Stevens High School AP Physics I Work for Not-school

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1 1. We have discussed how = 45 o gives the optimal angle for a projectile thrown over level ground, but let s consider something slightly different. What is the optimal angle (in terms of maximizing range for a given initial speed) for a projectile thrown off of a cliff? Justify your answer. a. < 45 o b. = 45 o c. > 45 o 2. Similarly, what is the optimal angle (in terms of maximizing range for a given initial speed) for a projectile thrown up onto a higher plateau? Justify your answer. a. < 45 o b. = 45 o c. > 45 o 3. A car of mass m collides perfectly inelastically with a truck of mass 2m. If the car has an initial velocity of V o, and the truck is initially at rest, what is the speed of the car-truck system immediately following the collision? a. V o/2 b. V o/3 c. V o/4 d. There is insufficient information to determine the post-collision velocity. 4. Two blocks, of mass m and 2m, are initially at rest on a horizontal frictionless surface. A force F is exerted individually on each block, as shown above. The graph shows how F varies with time t. Which block has the greatest average power provided to it between t = 0 s and t = 3 s? a. The block of mass m b. The block of mass 2m c. Both blocks have the same power provided to them. d. It cannot be determined without knowing the ratio of the maximum force to the mass m. Page 1

2 Questions 5-7 refer to this material: Block 1 of mass m 1 and block 2 of mass m 2 are sliding along the same line on a horizontal frictionless surface when they collide at time t c. The graph above shows the velocities of the blocks as a function of time. 5. Which block has the greater mass, and what information indicates this? a. Block 1, because it had a greater speed before the collision. b. Block 1, because the velocity after the collision is in the same direction as its velocity before the collision. c. Block 2, because it had a smaller speed before the collision. d. Block 2, because the final velocity is closer to the initial velocity of block 2 than it is to the initial velocity of block How does the kinetic energy of the two-block system after the collision compare with its kinetic energy before the collision, and why? a. It is less, because the blocks have the same velocity after the collision, so some of their kinetic energy was transformed into internal energy. b. It is less, because the blocks have velocities in opposite directions before the collision, so some of their kinetic energy cancels. c. It is the same, because the collision was instantaneous, so the effect of external forces during the collision is negligible. d. It is the same, because the blocks have the same velocity after the collision, and there is no friction acting on them. 7. Which of the following is true of the motion of the center of mass of the two-block system during the time shown? a. The center of mass does not move because the blocks are moving in opposite directions before the collision. b. The center of mass moves at a constant velocity of +1.0 m/s because there is no friction acting on the system. c. The center-of-mass velocity starts out greater than +1.0 m/s but decreases to +1.0 m/s during the collision because the collision is inelastic. d. The center-of-mass velocity increases as the blocks get closer together, and then becomes constant after the collision. Page 2

3 8. In a Hollywood movie, a hero drops vertically off a bridge onto a motorcycle driven by a fleeing wrongdoer (this might be the first time I have ever typed that word). The hero has a mass of m, and the motorcycle and rider have a mass of 3m. If the hero lands on the back of the motorcycle in a perfectly inelastic collision, how does the kinetic energy of the system (hero-bike-rider) change after the collision? a. K = 3 16 K o b. K = 1 2 K o c. K = 9 16 K o d. K = 3 4 K o e. K = K o 9. Consider the following graph. An object is moving in the positive x-direction while a net force directed along the x-axis is exerted on the object. The figure shows the force as a function of position. What is the net work done on the object over the distance shown? a. F 0 d b. 3F 0 d c. 2F 0 d d. 4F 0 d 10. Two gas molecules collide elastically. Molecule A has an initial velocity of +540 m/s (to the right) while molecule B has an initial velocity of -760 m/s (to the left). Without knowledge of the masses, which of the following post-collision velocities are possible. Choose all that apply. Options Post-Collision Velocities (m/s) Molecule A Molecule B A B C D A rocket blasts off from the surface of Earth, and sends a space probe hurtling out into the distant reaches of the solar system and beyond. It has sufficient speed to leave the Solar System forever. If we take our system to be the Rocket-Spaceprobe-Earth, conservation of momentum seems to be violated. Why isn t it? Page 3

4 A cart is constrained to move along a straight line. A varying net force along the direction of motion is exerted on the cart. The cart s velocity v as a function of time is shown in the graph above. The five labeled points divide the graph into four sections. 12. During some part of the motion, the work done on the cart is negative. What feature of the motion indicates this? 13. Sticking with the rocket theme for a bit, here s a graph showing the thrust force as a function of time for a hypothetical satellite. If the mass of the satellite is 350 kg, which of the following gives the approximate change in velocity during this time? a. 315 m/s b. 129 m/s c. 86 m/s d. 24 m/s 14. Is it possible for two objects with different mass to have equal kinetic energy and equal momentum? Explain why or why not. Ignore the trivial solution of zero velocity. 15. A block is given a short push and then slides with constant friction across a horizontal floor. The graph shows the kinetic energy of the block after the push ends as a function of an unidentified quantity. The quantity could be which of the following? Select two answers. a. The time elapsed since the push b. Distance traveled by the block c. Speed of the block d. Magnitude of the net work done on the block. Page 4

5 1. Engineers envision that a space elevator could one day replace a great deal of rocket propulsion. The concept is that a very long tether would be attached to a massive satellite thousands of miles in space. The centripetal force on this satellite would be provided by Earth s gravitational pull and tension in the cable. Right now, we don t have materials strong enough, but there are promising candidates (like carbon nanotubes). a. Calculate the work required to lift a space elevator (m SE = 1.45 x 10 4 kg) from Earth s surface to an orbital radius of 3.58 x 10 3 km above Earth s surface. Neglect any variation in tangential velocity at various heights. You may also assume that g = m/s 2. b. Calculus students only. Earth s gravitational acceleration is not a constant value of m/s 2. It may be calculated as g = Gm E. The weight of the space elevator can be expressed as F r 2 g = Gm E m SE. Remember that W = F g dr and m E = 5.97 x kg. Recalculate part a) with an r 2 integration between r = 6.38 x 10 3 km and r = 9.96 x 10 3 km (the upper orbit). 2. A block of wood (m w = 1.4 kg) hangs from a pendulum 35 cm long. A bullet (m b = 3.5 g) is fired at the block with an initial velocity of 400 m/s. It strikes the block and passes out the other side at 135 m/s. a. What is the initial tangential velocity of the pendulum? b. How high will the pendulum rise (in terms of angle)? c. What is the change in energy of the bullet-block-earth system during the collision? Page 5

6 3. The rope broke. We ll assume you were using the calculus hill, so that it reached a speed of 29.3 m/s at x = 0. In this reference frame, we should say m/s. Furthermore, due to the significant beefiness of the whale, a thin film of liquid water has formed between it and the icy ground, lowering the coefficient of kinetic friction to a. How fast is the whale moving when it reaches your house (x house = -36 m)? A perfectly inelastic collision ensues. That is, the whale slams into your house, ripping it from its foundation and dragging it along in a whale-house heap. A typical house has a weight of 50 tons. b. What is the velocity of the whale-house immediately following the collision? c. Assuming the coefficient of friction doesn t change, how far does the whale-house slide? 4. A child sees a turtle on a rock 10.0 meters from the end of a pier. The child knows nothing about momentum conservation, and steps gently onto the stern of a canoe floating adjacent to the pier, then begins to walk towards the turtle. Take the child s mass to be m and the canoe s mass to be 3m (before the kid steps on it). The overall length of the canoe is L = 3.0 m. The water may be assumed frictionless for this problem. a. What will happen to the boat as the child walks toward the turtle? b. If the kid walks forward at 1.3 m/s relative to the water, how fast is the boat moving backward, relative to the water? c. What is the kid s speed relative to the top of the boat? d. Without paddling or throwing items overboard, how close will the child be to the turtle when he reaches the bow of the boat? Hint: Momentum conservation implies that the center of mass velocity of a system remains constant unless that system is acted upon by an outside force! Page 6

7 5. A 60 N rifle fires a 3.4g bullet with a muzzle velocity of 415 m/s. What is the recoil velocity of the gun? 6. Your car rests on the edge of a precipice so that you can enjoy a view with your significant other. Whetzal, himself enjoying the view from above, sees you embrace and assumes a murder is about to take place. He jumps in his car and decides to come to the rescue. His car rolls down the icy hill, starting from rest (to be stealthy). By the time Whetzal realizes that he has made a mistake, it is too late. He tries to slam on the brakes, but the hill is icy, so k = 0. Take m w = 1800 kg and m c = 1800 kg. a. How fast is Whetzal s car moving just before the collision? Call this V w_1. A perfectly elastic collision ensues. b. What is the velocity of your car after the collision? Call this V c_2. c. What is the velocity of WHetzal s car just after the collision? Call this V w_2. d. How far will your car be from the bottom of the cliff? Hint: This is just kinematics. Page 7