AP PHYSICS 1 UNIT 4 / FINAL 1 PRACTICE TEST

Transcription

1 AP PHYSICS 1 UNIT 4 / FINAL 1 PRACTICE TEST NAME FREE RESPONSE PROBLEMS Put all answers on this test. Show your work for partial credit. Circle or box your answers. Include the correct units and the correct number of significant figures in your answers! Questions 1-3 cover Unit 4: 1. A spring that can be assumed to be ideal hangs from a stand, as shown at right. You wish to determine experimentally the spring constant k of the spring. (a) What additional, commonly available equipment would you need? (b) What measurements would you make? (c) How would k be determined from these measurements?

2 (d) Assume the spring constant is determined to be 500 N/m. A 2.0-kg mass is attached to the lower end of the spring and released from rest. Find the farthest distance the spring is stretched as the mass drops. (e) Suppose the spring is now used in a spring scale that is limited to a maximum value of 25 N, but you would like to weight an object of mass M that weighs more than 25 N. You must use commonly available equipment and the spring scale to determine the weight of the object without breaking the scale. Draw a clear diagram that shows one way that the equipment you choose could be used with the spring scale to determine the weight of the object, and explain how you would make the determination.

3 2. A block is initially at position x = 0 and in contact with an uncompressed spring of negligible mass. The block is pushed back along a frictionless surface from position x = 0 to x = D. The block is then released. At x = 0 the block enters a rough part of the track and eventually comes to rest at position x = 3D. The coefficient of kinetic friction between the block and the rough track is μ. (a) On the axes below, sketch and label graphs of the kinetic energy K of the block as a function of the position of the block between x = D and x = 3D. You do not need to calculate values for the vertical axis. (b) On the same axes above, sketch and label a graph of the potential energy U of the block-spring system as a function of the position of the block between x = D and x = 3D. You do not need to calculate values for the vertical axis, but use the same vertical scale that you used for the kinetic energy. The spring is now compressed twice as much, to x = 2D. A student is asked to predict the final position of the block. The student reasons that since the spring is compressed twice as much as before, the block will have twice as much energy when it leaves the spring, so it will slide twice as far along the track, stopping at position x = 6D. (c) Which aspects of the student s reasoning, if any, are correct? Explain how you arrived at your answer.

4 (d) Which aspects of the student s reasoning, if any, are incorrect? Explain how you arrived at your answer. (e) Use quantitative reasoning, including equations as needed, to develop an expression for the new final position of the block. Express your answer in terms of D. (f) Use your reasoning in (e) to justify your answers to (c) and (d) explain how the correct and incorrect aspects of the student s reasoning identified in (c) and (d) are confirmed by your mathematical relationships in part (e).

5 3. Starting from rest at point A, a 50 kg person swings along a circular arc from a rope attached to a tree branch over a lake, as shown in the figure at right. Point D is at the same height as point A. The distance from the point of attachment to the center of mass of the person is 6.4 m. Ignore air resistance and the mass and elasticity of the rope. The person swings two times, each time letting go of the rope at a different point. (a) On the first swing, the person lets go of the rope when first arriving at point C. Draw a solid line on the diagram above to represent the trajectory of the center of mass after the person releases the rope. (b) On the second swing, the person lets go of the rope at point D. Draw a dotted line on the diagram above to represent the trajectory of the center of mass after the person releases the rope. (c) The center of mass of the person standing on the platform is at point A, 4.1 m above the surface of the water. Calculate the gravitational potential energy when the person ins at point A relative to when the person is at the surface of the water.

6 (d) The center of mass of the person at point B, the lowest point along the arc, is 2.4 m above the surface of the water. Calculate the person s speed at point B. (e) Suppose the person swings from the rope a third time, letting go of the rope at point B. Calculate R, the horizontal distance moved from where the person releases the rope at point B to where the person hits the water. (f) If the person does not let go of the rope, how does the person s kinetic energy K c at point C compare with the person s kinetic energy K B at point B? K c > K b K c < K b K c = K b Provide a physical explanation to justify your answer.

7 Questions 4-5 cover Final 1: 4. Two identical spheres are released from a device at time t = 0 from the same height H, as shown at right. Sphere A has no initial velocity and falls straight down. Sphere B is given an initial horizontal velocity of magnitude v 0 and travels a horizontal distance D before it reaches the ground. The spheres reach the ground at the same time r f, even though sphere B has more distance to cover before landing. Air resistance is negligible. (a) The dots below represent spheres A and B. Draw a free-body diagram showing and labeling the forces (not components) exerted on each sphere at time t f 2. (b) On the axes below, sketch and label a graph of the horizontal component of the velocity of sphere A and of sphere B as a function of time.

8 (c) in a clear, coherent, paragraph-length response, explain why the spheres reach the ground at the same time even though they travel different distances. Include references to you answers to parts (a) and (b).

9 5. Beginning at time t = 0, a student exerts a horizontal force on a box of mass 30 kg, causing it to move at 1.2 m/s toward an elevator door located 16 m away, as shown at right. The coefficient of kinetic friction μ k between the box and the floor is (a) on the dot below that represents the box, draw and label the forces (not components) that act on the box as it moves at constant speed. (b) Calculate the magnitude of the horizontal force the student must exert on the box to keep it moving at 1.2 m/s. If you need to draw anything other than what you have shown in part (a) to assist in your solution, use the space below. Do NOT add anything to the figure in part (a).

10 At t = 4.0 s, the elevator door opens and remains open for 5.0 s. The student immediately exerts a larger constant force on the box and the front of the box reaches the elevator door just as it starts to close. (c) Calculate the magnitude of the new force that the student exerts. (d) On the axes below, sketch graphs of the acceleration a, velocity v, and position x of the box versus time t between t = 0 and the time the front of the box reaches the elevator.