chapter F IMPULSE AND MOMENTUM Section 7.1 The Impulse Momentum Theorem 1. Which one of the following statements concerning momentum is true? (a) Momentum is a force. (b) Momentum is a scalar quantity. (c) The SI unit of momentum is kg m /s. (d) The momentum of an object is always positive. (e) Momentum and impulse are measured in the same units.. A rock is dropped from a high tower and falls freely under the influence of gravity. Which one of the following statements concerning the rock as it falls is true? Neglect the effects of air resistance. (a) The rock will gain an equal amount of momentum during each second. (b) The rock will gain an equal amount of kinetic energy during each second. (c) The rock will gain an equal amount of speed for each meter through which it falls. (d) The rock will gain an equal amount of momentum for each meter through which it falls. (e) The amount of momentum the rock gains will be proportional to the amount of potential energy that it loses. 3. A stunt person jumps from the roof of a tall building, but no injury occurs because the person lands on a large, air-filled bag. Which one of the following best describes why no injury occurs? (a) The bag provides the necessary force to stop the person. (b) The bag reduces the impulse to the person. (c) The bag increases the amount of time the force acts on the person and reduces the change in momentum. (d) The bag decreases the amount of time during which the momentum is changing and reduces the average force on the person. (e) The bag increases the amount of time during which the momentum is changing and reduces the average force on the person. 4. Jennifer is walking at 1.63 m/s. If Jennifer weighs 583 N, what is the magnitude of her momentum? (a) 97.0 kg m/s (c) 68.6 kg m/s (e) 951 kg m/s (b) 137 kg m/s (d) 67 kg m/s 5. A 1.0-kg ball has a velocity of 1 m/s downward just before it strikes the ground and bounces up with a velocity of 1 m/s upward. What is the change in momentum of the ball? (a) zero kg m/s (c) 1 kg m/s, upward (e) 4 kg m/s, upward (b) 1 kg m/s, downward (d) 4 kg m/s, downward 6. A projectile is launched with 00 kg m/s of momentum and 1000 J of kinetic energy. What is the mass of the projectile? (a) 5 kg (c) 0 kg (e) 50 kg (b) 10 kg (d) 40 kg 7. A 0.1-kg steel ball is dropped straight down onto a hard, horizontal floor and bounces straight up. The ball s speed just before and just after impact with the floor is 10 m/s. Determine the magnitude of the impulse delivered to the floor by the steel ball. (a) zero N s (c) N s (e) 100 N s (b) 1 N s (d) 10 N s
Physics, 7e TEST BANK 75 8. A machine gun fires 50-g bullets at the rate of 4 bullets per second. The bullets leave the gun at a speed of 1000 m/s. What is the average recoil force experienced by the machine gun? (a) 10 N (c) 100 N (e) 1000 N (b) 0 N (d) 00 N 9. A 0.065-kg tennis ball moving to the right with a speed of 15 m/s is struck by a tennis racket, causing it to move to the left with a speed of 15 m/s. If the ball remains in contact with the racquet for 0.00 s, what is the magnitude of the average force experienced by the ball? (a) zero newtons (c) 160 N (e) 30 N (b) 98 N (d) 40 N 10. A baseball of mass m, initially at rest, is struck by a bat so that it acquires a speed v. If t represents the duration of the collision between the bat and the ball, which expression determines the magnitude of the average force exerted on the ball? (a) (1/)mv (c) (1/)mv t (e) mvt (b) mv/t (d) mt /(v) 11. An airplane is traveling at 5 m/s when it strikes a weather balloon (m = 1.8 kg), which can be considered to be at rest relative to the ground below. After the collision, the balloon is caught on the fuselage and is traveling with the airplane. The collision takes place over a time interval of 4.44 10 3 N. What is the average force that the balloon exerts on the airplane? (a) 415 N (c) 9. 10 4 N (e) 5.07 10 6 N (b).78 10 4 N (d) 4.61 10 5 N 1. While a car is stopped at a traffic light in a storm, raindrops strike the roof of the car. The area of the roof is 5.0 m. Each raindrop has a mass of 3.7 10 4 kg and speed of.5 m/s before impact and is at rest after the impact. If, on average at a given time, 150 raindrops strike each square meter, what is the impulse of the rain striking the car? (a) 0.69 N s (c) 0.14 N s (e) 1 N s (b) 0.046 N s (d) 11 N s 13. A bat strikes a 0.050-kg baseball so that its velocity changes by +30 m/s in 0.10 s. With what average force was the ball struck? (a) +15 N (c) +300 N (e) +150 N (b) 15 N (d) 300 N 14. The head of a hammer (m = 1.5 kg) moving at 4.5 m/s strikes a nail and bounces back with the same speed after an elastic collision lasting 0.075 s. What is the magnitude of the average force the hammer exerts on the nail? (a) 6.8 N (c) 90 N (e) 40 N (b) 60 N (d) 180 N 15. A football player kicks a 0.41-kg football initially at rest; and the ball flies through the air. If the kicker s foot was in contact with the ball for 0.051 s and the ball s initial speed after the collision is 1 m/s, what was the magnitude of the average force on the football? (a) 9.7 N (c) 81 N (e) 10 N (b) 46 N (d) 170 N
76 Chapter 7 Impulse and Momentum Questions 16 and 17 pertain to the situation described below: A 4.0-kg block slides along a frictionless surface with a constant speed of 5.0 m/s as shown. Two seconds after it begins sliding, a horizontal, time-dependent force is applied to the mass. The force is removed eight seconds later. The graph shows how the force on the block varies with time. 4.0 kg 0 0 4 6 8 10 Time (s) 16. What is the magnitude of the total impulse of the force acting on the block? (a) 0 N s (c) 48 N s (e) 60 N s (b) 4 N s (d) 54 N s v Force (N) 6 3 17. What, approximately, is the speed of the block at t = 11 seconds? (a) 5.0 m/s (c) 5 m/s (e) 75 m/s (b) 16 m/s (d) 65 m/s Section 7. The Principle of Conservation of Linear Momentum 18. In which one of the following situations is linear momentum not conserved? (a) A bomb suspended by a string explodes into one hundred fragments. (b) A bowling ball collides with a set of ten pins. (c) A golf ball is struck by a club. (d) An astronaut floating in space throws a hammer away and subsequently moves in the opposite direction. (e) A tree limb is struck by lightning and falls to the ground. 19. A stationary bomb explodes in space breaking into a number of small fragments. At the location of the explosion, the net force due to gravity is zero newtons. Which one of the following statements concerning this event is true? (a) Kinetic energy is conserved in this process. (b) The fragments must have equal kinetic energies. (c) The sum of the kinetic energies of the fragments must be zero. (d) The vector sum of the linear momenta of the fragments must be zero. (e) The velocity of any one fragment must be equal to the velocity of any other fragment. 0. An object of mass 3m, initially at rest, explodes breaking into two fragments of mass m and m, respectively. Which one of the following statements concerning the fragments after the explosion is true? (a) They will fly off at right angles. (b) They will fly off in the same direction. (c) The smaller fragment will have twice the speed of the larger fragment. (d) The larger fragment will have twice the speed of the smaller fragment. (e) The smaller fragment will have four times the speed of the larger fragment. 1. A 100-kg cannon at rest contains a 10-kg cannon ball. When fired, the cannon ball leaves the cannon with a speed of 90 m/s. What is the recoil speed of the cannon? (a) 4.5 m/s (c) 45 m/s (e) zero m/s (b) 9 m/s (d) 90 m/s
Physics, 7e TEST BANK 77. A 50-kg toboggan is coasting on level snow. As it passes beneath a bridge, a 0-kg parcel is dropped straight down and lands in the toboggan. If (KE) 1 is the original kinetic energy of the toboggan and (KE) is the kinetic energy after the parcel has been added, what is the ratio (KE) /(KE) 1. (a) 0.4 (c) 0.7 (e) 1 (b) 0.6 (d) 0.8 3. A sled of mass m is coasting on the icy surface of a frozen river. While it is passing under a bridge, a package of equal mass m is dropped straight down and lands on the sled (without causing any damage). The sled plus the added load then continue along the original line of motion. How does the kinetic energy of the sled + load compare with the original kinetic energy of the sled? (a) It is 1/4 the original kinetic energy of the sled. (b) It is 1/ the original kinetic energy of the sled. (c) It is 3/4 the original kinetic energy of the sled. (d) It is the same as the original kinetic energy of the sled. (e) It is twice the original kinetic energy of the sled. 4. A bullet of mass m is fired at speed v 0 into a wooden block of mass M. The bullet instantaneously comes to rest in the block. The block with the embedded bullet slides along a horizontal surface with a coefficient of kinetic friction µ. initial position final position v 0 M s Which one of the following expressions determines how far the block slides before it comes to rest (the magnitude of displacement s in the figure)? mv0 m v0 v0 (a) s = (c) s = (e) s = Mµ g m + M µ g µ g (b) m v 0 s = m + M (d) µ g m s = m + M v0 µ g 5. While in Earth s orbit, an 80-kg astronaut carrying a 0-kg tool kit is initially drifting toward a stationary (to her) space shuttle at a speed of m/s. If she throws the tool kit toward the shuttle with a speed of 6 m/s as seen from the shuttle, her final speed is (a) 1 m/s toward the shuttle. (d) 4 m/s toward the shuttle. (b) 1 m/s away from the shuttle. (e) 6 m/s away from the shuttle. (c) m/s toward the shuttle. 6. On an interplanetary mission, a 58.5-kg astronaut is floating toward the front of her ship at 0.15 m/s, relative to the ship. She wishes to stop moving, relative to the ship. She decides to throw away the.50-kg book she s carrying. What should the speed and direction of the book be to achieve her goal? (a) 0.15 m/s, toward the front of the ship (d) 0.30 m/s, toward the back of the ship (b) 3.5 m/s, toward the back of the ship (e) 1.8 m/s, toward the front of the ship (c) 3.7 m/s, toward the front of the ship
78 Chapter 7 Impulse and Momentum Section 7.3 Collisions in One Dimension Section 7.4 Collisions in Two Dimensions 7. Complete the following statement: Different types of collisions between interacting bodies are categorized on the basis of (a) kinetic energy conservation. (d) the magnitude of the forces involved. (b) mechanical energy conservation. (e) the temporal duration of the collision. (c) linear momentum conservation. 8. Complete the following statement: A collision is elastic if (a) the final velocities are zero. (d) the final momentum is zero. (b) the objects stick together. (e) the total kinetic energy is conserved. (c) the final kinetic energy is zero. 9. Which one of the following is characteristic of an inelastic collision? (a) Total mass is not conserved. (d) Kinetic energy is not conserved. (b) Total energy is not conserved. (e) The change in momentum is less than (c) Linear momentum is not conserved. the total impulse. 30. Two objects of equal mass traveling toward each other with equal speeds undergo a head on collision. Which one of the following statements concerning their velocities after the collision is necessarily true? (a) They will exchange velocities. (d) Their velocities will be zero. (b) Their velocities will be reduced. (e) Their velocities may be zero. (c) Their velocities will be unchanged. 31. Complete the following statement: Momentum will be conserved in a two-body collision only if (a) both bodies come to rest. (b) the collision is perfectly elastic. (c) the kinetic energy of the system is conserved. (d) the net external force acting on the two-body system is zero. (e) the internal forces of the two body system cancel in action-reaction pairs. 3. Two cars of equal mass collide on a horizontal frictionless surface. Before the collision, car A is at rest while car B has a constant velocity of 1 m/s. After the collision, the two bodies are stuck together. What is the speed of the composite body (A + B) after the collision? (a) 3.0 m/s (c) 1 m/s (e) 36 m/s (b) 6.0 m/s (d) 4 m/s 33. A stone of mass kg falls 100 meters near the surface of the earth. It strikes the ground without any rebound thereby making a completely inelastic collision with the earth. Approximately how much kinetic energy is transferred to the earth in this process? (a) zero joules (c) 000 J (e) 0 000 J (b) 00 J (d) 10 000 J 34. A tennis ball has a velocity of 1 m/s downward just before it strikes the ground and bounces up with a velocity of 1 m/s upward. Which statement is true concerning this situation? (a) The momentum of the ball and the momentum of the earth both change. (b) Neither the momentum of the ball nor the momentum of the earth changes. (c) The momentum of the ball is changed; the momentum of the earth is not changed. (d) The momentum of the ball is unchanged; the momentum of the earth is changed. (e) Both the momentum and the kinetic energy of the ball change because of the collision.
Physics, 7e TEST BANK 79 35. A 3.0-kg cart moving to the right with a speed of 1.0 m/s has a head-on collision with a 5.0-kg cart that is initially moving to the left with a speed of.0 m/s. After the collision, the 3.0-kg cart is moving to the left with a speed of 1.0 m/s. What is the final velocity of the 5.0-kg cart? (a) zero m/s (c) 0.80 m/s to the left (e).0 m/s to the left (b) 0.80 m/s to the right (d).0 m/s to the right 36. A 1000-kg car traveling east at 0 m/s collides with a 1500-kg car traveling west at 10 m/s. The cars stick together after the collision. What is the common velocity of the cars after the collision? (a) 16 m/s, east (c) 4 m/s, east (e) 1 m/s, west (b) 6 m/s, west (d) m/s, east 37. A 0.050-kg lump of clay moving horizontally at 1 m/s strikes and sticks to a stationary 0.10-kg cart that can move on a frictionless air track. Determine the speed of the cart and clay after the collision. (a) m/s (c) 6 m/s (e) 1 m/s (b) 4 m/s (d) 8 m/s 38. A 0.10-kg cart traveling in the positive x direction at 10.0 m/s collides with a 0.30-kg cart at rest. The collision is elastic. What is the velocity of the 0.10-kg cart after the collision? (a) +.5 m/s (c) +5 m/s (e) +3.3 m/s (b).5 m/s (d) 5 m/s.5 m/s 39. A 50.0-kg boy runs at a speed of 10.0 m/s 10 m/s and jumps onto a cart as shown in the figure. The cart is initially at rest. If the v = 0 speed of the cart with the boy on it is.50 m/s, what is the mass of the cart? (a) 150 kg (c) 10 kg (e) 300 kg (b) 175 kg (d) 60 kg 40. A 0.015-kg marble moving to the right at 0.40 m/s has a head-on, elastic collision with a 0.045-kg marble sitting at rest on a smooth, level surface. Which of the following are the correct magnitudes and directions of the velocities of the two marbles after the collision? 0.015 kg marble 0.045 kg marble (a) 0.15 m/s, left 0.5 m/s, right (b) 0.10 m/s, right 0.30 m/s, right (c) zero m/s 0.5 m/s, right (d) 0.0 m/s, left 0.0 m/s, right (e) 0.40 m/s, left zero m/s 41. A 7.30-kg bowling ball strikes a 1.60-kg pin at rest head-on. Before the collision, the velocity of the ball is +6.00 m/s. After the collision, the velocity of the ball is +5.40 m/s. What is the velocity of the pin after the collision? (a) +0.6 m/s (c) +1. m/s (e) +3. m/s (b) +5.4 m/s (d) +.7 m/s 4. A.5-kg ball and a 5.0-kg ball have an elastic collision. Before the collision, the.5-kg ball was at rest and the other ball had a speed of 3.5 m/s. What is the kinetic energy of the.5-kg ball after the collision? (a) 1.7 J (c) 8.1 J (e) 7 J (b) 3.4 J (d) 14 J
80 Chapter 7 Impulse and Momentum 43. Two objects constitute an isolated system. In an elastic collision between the two objects, which one of the following statements is a false statement? (a) The total kinetic energy is conserved. (b) The kinetic energy of each object is the same before and after the collision. (c) The total momentum is conserved. (d) The magnitude of the force exerted by each object on the other object is equal. (e) The total kinetic energy before the collision is equal to the total kinetic energy after the collision. 44. A 35-kg girl is standing near and to the left of a 43-kg boy on the frictionless surface of a frozen pond. The boy throws a 0.75-kg ice ball to the girl with a horizontal speed of 6. m/s. What are the velocities of the boy and the girl immediately after the girl catches the ice ball? girl boy (a) 0.81 m/s, left 0.67 m/s, right (b) 0.17 m/s, left 0.14 m/s, left (c) 0.18 m/s, right 0.13 m/s, left (d) 0.4 m/s, left 0.49 m/s, right (e) 0.13 m/s, left 0.11 m/s, right Questions 45 and 46 pertain to the following situation. A comet fragment of mass 1.96 10 13 kg is moving at 6.50 10 4 m/s when it crashes into Callisto, a moon of Jupiter. The mass of Callisto is 1.08 10 3 kg. The collision is completely inelastic. 45. Assuming for this calculation that Callisto s initial momentum is zero kg m/s, what is the recoil speed of Callisto immediately after the collision? (a) 3.34 10 18 m/s (c) 3.58 10 1 m/s (e) 1.18 10 5 m/s (b) 1.7 10 14 m/s (d) 6.13 10 7 m/s 46. How much kinetic energy was released in the collision? (a) 8.8 10 J (c) 7.0 10 7 J (e) 1.50 10 13 J (b) 3.51 10 7 J (d) 4.14 10 J 47. Car One is traveling due north and Car Two is traveling due east. After the collision shown, Car One rebounds in the due south direction. Which of the numbered arrows is the only one that can represent the final direction of Car Two? (a) 1 (b) (c) 3 (d) 4 (e) 5 (1) Two () One (3) (4) (5) 48. A 0.50-kg bomb is sliding along an icy pond (frictionless surface) with a velocity of.0 m/s to the west. The bomb explodes into two pieces. After the explosion, a 0.0-kg piece moves south at 4.0 m/s. What are the components of the velocity of the 0.30-kg piece? (a) 4.0 m/s north, 0 m/s (d) 0 m/s,.0 m/s east (b).7 m/s north, 3.3 m/s west (e) 4.0 m/s north,.0 m/s east (c) 4.0 m/s north,.7 m/s west
Physics, 7e TEST BANK 81 49. Two asteroids are drifting in space with trajectories shown. Assuming the collision at point O between them is completely inelastic, at what angle from its original direction is the larger asteroid deflected? (a) 80 above the +x axis (d) 47 above the +x axis (b) 69 above the +x axis (e) 90 above the +x axis (c) 4 above the +x axis 45 m/s 0.10m y O x 47 15 m/s m 50. In the game of billiards, all the balls have approximately the same mass, about 0.17 kg. In the figure, the cue ball strikes another ball such that it follows the path shown. The other ball has a speed of 1.5 m/s immediately after the collision. What is the speed of the cue ball after the collision? 3.0 m/s 30.0 60.0 1.5 m/s (a) 1.5 m/s (c).6 m/s (e) 5. m/s (b) 1.8 m/s (d) 4.3 m/s Section 7.5 Center of Mass 51. Which one of the following statements concerning center of mass is true? (a) All of an object s mass is located at its center of mass. (b) The center of mass of an object must be located within the object. (c) The center of mass of a system of objects cannot change even if there are forces acting on the objects. (d) The velocity of the center of mass of a system of objects is greatly affected by a collision of objects within the system. (e) The velocity of the center of mass of a system of objects is constant when the sum of the external forces acting on the system is zero. 5. The drawing shows two 4.5-kg balls located on the y axis at 1.0 and 9.0 m, respectively; a third ball with a mass.3 kg is located at 6.0 m. What is the location of the center of mass of this system? (a) 4.8 m (b) 5. m (c) 5.6 m (d) 6.0 m (e) 6.4 m y (m) 10.0 8.0 6.0 4.0.0 0 4.5 kg.3 kg 4.5 kg 53. During hockey practice, two pucks are sliding across the ice in the same direction. At one instant, a 0.18-kg puck is moving at 16 m/s while the other puck has a mass of 0.14 kg and a speed of 3.8 m/s. What is the velocity of the center of mass of the two pucks? (a) 5.0 m/s (c) 9.0 m/s (e) 13 m/s (b) 7.0 m/s (d) 11 m/s
8 Chapter 7 Impulse and Momentum 54. A juggler demonstrates his abilities by keeping a.3-kg pipe wrench, a 1.5-kg hatchet, and a 1.0-kg hammer flying through the air above his head. The white circles on the graph represent the positions of the center of mass of each of the flying objects at one instant. What are the x and y coordinates of the center of mass for the system of these three objects? x y (a) 0.46 m 0.47 m (b) 0.30 m 0.54 m (c) 0.4 m 0.60 m (d) 0.47 m 0.6 m (e) 0.60 m 0.4 m y (m) 1.0 0.80 0.60 0.40 0.0 0 0 0.0 0.40 0.60 0.80 1.0 1. x (m) Additional Problems Questions 55 through 57 pertain to the following situation: A space vehicle of mass m has a speed v. At some instant, it separates into two pieces, each of mass 0.5m. One of the pieces is at rest just after the separation. 55. Which one of the following statements concerning this situation is true? (a) The moving piece has speed v. (b) This process conserves kinetic energy. (c) The piece at rest possesses kinetic energy. (d) The process does not conserve total energy. (e) This process does not conserve momentum. 56. What is the kinetic energy of the moving piece just after the separation? (a) zero joules (c) 1 mv (e) mv (b) 1 mv (d) mv 4 57. How much work was done by the internal forces that caused the separation? (a) zero joules (c) 1 mv (e) mv (b) 1 mv (d) mv 4 58. A mother is holding her 4.5-kg baby in her arms while riding in a car moving at m/s. The car is involved in a head-on collision and stops within 1.5 seconds. What is the magnitude of the force exerted by the baby on his mother s arms? (a) 45 N (c) 90 N (e) 150 N (b) 66 N (d) 99 N 59. A rocket is launched vertically from rest; and it burns fuel at a constant rate of 136 kg/s. Exhaust gases are expelled with a speed of 5.5 10 3 m/s relative to the rocket. What is the magnitude of the thrust? (a) 7.14 10 5 N (c).59 10 N (e) 38.6 N (b) 3.64 10 6 N (d) 808 N
Physics, 7e TEST BANK 83 60. A 100-kg fisherman and a 500-kg supply crate are on a frozen pond that is essentially frictionless. The man and the crate are initially separated by a distance of 600 meters. The fisherman uses a very light rope to pull the crate closer to him. How far has the man moved when the crate reaches the fisherman? (a) zero meters (c) 50 m (e) 500 m (b) 10 m (d) 100 m 61. A 160-kg space probe is moving in the positive x direction at 18 km/s when it encounters a timedependent force directed in the negative x direction. The force is as follows: 0 N for 0 t < 1.5 s F = 750 N for 1.5 s t 3.5 s 0 N for t > 3.5 s Determine the final speed of the space probe. (a) 8.6 km/s (c) 11 km/s (e) 3 km/s (b) 5.3 km/s (d) 16 km/s Questions 6 through 64 pertain to the situation described below: A.0-kg pistol fires a 1.0-g bullet with a muzzle speed of 1000 m/s. The bullet then strikes a 10-kg wooden block resting on a horizontal frictionless surface. The block and the embedded bullet then slide across the surface. 1000 m/s 6. What is the kinetic energy of the bullet as it travels toward the block? (a) 100 J (c) 1000 J (e) 10 000 J (b) 500 J (d) 5000 J 63. The explosive charge in the pistol acts for 0.001 s. What is the average force exerted on the bullet while it is being fired? (a) 0.001 N (c) 100 N (e) 1000 N (b) 1.0 N (d) 500 N 64. What is the speed of the "bullet + block" system immediately after the bullet is embedded in the block? (a) 0.1 m/s (c) 1000 m/s (e) zero m/s (b) 10 m/s (d) 10 000 m/s Questions 65 and 66 pertain to the following situation: A stationary 4-kg shell explodes into three pieces. Two of the fragments have a mass of 1 kg each and move along the paths shown with a speed of 10 m/s. The third fragment moves upward as shown. 65. What is the speed of the third fragment? (a) zero m/s (d) 10 m/s (b) 1 m/s (e) 0 m/s (c) 5 m/s kg 1 kg 60 60 1 kg 10 m/s 10 m/s 66. What is the speed of the center of mass of this system after the explosion? (a) zero m/s (c) 3 m/s (e) 7 m/s (b) 1 m/s (d) 5 m/s