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AP PHYSICS FINAL 1 PRACTICE TEST NAME_________________________________ MULTIPLE CHOICE β Put your answers to the multiple choice questions here: Question Your Answer Question Your Answer 1 2 3 4 5 6 7 8 D C E A E D B A 9 10 11 12 13 14 15 16 A A C B E E B A 1. The position of an object is given as a function of time by π₯ = 7π‘ β 3π‘ 2 , where x is in meters, and t is in seconds. Its average velocity over the interval from π‘ = 2 to π‘ = 4 is A. 5 m/s B β5 m/s C. 11 m/s D. β11 m/s E. β14.5 m/s 2. An object is thrown vertically into the air. Which of the following five graphs represents the velocity of the object as a function of time? Upward is positive. 3. Two objects are traveling around different circular orbits with constant speed. They both have the same acceleration but object A is traveling twice as fast as object B. The orbit radius for object A is _____ the orbit radius for object B. A. one-fourth B. one-half C. the same as D. twice E. four times 4. A girl wishes to swim across a river to a point directly opposite, as shown at right. She can swim at 2 m/s in still water and the river is flowing at 1 m/s. At what angle π with respect to the line joining the starting and finishing points should she swim? A. 30º B. 45º C. 60º D. 63º E. 90º 5. A crate rests on a horizontal surface and a person pulls on it with a 10-N force. Rank the situations shown at right according to the magnitude of the normal force exerted by the surface on the crate, least to greatest. A. 1,2,3 B. 2,1,3 C. 2,3,1 D. 1,3,2 E. 3,2,1 6. A mass m moves on a curved path from point π to point π. Which of the diagrams at right indicates a possible combination of the net force πΉ on the mass, and the velocity π£ and acceleration π of the mass at the location shown? 7. The position of an object is given as a function of time by π₯ = 16π‘ β 3π‘ 3 , where x is in meters, and t is in seconds. The particle is momentarily at rest as π‘ = A. 0.75 s B. 1.3 s C. 5.3 s D. 7.3 s E. 9.3 s 8. A block of mass π is pulled at constant velocity along β as a rough horizontal floor by an applied force π shown. The magnitude of the frictional force is A. ππππ π B. ππ πππ C. zero D. ππ E. πππππ π 9. A stone is thrown horizontally and follows the path XYZ shown at right. The direction of the acceleration of the stone at point Y is A. B. C. D. E. 10. Block π΄, with a mass of 50 kg, rests on a horizontal table top. The coefficient of static friction is 0.40. A horizontal string is attached to π΄, passes over a massless, frictionless pulley, and then is attached to block π΅, which hangs freely. The smallest mass ππ΅ of block π΅ that will start block π΄ moving is A. 20 kg B. 30 kg C. 40 kg D. 50 kg E. 70 kg 11. A ball is held at a height π» above a floor. It is then released and falls to the floor. If air resistance can be ignored, which of the five graphs below correctly gives the gravitational potential energy of the ball as a function of the altitude π¦ of the ball? U U U U U 12. A particle is released from rest at the point π₯ = π and moves along the π₯ axis subject to the potential energy function shown at right. The particle A. moves to a point to the left of π₯ = π, stops, and remains at rest B. moves to the point π₯ = π, then moves to the left C. moves to infinity at varying speeds D. moves to π₯ = π, where it remains at rest E. moves to π₯ = π and then to π₯ = π, where it remains at rest 13. When a certain rubber band is stretched a distance π₯, it exerts a restoring force of magnitude πΉ = ππ₯ + ππ₯ 2 , where a and b are constants. The work done in stretching this rubber band from π₯ = 0 to π₯ = πΏ is 1 1 A. ππΏ2 + ππΏπ₯ 3 B. ππΏ + 2ππΏ2 C. π + 2ππΏ D. ππΏ E. 2 ππΏ2 + 3 ππΏ3 14. An elevator is rising at constant speed. Consider the following statements: I. the upward cable force is constant II. the kinetic energy of the elevator is constant III. the gravitational potential energy of the elevator is constant IV. the acceleration of the elevator is zero V. the mechanical energy of the elevator is constant A. all five are true D. only I, II, and III are true B. only II and V are true E. only I, II, and IV are true C. only IV and V are true 15. A particle has a displacement π = (5πΜ β 3πΜ) π while being acted upon by a constant force πΉ = (4πΜ + 2πΜ β 4πΜ) π. The work done on the particle by this force is A. 20 J B. 32 J C. 12 J D. 10 J E. 14 J 16. A block of mass π is initially moving to the right on a horizontal frictionless surface at a speed π£. It then compresses a spring of spring constant π. At the instant when the kinetic energy of the block is equal to the potential energy of the spring, the spring is compressed a distance of π A. π£β2π 1 B. 2 ππ£ 2 1 C. 4 ππ£ 2 D. ππ£ 2 4π 1 ππ£ E. 4 β π FREE RESPONSE PROBLEMS β 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! 1. A 0.10-kilogram solid rubber ball is attached to the end of a 0.80-meter length of light thread. The ball is swung in a vertical circle, as shown in the diagram. Point P, the lowest point of the circle, is 0.20 meter above the floor. The speed of the ball at the top of the circle is 6.0 meters per second, and the total energy of the ball is kept constant. (a) Determine the speed of the ball at point P, the lowest point of the circle. (b) Determine the tension in the thread at the top of the circle. (c) Determine the tension in the thread at the bottom of the circle. β (d) The thread breaks when the ball is at the lowest point of the circle. Determine the horizontal distance that the ball travels (from point P) before hitting the floor. (e) You measure the speed of the ball at the lowest point of the circle, and find that it is only 7.8 m/s. Determine the work done by air friction on the ball as it swung down from the highest point to the lowest point. 2. A skier of mass m will be pulled up a hill by a rope, as shown at right. The magnitude of the acceleration of the skier as a function of time t can be modeled by the equations where ππππ₯ and T are constants. The hill is inclined at an angle ο± above the horizontal, and friction between the skis and the snow is negligible. Express your answers in terms of given quantities and fundamental constants. (a) Derive an expression for the velocity of the skier as a function of time during the acceleration. Assume the skier starts from rest. (b) Derive an expression for the work done by the net force on the skier from rest until terminal speed is reached. (c) Determine the magnitude of the force exerted by the rope on the skier at terminal speed. (d) Suppose that the magnitude of the acceleration is instead modeled as for all t > 0 , where amax and T are the same as in the original model. On the axes below, sketch the graphs of the force exerted by the rope on the skier for the two models, from t = 0 to a time t > T . Label the original model and the new model. 3. An amusement park ride features a passenger compartment of mass M that is released from rest at point A, as shown in the figure above, and moves along a track to point E. The compartment is in free fall between points A and B, which 3π are a distance of 4 apart, then moves along the circular arc of radius R between points B and D. Assume the track is frictionless from point A to point D and the dimensions of the passenger compartment are negligible compared to R. (a) On the dot below that represents the passenger compartment, draw and label the forces (not components) that act on the passenger compartment when it is at point C, which is at an angle π from point B. (b) In terms of π and the magnitudes of the forces drawn in part (a), determine an expression for the magnitude of the centripetal force acting on the compartment at point C. If you need to draw anything besides 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). (c) Derive an expression for the speed π£π· of the passenger compartment as it reaches point D in terms of M, R, and fundamental constants, as appropriate. A force acts on the compartment between points D and E and brings it to rest at point E. (d) Suppose the compartment is brought to rest by friction. Calculate the numerical value of the coefficient of friction π between the compartment and the track. (e) Now consider the case in which there is no friction between the compartment and the track, but instead the compartment is brought to rest by a braking force βππ, where k is a constant and π is the velocity of the compartment. Express all algebraic answers to the following in terms of M, R, k, π£, and fundamental constants, as appropriate. i. Derive an expression for the acceleration π of the compartment. ii. On the axes below, sketch a graph of the magnitude of the acceleration of the compartment as a function of time. On the axes, explicitly label any intercepts, asymptotes, maxima, or minima with numerical values of algebraic expressions, as appropriate.