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Impulse and Momentum HW 1. How long must a 100 N net force act to produce a change in momentum of 200 kg m/s? (A) 0.25 s (B) 0.50 s (C) 1.0 s (D) 2.0 s (E) 4.0 s 2. Two football players with mass 75 kg and 100 kg run directly toward each other with speeds of 6 m/s and 8 m/s respectively. If they grab each other as they collide, the combined speed of the two players just after the collision would be: (A) 2 m/s (B) 3.4 m/s (C) 4.6 m/s (D) 7.1 m/s (E) 8 m/s 3. A rubber ball is held motionless a height ho above a hard floor and released. Assuming that the collision with the floor is elastic, which one of the following graphs best shows the relationship between the total energy E of the ball and its height h above the surface. 4. Two carts are held together. Cart 1 is more massive than Cart 2. As they are forced apart by a compressed spring between them, which of the following will have the same magnitude for both carts. (A) acceleration (B) change of velocity (C) force (D) speed (E) velocity 5. A cart with mass 2m has a velocity v before it strikes another cart of mass 3m at rest. The two carts couple and move off together with a velocity of (A) v/5 (B) 2v/5 (C) 3v/5 (D) 2v/3 (E) (2/5)1/2 v 6. A 50 kg skater at rest on a frictionless rink throws a 2 kg ball, giving the ball a velocity of 10 m/s. Which statement describes the skater’s subsequent motion? (A) 0.4 m/s in the same direction as the ball. (B) 0.4 m/s in the opposite direction of the ball (C) 2 m/s in the same direction as the ball (D) 4 m/s in the same direction as the ball (E) 4 m/s in the opposite direction of the ball 7. The data in the table below were recorded during an experiment in which two carts on a frictionless one-dimensional track collide head-on. What are the values of the magnitude of the change in momentum Δp2 of cart 2 and the magnitude of its average acceleration a2 during the collision? 8. A 1.0 kg lump of clay is sliding to the right on a frictionless surface with speed 2 m/s. It collides head-on and sticks to a 0.5 kg metal sphere that is sliding to the left with speed 4 m/s. What is the kinetic energy of the combined objects after the collision? (A) 6 J (B) 4 J (C) 2 J (D) 0 J 9. The graph above shows the position x as a function of time for the center of mass of a system of particles of total mass 6.0 kg. For a very short time interval around 2.0 s, an external force is exerted on an object in the system. What is the resulting change in momentum of the system? (A) 52 kg m/s (B) 6 kg m/s (C) -6 kg m/s (D) -18 kg m/s 10. A 2 kg object traveling at 5 m s on a frictionless horizontal surface collides head-on with and sticks to a 3 kg object initially at rest. Which of the following correctly identifies the change in total kinetic energy and the resulting speed of the objects after the collision? 11. A student stands at one end of a raft floating in a pool with equally spaced marks along the bottom, as shown above. The student and the raft have the same mass. The student walks to the opposite end of the raft. Which of the following best shows the final locations of the raft and student relative to the marks at the bottom of the pool? Assume that there is no drag force between the raft and the water. 12. A spaceship and its shuttle pod are traveling to the right in a straight line with speed v, as shown in the top figure above. The mass of the pod is m, and the mass of the spaceship is 6m. The pod is launched, and afterward the pod is moving to the right with speed v p and the spaceship is moving to the right with speed vf, where vf > v, as shown in the bottom figure. Which of the following is true of the speed vc of the center of mass of the system after the pod is launched? 13. The figure above represents two carts, with magnets attached, that make up a system. The mass of one cart and magnet is 1 kg and the mass of the other is 5 kg. The carts are initially at rest on a frictionless track. They are released from rest and exert a repulsive force on each other. The track is not quite horizontal, with the right side slightly lower than the left side. The speeds of the carts are measured over a 10 s interval. The graph below shows the momentum of the two carts as a function of time for this interval as they move along the x-axis. (a) Based on the graph, were the measurements started at the instant the carts were released? Justify your answer. (b) Calculate the magnitude of the external force exerted on the system. (c) Suppose the experiment is repeated with different carts, so that the masses of cart plus magnet are 2 kg and 4 kg. Would your answer to part (b) be different with the new masses? Justify your answer. 14. A 2.0 kg frictionless cart is moving at a constant speed of 3.0 m/s to the right on a horizontal surface, as shown above, when it collides with a second cart of undetermined mass m that is initially at rest. The force F of the collision as a function of time t is shown in the graph below, where t = 0 is the instant of initial contact. As a result of the collision, the second cart acquires a speed of 1.6 m/s to the right. Assume that friction is negligible before, during, and after the collision. (a) Calculate the magnitude and direction of the velocity of the 2.0 kg cart after the collision. (b) Calculate the mass m of the second cart. After the collision, the second cart eventually experiences a ramp, which it traverses with no frictional losses. The graph below shows the speed v of the second cart as a function of time t for the next 5.0 s, where t = 0 is now the instant at which the carts separate. (c) Calculate the acceleration of the cart at t = 3.0 s. (d) Calculate the distance traveled by the second cart during the 5.0 s interval after the collision (0 s < t < 5.0 s). (e) State whether the ramp goes up or down and calculate the maximum elevation (above or below the initial height) reached by the second cart on the ramp during the 5.0 s interval after the collision (0 s < t < 5.0 s). 15. Two blocks A and B of equal mass m are on a frictionless track, as shown in the figure above. Block A, initially moving with speed v1, has a perfectly elastic collision with block B. Block B has a speed v1 immediately after the collision, and then it travels around a circular loop of radius R, where R is much larger than the size of the blocks. The speed of block B at the top of the loop is vtop. Block B then slides up a ramp until it comes momentarily to rest at a height h above the floor. (a) Derive an equation for the height h in terms of m, R, v top, and g, as appropriate. (b) Suppose that the speed v1 of block A is doubled. Will the final height of block B be greater than, less than, or equal to 2h? ____ Greater than 2h ____ Less than 2h ____ Equal to 2h Briefly explain how you arrived at your answer. (c) Blocks A and B (both of mass m) are moved to a different frictionless track, as shown above. Let v A be the minimum initial speed for block A that allows block B to make it over the hump in the track. Block A is then replaced with a larger block, block C, which has mass 2m, as shown below. Block C makes a completely inelastic collision with block B so that both blocks stick together and travel along the track. What is the minimum initial speed v C that block C must have so that the two-block system makes it over the hump? Express your answer in terms of v A.