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F (N) 2Fot Fot 10 /2 to - 1 (5 ) Object X 5. Object X is constrained to move along a straight line. The graph above shows the net force exerted along that line as a function of time. Write an expression for the change in momentum of the object as a function of Fo and to. Answer: AP = Fest 6. During practice, a student kicks a 0.40 kg soccer ball with a velocity of 8.5 m/s into a 0.15 kg bucket lying on its side. The bucket travels with the ball after the collision. What is the velocity of the combined bucket and ball after the collision? (. 4 kg) (8m/s ) + (.Iskgt (0) = (6kg)(?m/s) voiq 2905 Answer : 5 3 beTs 3.2kam/s = 6kq (?m/s ) + me graph for it 3 Extra Credit: A ball is moving to the right on a frictionless surface, as shown below, due to a previously applied force. Draw a vector to indicate how you would need to hit the ball to both change its direction AND decrease the ball's kinetic energy? END SECTION II2.5 2.0 Force (x 103 N) 1.5 / A=10 1.0 0.5 2.0 4.0 6.0 8.0 10.0 Time (x 10-3 s) mebi 2. While playing basketball in PE class, Logan lost his balance after making a lay-up and collided with the padded wall behind the basket. The collision lasted 10 milliseconds, as shown in the graph above, during which time his 27 kg body decelerated to a stop. The y-axis of this graph represents the force exerted by the wall on Logan as he slowed to a stop. What was Logan's initial speed when he first impacted with the wall? FAC = AP 10 = 27 ( ? ) + 0 = 0 6 25 Answer : X 3. Two identical carts of mass m collide elastically. A blue cart is initially at rest. The red cart is initially moving forward with speed v. After the collision, the blue cart is moving forward with speed 2v. (a) What is the speed and direction of the red cart after the collision in terms of v? AtV ) + mr 5 + Miv = mb( 2v)+ mr( ? ) V - 2V = - V Answer: V PArV MD (21 ) - Vr (b) Sketch a momentum-time graph for the blue cart on the axes below. Assume any changes in speed are instantaneous. p (kgm/s) + 5 close ! 2 v > t (s) Extra credit: Is this scenario "real" or does it break the laws of physics? Justify in a few words. X9 +1 SECTION II: Free-Response Time-30 minutes 20 6 Questions Plunger 1 1. Identical blocks 1 and 2 are placed on a horizontal surface at points A and E, respectively, as shown. The surface is frictionless except for the region between points C and D, where the surface is rough. Beginning at time tA, block 1 is pushed with constant horizontal force from point A to B by a mechanical plunger. Upon reaching point B, block 1 loses contact with the plunger and continues moving to the right along the horizontal surface toward block 2. Block 1 collides with and sticks to block 2 at point E, after which the two-block system continues moving across the surface, eventually passing point F. On the axes below, sketch the kinetic energy of block 1 as a function of time, from ta until the blocks pass point F at time t. The times at which block 1 reaches points A through F are indicated on the time axis. Kinetic Energy of Block 1 X X 0 0 - TB D Time * 2 / 4Cart A Cart B 2H 2M 20 Cart A has mass Mand is released from rest at a height 2H on a ramp, as shown above. Cart B has mass 2M and is released from rest at a height Hon a different ramp. The carts roll toward each other, have a head-on collision on the horizontal portion of the ramp, and stick together. The masses of the carts' wheels are negligible, as are any frictional or drag forces. (a) Express the velocities of these carts at the bottom of the ramps, before the collision, as a function of height / (and any fundamental constants such as g). Write your answers in the spaces provided below. the speed of Cart A is the speed of Cart B is (b) Express the momentum of Cart B at the bottom of the ramp, just before it collides with Cart A, as a function of height H, mass, (and any fundamental constants such as g). Write your answers in the spaces provided below. You do not need to simplify. Answer: (c) Indicate the direction in which the two carts move after the collision. Carts remain at rest Carts move to the left Carts move to the right (d) Consider the time interval from when the two carts are released until just after they collide and stick. For the system consisting of the two carts and Earth, indicate whether the total mechanical energy increases, decreases, or remains the same. Increases Decreases _ Remains the same (No need to justify)