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284 Chapter 7 Momentum, Collisions, and the Center of Mass zero. Therefore ptruck, i = mtruck vtruck, i = (7.50 * 103 kg)vtruck, i = 5.25 * 104 kg # m>s, and vtruck, i = (5.25 * 104 kg # m>s)>(7.50 * 103 kg) = 7.00 m>s. 7-4 (a) inelastic, (b) elastic, (c) inelastic. In (a) the ball collides with Earth, which is very much more massive than the ball. If the collision were elastic, the ball would rebound with nearly the same kinetic energy as it had just before hitting the ground, and so it would bounce back to its original height. Since this does not happen, mechanical energy must have been lost and the collision must have been inelastic. In (b) the total kinetic energy just after the collision is 125 J + 75 J = 200 J, the same as just before the collision. So mechanical energy is conserved and the collision is elastic. In (c) the colliding objects (the dog and the ball) move together after the collision, so this must be a completely inelastic collision as described in Section 7-4. 7-5 (d) This is the same situation as Example 7-9, so we can use the same equation for the final velocity of the ball: vfx = Fcollision, x Dt>m = (1700 N)(8.6 * 1023 s)>(0.43 kg) = 34 m>s (about 120 km>h or 76 mi>h). 7-6 (d) If the shell did not explode, its center of mass would hit the target. The force that blows the cannon shell apart is internal to the shell, so it does not affect the motion of the center of mass. So the center of mass still hits the target. The explosion happens when the shell is halfway along its trajectory, so the half that falls vertically lands 100 m short of the target (half the horizontal distance from cannon to target). We saw in Example 7-10 that the center of mass of a system of two equal masses is halfway between the two masses. So the other mass must land 100 m on the other side of the target. Questions and Problems In a few problems, you are given more data than you actually need; in a few other problems, you are required to supply data from your general knowledge, outside sources, or informed estimate. Interpret as significant all digits in numerical values that have trailing zeros and no decimal points. For all problems, use g = 9.80 m>s2 for the free-fall acceleration due to gravity. • Basic, single-concept problem •• Intermediate-level problem, may require synthesis of concepts and multiple steps ••• Challenging problem SSM Solution is in Student Solutions Manual Conceptual Questions 1. •Using the common definition of the word impulse, comment on physicists’ choice to define impulse as the change in momentum. 2. •Starting from Newton’s second law, explain how a collision that is free from external forces conserves momentum. In other words, explain how the momentum of the system remains constant with time. 3. •If the mass of a basketball is 18 times that of a tennis ball, can they ever have the same momentum? Explain your answer. SSM 4. •Two objects have equal kinetic energies. Are the magnitudes of their momenta equal? Explain your answer. 5. •A glass will break if it falls onto a hardwood floor but not if it falls from the same height onto a padded, carpeted floor. Describe the different outcomes in the collision between a glass and the floor in terms of fundamental physical quantities. 6. •A child stands on one end of a long wooden plank that rests on a frictionless icy surface. (a) Describe the motion of the plank when she runs to the other end of the plank. (b) Describe the motion of the center of mass of the system. (c) How would your answers change if she had walked the plank rather than run down it? 7. •Based on what you know about center of mass, why is it potentially dangerous to step off of a small boat before it comes to a stop at the dock? SSM Freed_c07_244-289_st_hr1.indd 284 8. •A man and his large dog sit at opposite ends of a rowboat, floating on a still pond. You notice from shore that the boat moves as the dog walks toward his owner. Describe the motion of the boat from your perspective. 9. •Astronomy An asteroid (2007 WD5) passed between Earth and Mars in 2007. Scientists initially estimated a 4% chance that the 50-m-wide asteroid would collide with Mars. If the asteroid had collided with Mars, could it have knocked the planet out of its orbit? Explain your answer. (For more information on Near Earth Objects, see neo.jpl.nasa.gov/index.html.) 10. •How would you determine if a collision is elastic or inelastic? 11. •A recent U.S. patent application describes a “damage avoidance system” for cell phones, which, upon detecting an impending, uncontrolled impact with a surface, deploys an airfilled bag around the phone. Explain how this could protect the cell phone from damage. 12. •Cite two examples of totally inelastic collisions that occur in your daily life. 13. •Why is conservation of energy alone not sufficient to explain the motion of a Newton’s cradle toy, shown in Figure 7-24? Consider the case when two balls are raised and released together. Figure 7-24 Problem 13 14. •After being thrown into the air, a lit firecracker explodes at the apex of its parabolic flight. (a) Is momentum conserved before or after the explosion? (b) Is the mechanical energy conserved? (c) What is the path of the center of mass? Neglect the effects of air resistance and explain your answers. 15. •An arrow shot into a straw target penetrates a distance that depends on the speed with which it strikes the target. How does the penetration distance change if the arrow’s speed is doubled? Be sure to list all the assumptions you make while arriving at your answer. 4/9/13 12:19 PM Questions and Problems 285 C. One of the particles continues with the same velocity, and the other comes to rest. D. One of the particles continues with the same velocity, and the other reverses direction at twice the speed. E. More information is required to determine the final velocities. SSM Multiple-Choice Questions 16. •A large semitrailer truck and a small car have equal momentum. How do their speeds compare? A. The truck has a much higher speed than the car. B. The truck has only a slightly higher speed than the car. C. Both have the same speed. D. The truck has only a slightly lower speed than the car. E. The truck has a much lower speed than the car. 17. •A tennis player smashes a ball of mass m horizontally at a vertical wall. The ball rebounds at the same speed v with which it struck the wall. Has the momentum of the ball changed, and if so, what is the magnitude of the change? A. mv B. 0 C. 12mv D. 2mv E. 4mv SSM 18. •You throw a bouncy rubber ball and a wet lump of clay, both of mass m, at a wall. Both strike the wall at speed v, but while the ball bounces off with no loss of speed, the clay sticks. What is the change in momentum of the clay and ball, respectively, assuming that toward the wall is the positive direction? A. 0; mv B. mv; 0 C. 0; 22mv D. 2mv; 2mv E. 2mv; 22mv 19. •Consider a completely inelastic, head-on collision between two particles that have equal masses and equal speeds. Describe the velocities of the particles after the collision. A. The velocities of both particles are zero. B. Both of their velocities are reversed. C. One of the particles continues with the same velocity and the other comes to rest. D. One of the particles continues with the same velocity and the other reverses direction at twice the speed. E. More information is required to determine the final velocities. 20. •An object is traveling in the positive x direction with speed v. A second object that has half the mass of the first is traveling in the opposite direction with the same speed. The two experience a completely inelastic collision. The final x component of the velocity is A. 0 B. v>2 C. v>3 D. 2v>3 E. v 21. •Consider a completely elastic head-on collision between two particles that have the same mass and the same speed. What are the velocities after the collision? A. Both are zero. B. The magnitudes of the velocities are the same, but the directions are reversed. Freed_c07_244-289_st_hr1.indd 285 22. •Two small, identical steel balls collide completely elastically. Initially, ball 1 is moving with velocity v1, and ball 2 is stationary. After the collision, the final velocities of ball 1 and ball 2 are A. 12 v1; 12 v1 B. v1; 2v1 C. 0; v1 D. 2v1; 0 E. 2v1; 2v1 23. •Two ice skaters, Lilly and John, face each other while stationary and push against each other’s hands. John’s mass is twice that of Lilly. How do their speeds compare after the push-off? A. Lilly’s speed is one-fourth of John’s speed. B. Lilly’s speed is one-half of John’s speed. C. Lilly’s speed is the same as John’s speed. D. Lilly’s speed is twice John’s speed. E. Lilly’s speed is four times John’s speed. 24. •A friend throws a heavy ball toward you while you are standing on smooth ice. You can either catch the ball or deflect it back toward your friend. Which of the following options will maximize your speed right after your interaction with the ball? A. You should catch the ball. B. You should deflect the ball back toward your friend at the same speed with which it hit your hand. C. You should let the ball go past you without touching it. D. It doesn’t matter—your speed is the same regardless of what you do. E. You should deflect the ball back toward your friend at half the speed with which it hit your hand. 25. •Two blocks are released from rest on either side of a frictionless half-pipe (Figure 7-25). Block B is more massive than block A. The height HB from which block B is released is less than HA, the height from which block A is released. The blocks collide elastically on the flat section. After the collision, which is correct? A. Block A rises to a height greater than HA and block B rises to a height less than HB. B. Block A rises to a height less than HA and block B rises to a height greater than HB. C. Block A rises to height HA and block B rises to height HB. D. Block A rises to height HB and block B rises to height HA. E. The heights to which the blocks rise depends on where along the flat section they collide. SSM A HA B HB Figure 7-25 Problem 25 4/9/13 12:19 PM 286 Chapter 7 Momentum, Collisions, and the Center of Mass Estimation/Numerical Analysis 26. •Estimate the momentum of a car driving the speed limit on a freeway. 27. •Sports Estimate the momentum of a fastball thrown by a major league pitcher. 28. •Sports Estimate the momentum of a tennis ball served by a professional tennis player. 29. •Medical, Biology Estimate the location of the center of mass of your body. SSM 30. •Estimate the momentum that a bumblebee has when it strikes a motorcycle rider. 31. •Astronomy Estimate the momentum of Earth as it orbits the Sun. 32. •Sports Compare the momentum of a fast-pitch softball to a major league fastball. 33. •Estimate the impulse delivered to a tennis ball that rebounds from a practice wall. SSM 34. •A car moving at 20 m>s slams into the back end of a car stopped at a red light. After the collision, the two cars stick together. If the cars have the same mass, estimate the distance the two cars travel before coming to rest. Assume that neither driver applies his brakes during the collision. 35. •The following gives the force (in newtons) acting on a 2-kg object as a function of time. (a) Make a graph of force versus time. (b) If the object starts from rest, what is its speed after 25 s? t (s) F (N) 0 1 2 3 4 5 6 7 8 220 220 210 0 10 15 18 20 25 t (s) 9 10 11 12 13 14 15 16 17 F (N) 25 25 25 25 25 25 25 25 25 t (s) 18 19 20 21 22 23 24 25 F (N) 25 25 25 20 15 10 5 0 Problems 7-2 Momentum is a vector that depends on an object’s mass, speed, and direction of motion 36. •A 10,000-kg train car moves east at 15 m>s. Determine the momentum of the train car. 37. •Sports The magnitude of the instantaneous momentum of a 57-g tennis ball is 2.6 kg # m>s. What is its speed? SSM 38. •Determine the initial momentum, final momentum, and change in momentum of a 1250-kg car initially backing up at 5.00 m>s, then moving forward at 14.0 m>s. 39. •Sports What is the momentum of a 135-kg defensive lineman running at 7.00 m>s? 40. •One ball has four times the mass and twice the speed of another. (a) How does the momentum of the more massive ball compare to the momentum of the less massive one? (b) How does the kinetic energy of the more massive ball compare to the kinetic energy of the less massive one? Freed_c07_244-289_st_hr1.indd 286 41. •A girl who has a mass of 55.0 kg rides her skateboard to class at a speed of 6.00 m>s. (a) What is her momentum? (b) If the momentum of the skateboard itself is 30.0 kg # m>s, what is its mass? SSM 7-3 The total momentum of a system of objects is conserved under certain conditions 42. •A 2.00-kg object is moving east at 4.00 m>s when it collides with a 6.00-kg object that is initially at rest. After the completely elastic collision, the larger object moves east at 1.00 m>s. What is the final velocity of the smaller object after the collision? 43. •A 3.00-kg object is moving toward the right at 6.00 m>s. A 5.00-kg object moves to the left at 4.00 m>s. After the two objects collide completely elastically, the 3.00-kg object moves toward the left at 2.00 m>s. What is the final velocity of the 5.00-kg object? 44. •Blythe and Geoff are ice skating together. Blythe has a mass of 50.0 kg and Geoff has a mass of 80.0 kg. Blythe pushes Geoff in the chest when both are at rest, causing him to move away at a speed of 4.00 m>s. (a) Determine Blythe’s speed after she pushes Geoff. (b) In what direction does she move? 45. ••An object of mass 3M, moving in the +x direction at speed v0, breaks into two pieces of mass M and 2M as shown in Figure 7-26. If u1 = 45° and u2 = 30°, determine the final velocities of the resulting pieces in terms of v0. SSM 3M v0 2M M v2 = ? θ2 θ1 v1 = ? Figure 7-26 Problem 45 46. •In a game of pool, the cue ball is rolling at 2.00 m>s in a direction 30.0° north of east when it collides with the eight ball (initially at rest). The mass of the cue ball is 170 g, but the mass of the eight ball is only 156 g. After the completely elastic collision, the cue ball heads off at 10.0° north of east and the eight ball moves off due north. What are the final speeds of each ball after the collision? 47. •Biology During mating season, male bighorn sheep establish dominance with head-butting contests which can be heard up to a mile away. When two males butt heads, the “winner” is the one that knocks the other backward. In one contest a sheep of a mass 95.0 kg and moving at 10.0 m>s runs directly into a sheep of mass 80.0 kg moving at 12.0 m>s. Which ram wins the head-butting contest? SSM 48. ••One way that scientists measure the mass of an unknown particle is to bounce a known particle, such as a proton or an electron, off the unknown particle in a bubble chamber. The initial and rebound velocities of the known particle are measured from photographs of the bubbles it creates as it moves; the information is used to determine the mass of the unknown particle. (a) If a known particle of mass m and initial speed v0 collides elastically, head-on with a stationary unknown particle and then rebounds with speed v, find the mass of the unknown particle in terms of m, v, and v0. (b) If the known particle is a proton and the unknown particle is a neutron, what will be the recoil speed of the proton and the final speed of the neutron? 4/9/13 12:19 PM Questions and Problems 287 7-4 In an inelastic collision, some of the mechanical energy is lost 60. •Determine the impulse delivered over the first 10 s to the object acted on by the force described by the graph (Figure 7-27). 49. •A 10,000-kg train car moving due east at 20.0 m>s collides with and couples to a 20,000-kg train car that is initially at rest. What is the common velocity of the two-car train after the collision? 50. •A large fish has a mass of 25.0 kg and swims at 1.00 m>s toward and then swallows a smaller fish that is not moving. If the smaller fish has a mass of 1.00 kg, what is the speed of the larger fish immediately after it finishes lunch? 51. •A 5.00-kg howler monkey is swinging due east on a vine. It overtakes and grabs onto a 6.00-kg monkey also moving east on a second vine. The first monkey is moving at 12.0 m>s at the instant it grabs the second, which is moving at 8.00 m>s. After they join on the same vine, what is their common speed? SSM 52. •A 1200-kg car is moving at 20.0 m>s due north. A 1500-kg car is moving at 18.0 m>s due east. The two cars simultaneously approach an icy intersection where, with no brakes or steering, they collide and stick together. Determine the speed and direction of the combined two-car wreck immediately after the collision. F (N) 100 t (s) 1 2 3 4 5 6 7 8 9 10 Figure 7-27 Problem 60 61. •Sports A baseball of mass 0.145 kg is thrown at a speed of 40.0 m>s. The batter strikes the ball with a force of 25,000 N; the bat and ball are in contact for 0.500 ms. Assuming that the force is exactly opposite to the original direction of the ball, determine the final speed of the ball. 62. •A 5.00-kg object is constrained to move along a straight line. Its initial speed is 12.0 m>s in one direction, and its final speed is 8.00 m>s in the opposite direction. Complete the graph of force versus time with appropriate values for both variables (Figure 7-28). Several answers are correct; just be sure that your answer is internally consistent. 53. •Sports An 85.0-kg linebacker is running at 8.00 m>s directly toward the sideline of a football field. He tackles a 75.0-kg running back moving at 9.00 m>s straight toward the goal line (perpendicular to the original direction of the linebacker). Determine their common speed and direction immediately after they collide. 7-5 In an elastic collision, both momentum and mechanical energy are conserved 54. •A 2.00-kg ball is moving at 3.00 m>s toward the right. It collides elastically with a 4.00-kg ball that is initially at rest. Determine the velocities of the balls after the collision. 55. •A 10.0-kg block of ice is sliding due east at 8.00 m>s when it collides elastically with a 6.00-kg block of ice that is sliding in the same direction at 4.00 m>s. Determine the velocities of the blocks of ice after the collision. SSM 56. •A 0.170-kg ball is moving at 4.00 m>s toward the right. It collides elastically with a 0.155-kg ball moving at 2.00 m>s toward the left. Determine the final velocities of the balls after the collision. 57. •A neutron traveling at 2.00 * 105 m>s collides elastically with a deuteron that is initially at rest. Determine the final speeds of the two particles after the collision. The mass of a neutron is 1.67 * 10227 kg, and the mass of a deuteron is 3.34 * 10227 kg. F (N) ? tf = ? Figure 7-28 Problem 62 ? 63. •Sports A baseball bat strikes a ball when both are moving at 31.3 m>s (relative to the ground) toward each other. The bat and ball are in contact for 1.20 ms, after which the ball is traveling at a speed of 42.5 m>s. The mass of the bat and the ball are 850 g and 145 g, respectively. Calculate the magnitude and direction of the impulse given to (a) the ball by the bat and (b) the bat by the ball. (c) What average force does the bat exert on the ball? (d) Why doesn’t the force shatter the bat? 7-7 The center of mass of a system moves as though all of the system’s mass were concentrated there 64. •Find the coordinates of the center of mass of the three objects shown in Figure 7-29 if m1 = 4.00 kg, m2 = 2.00 kg, and m3 = 3.00 kg. Distances are in meters. y m1 58. •A sudden gust of wind exerts a force of 20.0 N for 1.20 s on a bird that had been flying at 5.00 m>s. As a result, the bird ends up moving in the opposite direction at 7.00 m>s. What is the mass of the bird? Freed_c07_244-289_st_hr1.indd 287 t (s) ? 7-6 What happens in a collision is related to the time the colliding objects are in contact 59. •Determine the average force exerted on your hand as you catch a 0.200-kg ball moving at 20.0 m>s. Assume the time of contact is 0.0250 s. SSM –80 2 m2 x –6 –4 –2 2 –2 m3 Figure 7-29 Problem 64 –4 4/9/13 12:19 PM 288 Chapter 7 Momentum, Collisions, and the Center of Mass 65. •What are the coordinates of the center of mass for the combination of the three objects shown in Figure 7-30? The uniform rod has a mass of10.0 kg, has a length of 30.0 cm, and is located at x = 50.0 cm. The oval football has a mass of 2.00 kg, a semimajor axis of 15.0 cm,a semiminor axis of 8.00 cm, and is centered at x = 250.0 cm.The spherical volleyball has a mass of 1.00 kg, a radius of 10.0 cm, and is centered at y = 230 cm. SSM y x Figure 7-30 Problem 65 66. •Four beads each of mass M are attached at various locations to a hoop of mass M and radius R (Figure 7-31). Find the center of mass of the hoop and beads. y M R M M 45° 35° x 70° 50° M Figure 7-31 Problem 66 M General Problems 67. •Sports A major league baseball has a mass of 0.145 kg. Neglecting the effects of air resistance, determine the momentum of the ball when it hits the ground if it falls from rest on the roof of the Metrodome in Minneapolis, Minnesota, a height of 60.0 m. 68. •Forensic scientists can determine the speed at which a rifle fires a bullet by shooting into a heavy block hanging by a wire. As the bullet embeds itself in the block, the block and embedded bullet swing up; the impact speed is determined from the maximum angle of the swing. (a) Which would make the block swing higher, a 0.204 Ruger bullet of mass 2.14 g and muzzle speed 1290 m>s or a 7-mm Remington Magnum bullet of mass 9.71 g and muzzle speed 948 m>s? Assume the bullets enter the block right after leaving the muzzle of the rifle. (b) Using your answer in part (a), determine the mass of the block so that when hit by the bullet it will swing through a 60.0° angle. The block hangs from wire of length 1.25 m and negligible mass. (c) What is the speed of an 8.41-g bullet that causes the block to swing upward through a 30.0° angle? 69. •A friend suggests that if all the people in the United States dropped down from a 1-m-high table at the same time, Earth would move in a noticeable way. To test the credibility of this proposal, (a) determine the momentum imparted to Earth by 300 million people, of an average mass of 65.0 kg, drop- Freed_c07_244-289_st_hr1.indd 288 ping from 1.00 m above the surface. Assume no one bounces. (b) What change in Earth’s speed would result? SSM 70. •Sally finds herself stranded on a frozen pond so slippery that she can’t stand up or walk on it. To save herself, she throws one of her heavy boots horizontally, directly away from the closest shore. Sally’s mass is 60 kg, the boot’s mass is 5 kg, and Sally throws the boot with speed equal to 30.0 m>s. (a) What is Sally’s speed immediately after throwing the boot? (b) Where is the center of mass of the Sally–boot system, relative to where she threw the boot, after 10.0 s? (c) How long does it take Sally to reach the shore, a distance of 30.0 m away from where she threw the boot? For all parts, assume the ice is frictionless. 71. •You have been called to testify as an expert witness in a trial involving a head-on collision. Car A weighs 680 kg and was traveling eastward. Car B weighs 500 kg and was traveling westward at 72.0 km>h. The cars locked bumpers and slid eastward with their wheels locked for 6.00 m before stopping. You have measured the coefficient of kinetic friction between the tires and the pavement to be 0.750. How fast (in miles per hour) was car A traveling just before the collision? 72. •A 5000-kg open train car is rolling at a speed of 20.0 m>s when it begins to rain heavily and 200 kg of water collects quickly in the car. If only the total mass has changed, what is the speed of the flooded train car? For simplicity, assume that all of the water collects at one instant and that the train tracks are frictionless. 73. •An 8000-kg open train car is rolling at a speed of 20.0 m>s when it begins to rain heavily. After water has collected in the car, it slows to 19.0 m>s. What mass of water has collected in the car? For simplicity, assume that all of the water collects at one instant and that the train tracks are frictionless. SSM 74. •An open rail car of initial mass 10,000 kg is moving at 5.00 m>s when rocks begin to fall into it from a conveyor belt. The rate at which the mass of rocks increases is 500 kg>s. Find the speed of the train car after rocks have fallen into the car for a total of 3.00 s. 75. •A skier and a snowboarder of equal mass collide in an area where the snow is level. Just before the collision, the skier was moving south at 8.00 m>s and the snowboarder was moving west at 12.0 m>s. After the unplanned meeting, the skier slid 45° south of west and the snowboarder slid 45° north of west. What was the speed of each athlete after the collision, assuming that the collision was completely elastic? 76. •Sports The sport of curling is quite popular in Canada. A curler slides a 19.1-kg stone so that it strikes a competitor’s stationary stone at 6.40 m>s before moving at an angle of 120° from its initial direction. The competitor’s stone moves off at 5.60 m>s. Determine the final speed of the first stone and the final direction of the second one. 77. ••Biology Lions can run at speeds up to approximately 80.0 km>h. A hungry 135-kg lion running northward at top speed attacks and holds onto a 29.0-kg Thomson’s gazelle running eastward at 60.0 km>h. Find the speed and direction of travel of the lion–gazelle system just after the lion attacks. SSM 4/9/13 12:19 PM Questions and Problems 289 78. •Biology The mass of a pigeon hawk is twice that of the pigeons it hunts. Suppose a pigeon is gliding north at a speed of vP = 23.0 m>s when a hawk swoops down, grabs the pigeon, and flies off (Figure 7-32). The hawk was flying north at speed of vH = 35.0 m>s, at an angle u = 45° below the horizontal, at the instant of the attack. Find the final velocity vector of the birds just after the attack. Hawk up vH θ north vP Pigeon Figure 7-32 Problem 78 79. ••A 12.0-g bullet is fired into a block of wood with speed v = 250 m>s (Figure 7-33). The block is attached to a spring that has a spring constant of 200 N>m. The block with the embedded bullet compresses the spring a distance d = 30.0 cm to the right, before momentarily coming to a stop. Determine the mass of the wooden block. SSM v m d Freed_c07_244-289_st_hr1.indd 289 Figure 7-33 Problem 79 80. ••In a ballistic pendulum experiment, a small marble is fired into a cup attached to the end of a pendulum. If the mass of the marble is 0.00750 kg and the mass of the pendulum is 0.250 kg, how high will the pendulum swing if the marble has an initial speed of 6.00 m>s? Assume that the mass of the pendulum is concentrated at its end. 81. •••A 2.50-kg object (1) elastically collides with a 3.60-kg object (2) that is initially at rest. The less massive object has a speed of v1 = 4.00 m>s and travels at an angle of u1 with its original direction after the collision; the more massive object has a speed of v2 = 2.50 m>s and travels at an angle of u2 after the collision (Figure 7-34). What are the initial speed of the less massive object and the two scattering angles, u1 and u2? Before 1 v0 = ? at rest 2 After v1 1 2 θ1 = ? θ2 = ? v2 Figure 7-34 Problem 81 82. ••A 0.0750-kg ball is thrown at 25.0 m>s toward a brick wall. (a) Determine the impulse that the wall imparts to the ball when it hits and rebounds at 25.0 m>s in the opposite direction. (b) Determine the impulse that the wall imparts to the ball when it hits and rebounds at an angle of 45.0°. (c) If the ball thrown in part (b) contacts the wall for 0.0100 s, determine the magnitude and direction of the force that the wall exerts on the ball. 83. ••The mass of an oxygen nucleus is about 16 times that of a proton. A proton traveling at 5.00 * 105 m>s collides completely elastically with an oxygen nucleus and leaves the interaction at 5.00 * 105 m>s. (a) What fraction of the initial kinetic energy is transferred to the oxygen nucleus? (b) Determine the final directions of the proton and the oxygen nucleus. 4/9/13 12:19 PM