a point on its rim will have (A) no acceleration. (B) a constant magnitude tangential acceleration but no radial acceleration. (C) a constant magnitude radial acceleration but no tangential acceleration. (D) a constant magnitude tangential acceleration and constant magnitude tangential acceleration. (E) impossible to tell since tangential and radial acceleration are not related to angular velocity. The moment of inertia of an object (A) will be greater if the mass is distributed away from the axis of rotation. (B) will be greater if the mass is distributed closer to the axis of rotation. (C) will not depend on how the mass is distributed from the axis of rotation, but will depend on how the mass is distributed along the axis of rotation. (D) will not depend on how the mass is distributed at all. (E) does not depend on mass in any way shape or form. The moment of inertia of an object (A) will not depend on how the mass is distributed from the axis of rotation, but will depend on how the mass is distributed along the axis of rotation. (B) will be greater if the mass is distributed away from the axis of rotation. (C) will be greater if the mass is distributed closer to the axis of rotation. (D) will not depend on how the mass is distributed at all. (E) does not depend on mass in any way shape or form. 6

7 . A uniform disk is to be rotated about any of 4 axis as shown. The axis corresponding to the greatest moment of inertia is (A) the axis 2 radii from the center of the disk. (B) the axis right at the edge of the disk (C) the axis halfway between the center of the disk and the edge of the disk. (D) the axis through the center of the disk. A B C D (E) none of the above, since the moment of inertia does not depend upon the location of the axis of rotation.. A uniform disk is to be rotated about any of 5 axis as shown. If the axis are ranked from highest to lowest in terms of the moment of inertia of the disk about that axis, then the most correct ranking would be: (A) A=B=C=D=E. (B) A>B>C>D>E. (C) A=E>B=D>C. (D) C>B=D>A=E. (E) E>D>C>B>A. A B C D E To maximize the moment of inertia of a flywheel while minimizing its weight, the flywheel should be (A) a uniform disk. (B) a thin walled hollow cylinder (i.e. a hoop). (C) a uniform solid sphere. (D) a thin walled hollow sphere. (E) a slender rotated about an axis through one end. For the next two questions: A thin hoop and uniform disk of the same mass and radius are released from rest from the same height at the top of an inclined plane. If the objects roll without slipping, then (A) the hoop will reach the bottom first because it has a greater moment of inertia. (B) the hoop will reach the bottom first because it has a smaller moment of inertia. (C) the disk will reach the bottom first because it has a greater moment of inertia. (D) the disk will reach the bottom first because it has a smaller moment of inertia. (E) any of the above depending upon the initial height, and the details of construction of the hoop and disk. If the slope is frictionless, (A) the hoop will reach the bottom first because it has a greater moment of inertia. (B) the hoop will reach the bottom first because it has a smaller moment of inertia. (C) the disk will reach the bottom first because it has a greater moment of inertia. (D) the disk will reach the bottom first because it has a smaller moment of inertia. (E) the disks will reach the bottom at the same time since there is no torque, making the moment of inertia irrelevant. 7

8 A solid disk and a hoop of the same radius and mass are released from rest at the top of an inclined plane (as in the lecture demonstration). The object which has the greatest kinetic energy at the bottom of the plane is the (A) hoop. (B) disk. (C) both have the same final KE. (D) more information would be required to answer this question. (E) neither, since an interdimensional wormhole will spontaneously open to annihilate both objects before they reach the bottom. A thin hoop and uniform disk of the same mass and radius are released from rest from the same height at the top of an inclined plane. If the slope is frictionless, (A) the hoop will reach the bottom first because it has a greater moment of inertia. (B) the hoop will reach the bottom first because it has a smaller moment of inertia. (C) the disk will reach the bottom first because it has a greater moment of inertia. (D) the disk will reach the bottom first because it has a smaller moment of inertia. (E) the disks will reach the bottom at the same time since there is no torque, making the moment of inertia irrelevant. A force is applied to a to a wrench as shown. The distance which best indicates the moment arm l of the applied force as it creates a torque about the nut as shown is (A) distance (A) from the diagram. (B) distance (B) from the diagram. (C) distance (C) from the diagram. (D) 0, since the force does not act parallel to the radial line. (E) 0, since the force does not act perpendicular to the radial line. A C B F. A force F is applied to a wrench as shown. The distance which best indicates the moment arm l of the applied force as it creates a torque about the nut as shown is (A) distance (A) from the diagram. (B) distance (B) from the diagram. (C) distance (C) from the diagram. (D) 0, since the force does not act parallel to the radial line. (E) 0, since the force does not act perpendicular to the radial line. A B C F 8

9 Which of the following equations requires that angles be measured in radians. (A). = d dt (B) = 0 0 t 1 2. t2 (C) v= r. (D) all of the above. (E) none of the above.. Which of the following equations requires that angles be measured in radians. (A) a tan = r (B) v= r (C) s= r (D) all of the above. (E) none of the above. When calculating the work done by a torque τ acting through an angular displacement θ via the equation W = τ θ, the units for τ and θ are (A) Newton. meters and degrees. (B) Newton. meters and rotations. (C) Watts and degrees. (D) Newtons and radians. (E) Newton. meters and radians. The pivoting motion (constant steady rotation) of the gyroscope/bicycle wheel when suspended by one side only (as demonstrated in class) is called (A) percussion. (B) deflection. (C) precession. (D) inflation. (E) desertion. The pivoting motion (constant steady rotation) of the gyroscope when mass is suspended from the axis of rotation (as demonstrated in class) is called, while the repeated bouncing motion the gyroscope exhibited when the rotation axis was tapped is called. (A) nutation, desertion. (B) percussion, nutation. (C) perturbation, deflection. (D) inflation, recession. (E) precession, nutation. 9

10 . In a classroom demonstration, the professor sat on a spinning chair with weights held out in his extended arms. As he brought his arms in to his torso, his rotation rate increased. This was because (A) his angular momentum was constant, and so by decreasing his moment of inertia his angular velocity necessarily increased. (B) his angular momentum was constant, and so by increasing his moment of inertia his angular velocity necessarily increased. (C) he was creating an external torque with the motion of his arms. (D) by changing his moment of inertia, he was able to use the principle of nutation to increase his rotation rate. (E) by signaling extraterrestrials his desire for increased angular kinetic energy, he was able to initiate an alien insurrection. 10

11 Part II Problems Show all work. No work = no credit! (15 points each) A kg baseball is pitched with a speed of 45 m/s. It is struck with a bat, rebounding in the opposite direction with a speed of 55 m/s. (A) What is the initial and final momentum of the ball? (B) What is the magnitude of the impulse exerted on the ball? (C) If the bat is in contact with the ball for 2.00 ms, what is the average force the bat exerts upon the ball? A 4.00 g bullet traveling horizontally with a velocity of magnitude 400 m/s is fired into a wooden block with mass kg, which is initially at rest on a level surface. The bullet passes through the block and emerges with a speed of 50.0 m/s. (A) Determine the initial momentum of the bullet. (B) Determine the momentum of the bullet just after it leaves the block. (C) Determine the momentum of the block just after the bullet exits. (D) Determine the speed of the block just after the bullet exits. (E) Determine how much energy was lost in this collision. (F) What the collision elastic or inelastic? A 2.00 kg cart initially moving at 24.0 m/s makes a head on collision with a 4.00 kg cart which is initially at rest. The 2.00 kg cart bounces back with a speed of 8.00m/s after the collision. Take the initial direction of the 2kg cart's motion as the positive direction. (A) What is the initial momentum of the 2 kg cart? (B) What is the final momentum of the 2 kg cart? (C) What is the final momentum of the 4 kg cart? (D) What is the total initial kinetic energy? (E) What is the total final kinetic energy? (F) Was this collision elastic? Ballistic Pendulum: A 5.00 g bullet is fired horizontally into a 2.00 kg block suspended by.800 m string. The bullet becomes imbedded into the block, which then swings to a maximum height of 3.00 cm. (A) How much potential energy was gained by the block (and embedded bullet) as the swung from the point of impact to the maximum height? (B) What was the speed of the block and bullet just after the collision? (C) What was the speed of the bullet just before the collision? (D) What was the initial Kinetic energy of the bullet? (E) How much energy was lost in the collision? (F) What kind of collision was this? Two identical masses A and B, each with mass 1.00 kg are moving down a track. A is moving with speed of 1.00 m/s and B is moving 3.00 m/s in the same direction. B rear ends A, hitting A from behind. They interact via the velcro interaction and stick together after the collision. (A) What kind of collision is this? (B) What is the final speed of A and B moving together after the collision? (C) How much kinetic energy is lost in this collision? 11

12 Ballistic Pendulum: A 10.0 g bullet is fired horizontally into a 3.00 kg block suspended by 1.20 m string. The bullet becomes embedded into the block, which then swings to a maximum height of 14 cm. (A) How much potential energy was gained by the block (plus embedded bullet) as the swung from the point of impact to the maximum height? (B) What was the speed of the block and bullet just after the collision? (C) What was the speed of the bullet just before the collision? (D) What was the initial Kinetic energy of the bullet? (E) How much energy was lost in the collision? (F) What kind of collision was this? h Our hero, Rocky the flying squirrel (.125 kg) is determined to stop Boris Badenov's truck (25,000 kg) which is traveling down the highway at 60 mph (26.8 m/s). Rocky intends to do this by flying into the truck in a head on collision. How fast must Rocky fly in order to bring the truck (more specifically, the truck/squirrel wreckage) to rest? A railroad handcar is moving along straight frictionless tracks. The car and its contents have initial total mass of 300 kg and is traveling at a speed of 8.00 m/s. Find the final speed of the car in each of the following cases: (A) A 50 kg mass (taken from the car s contents) is thrown forward out of the car with a speed of 5 m/s relative to the car. (B) A 50 kg mass (taken from the car s contents) is thrown backwards out of the car with a speed of 5 m/s relative to the car. (C) A 50 kg mass (taken from the car s contents) is thrown sideways out of the car with a speed of 5 m/s relative to the car. (D) A 50 kg mass is thrown into the car out of the car with a speed of 5 m/s relative to the ground in a direction opposite the car s motion. A kg baseball is pitched with a speed of 45 m/s. It is struck with a bat, rebounding in the opposite direction with a speed of 55 m/s. (A) What is the initial and final momentum of the ball? (B) What is the magnitude of the impulse exerted on the ball? (C) If the bat is in contact with the ball for 2.00 ms, what is the average force the bat exerts upon the ball? A soldier on a firing range fires a 15 shot burst from an assault weapon at a full automatic rate of 1000 rounds per minute. Each bullet has a mass of 7.50 g and a speed of 300 m/s relative to the ground. (A) What is the momentum of each bullet as it leaves the weapon? (B) What is the impulse each bullet exerts upon the weapon as it is discharged? (C) What is the total impulse exerted upon the weapon during the 15 shot burst? (D) What is the average force exerted on the weapon during that burst? 12

13 A torque of 100 N. m is applied to a disk which rotates on a fixed axle and which is initially at rest. After the disk has made 4 full rotations in 8 seconds, determine (A) the rotation of the disk in radians, (B) the work done on the disk, (C the final kinetic energy of the disk, (D) the angular acceleration of the disk, (E) the final angular velocity of the disk in rad/s, (F) the moment of inertia of the disk. A torque of 100 N. m is applied to a disk initially at rest. After 30.0 s the speed of the disk has reached 150 rad/s. (A) Determine the angular acceleration of the disk. (B) Determine the number of rotations made by the disk in the 30.0 s (C) Determine the moment of inertia of the disk. (D) Calculate the final rotational kinetic energy of the disk. (E) Determine the work done on the disk by the external torque. A grinding wheel starts from rest and reaches its final angular velocity of 5000 rpm in 8.00 s. (A) What is the final angular velocity in rad/s? (B) What is the angular acceleration of the wheel (in rad/s 2 )? (C) How much rotation (in radians) does the wheel undergo in this time? (D) How many revolutions does the disk make in this time? Consider the rod pictured at right. It is set to rotate about its center. A) What is the net torque on the rod pictured below? B) If the angular acceleration of the rod is 4.20 rad/s2, what is the moment of inertia of the rod? 5.00 N m m N 13

14 A string is wrapped around the inner radius a yoyo which has an outer radius of 4.00 cm and an inner radius of 1.50 cm. The yoyo has a mass of.150 kg and a moment of inertia of 1.00E 4 kg m 2. A constant tension of 1.6 N is applied horizontally to the string as shown. After the yoyo has moved (by rolling without slipping) a distance of.4 m, determine (A) How many revolutions the yoyo has made, (B) How much string has unwound from the inner radius of the yoyo, (C) How far the end of the string (from which the external force maintaining the tension is being applied) has moved, (D) The work done by this external force, (E) the final kinetic energy of the yoyo, (F) the final linear and angular velocities of the yoyo. A 2.00 Kg mass is suspended from a string wrapped around the inner disk of a pulley. The Pulley is composed of two uniform disks, a smaller disk of mass.5 kg and radius.25 meters and a larger disk of mass 1.00 kg and radius 1.00 m. (A) Draw a free-body diagram for each object (pulley and weight). (B) Calculate the total moment of inertia of the pulley. (C) Determine the acceleration of the mass. (D) Determine the angular acceleration of the disk. (E) Determine the tension in the string. A uniform disk (mass 2.50 kg, radius.250 m) is rotating without friction at an initial angular velocity of 12.0 rad/s. A second uniform disk (mass 5 kg, radius. 200 m) is initially at rest and is dropped gently onto the first disk so that they eventually rotate together about the common axis. (A) What are the moments of inertia of the two disks? (B) What is the initial angular momentum of the first disk? (C) What is the final angular momentum of the two disks moving together? (D) What is the final angular velocity of the two disks moving together? (E) What is the initial and final kinetic energies of the system? (F) Can this event be viewed as an elastic collision? Why or why not? at rest moving together A.500 kg lump of clay moving at 24.0 m/s hits the edge of a 2.00 kg turntable tangent to the turntable s rim and sticks to the edge of turntable, which subsequently rotates. The turntable can be treated as a uniform disk of radius m, and the lump of clay can be treated as a point mass. (A) What is the initial angular momentum of the lump of clay just before impact? (B) What is the total moment of inertia of the disk and clay after the clay becomes stuck to the edge of the turntable? (C) What is the angular velocity of the turntable after the impact? (D) How much kinetic energy is lost in this collision? 14

15 Block A (mass = 3.00 kg) and Block B (mass = 4.00 kg) are attached by a string which goes over a pulley (mass = 6.00 kg, uniform disk of radius.2m) as shown. Block B rests on a horizontal frictionless surface. (A) Draw a free body diagram for each block and for the pulley, indicating the forces and torques acting on each object. (B) Determine the acceleration of the masses. (C) Determine the angular acceleration of the pulley (D) Determine the tension in the string where it is attached to mass A. (E) Determine the tension in the string where it is attached to mass B. A B Block A (mass = 4.00 kg) and Block B (mass = 8.00 kg) are suspended by a string on either side of a friction-less pulley (mass = 4.00 kg, uniform disk of radius.2m). (a) Draw a free body diagram for each block and for the pulley, indicating the forces and torques acting on each object. (b) Determine the acceleration of the masses. (c) Determine the angular acceleration of the pulley (d) Determine the tensions in the string on the left side. (e) Determine the tensions in the string on the right side. A B Space Yo-Yo: A yoyo is operated in space, so that there are no other forces acting on it but the tension in the string. The yoyo has a mass of.150 kg and a moment of inertia of 1.00E 4 kg m 2. A string is wrapped around the inner radius the yoyo which has an outer radius of 4.00 cm and an inner radius of 1.50 cm. If a constant tension of N is applied to the string, determine (A) The acceleration of the yo-yo s center of mass, (B) the angular acceleration of the yo-yo about its center of mass. If the yo-yo starts from rest, determine the following after 2.00 s have elapsed: (C) the displacement of the yo-yo, (D) the rotation (in rad) of the yo-yo, (E) how much string has unwound from the yo-yo, (F) the displacement of the other end of the string (where the operator is applying the N) (G) the work done by the yo-yo operator (H) the final kinetic energy of the yo-yo A 2.00 Kg mass is suspended from a string wrapped around the inner disk of a pulley. The Pulley is composed of two uniform disks, a smaller disk of mass 1.50 kg and radius.150 meters and a larger disk of mass 5.00 kg and radius.600 m. (A) Draw a free-body diagram for each object (pulley and weight). (B) Calculate the total moment of inertia of the pulley. (C) Determine the acceleration of the mass. (D) Determine the angular acceleration of the disk. (E) Determine the tension in the string. 15

16 A cord is wrapped around a hollow 25.0 kg sphere which has a diameter of m, and which rotates (frictionlessly) about an axis through its center. A 15.0 N force is applied to the end of the cable, causing the cable to unwind and the sphere (initially at rest) to rotate. After the cable has unwound a distance 1.25 m, use work and energy methods to determine (A) the work done by the force, (B) the kinetic energy of the sphere, (C) the final rotational velocity of the sphere 16