AP Physics C: Mechanics Past Paper PDF

AP PHYSICS C: MECHANICS Scoring Guide Unit 3 Progress Check: MCQ 1. Car Mass Speed The masses and speeds of three cars are given in the table. Cars , , and have kinetic energies , , and , respectively. Which of...

AP PHYSICS C: MECHANICS Scoring Guide Unit 3 Progress Check: MCQ 1. Car Mass Speed The masses and speeds of three cars are given in the table. Cars , , and have kinetic energies , , and , respectively. Which of the following correctly compares , , and ? (A) (B) (C) (D) Answer B Correct. The kinetic energy is determined by the equation. Correctly substituting the mass and velocity of each car yields this ranking. 2. An object of mass moving in the -direction on a surface with negligible friction is pushed by a variable force parallel to its motion. The applied force varies with the object’s position as shown in the graph. At , the object’s velocity is. What is the object’s kinetic energy at ? AP Physics C: Mechanics Page 1 of 13  Scoring Guide Unit 3 Progress Check: MCQ (A) (B) (C) (D) Answer A Correct. The object’s final kinetic energy is equal to the amount the net force changes the object’s kinetic energy plus the initial kinetic energy of the object. This expression correctly relates the change in kinetic energy to the area under the force versus displacement graph and correctly evaluates the initial kinetic energy of the object. 3. A conservative force exerted on an object gives the object potential energy , where is the position of the object in meters, , and. What is the magnitude of when the object is at position ? (A) (B) (C) (D) Answer B Correct. The magnitude of the force is correctly calculated using the equation. The derivative of the potential energy function is evaluated at. Page 2 of 13 AP Physics C: Mechanics  Scoring Guide Unit 3 Progress Check: MCQ 4. A spring of spring constant is attached to the bottom of a ramp of negligible friction which makes an angle with the floor. A block of mass is pushed against the spring, compressing it a distance , as shown in the figure. The block is then released. What is the distance that the block slides up the ramp before momentarily coming to rest? (A) (B) (C) (D) Answer B Correct. This answer correctly applies the conservation of energy by identifying that the initial energy is entirely elastic potential, and the final energy is entirely gravitational potential energy for the mass- spring-Earth system. 5. A block of mass on a ramp with negligible friction is pressed against a spring with spring constant , compressing it a distance. The block is then released and travels up the ramp. What is the height of the block above its initial height when it has speed ? (A) (B) (C) (D) AP Physics C: Mechanics Page 3 of 13  Scoring Guide Unit 3 Progress Check: MCQ Answer A Correct. The energy of the block-spring-Earth system when the block is at rest against the compressed spring is elastic potential energy. The energy while it is moving at on the ramp is the sum of the kinetic energy of the block and the gravitational potential energy of the system. By applying the conservation of energy, one can solve for the height of the object. Taking the block’s initial height to be zero, the initial total energy of the system is. When the block is a distance above its initial position and moving with speed the total energy of the system is. Since energy is conserved, the initial and final energies are equal and the height can be calculated. 6. An object is pushed along the -axis by a varying force , where is a constant. The force does work on the object as it moves from to. How much work does the varying force do on the object as it moves from to ? (A) (B) (C) (D) Answer D Correct. The work done on an object by a force which varies with the object’s -position is determined using. Substituting the force function and limits of integration when the object moves from to yields. When the final position is changed to , the work increases by a factor of. 7. Relative to the ground, an object is moving rightward with a speed. Three observers each have a different constant velocity relative to the ground as follows: Observer is at rest, Observer is moving rightward at , and Observer is moving downward at. Which of the observers, if any, will measure the kinetic energy of the object to be the greatest? Page 4 of 13 AP Physics C: Mechanics  Scoring Guide Unit 3 Progress Check: MCQ (A) Observer (B) Observer (C) Observer (D) All three observers measure the kinetic energy of the object to be the same. Answer C Correct. The kinetic energy of the object is determined by the relative velocity of the object with respect to the observer. The object has a speed of relative to Observer. This speed is greater than the speed as measured by the other two observers. 8. A constant force delivers an average power of to a box. The average speed of the box is and the force is exerted in the direction of motion of the box. What is the magnitude of the force? (A) (B) (C) (D) Answer D Correct. Since power can be shown to be equal to the force exerted on the box times the speed of the box, the force exerted on the box is equal to the power delivered to the box divided by the speed of the box. 9. Four identical objects, , , , and , experience different net forces. The net work done on each object as a function of time are shown below. To which of the four objects is the greatest instantaneous power delivered at seconds? AP Physics C: Mechanics Page 5 of 13  Scoring Guide Unit 3 Progress Check: MCQ (A) (B) (C) (D) Page 6 of 13 AP Physics C: Mechanics  Scoring Guide Unit 3 Progress Check: MCQ Answer A Correct. The instantaneous power delivered to the object is equal to the slope of the graph of work as a function of time. At seconds the slope of the graph of work as a function of time for Object is the greatest and so the instantaneous power is also the greatest. 10. An object moves in the -direction with constant acceleration. Its path is described by the position versus time graph shown in the figure. The object’s kinetic energy at time is and its kinetic energy at time is. Which of the following correctly compares and and provides valid justification? (A) and are the same because the direction of velocity does not affect an object’s kinetic energy. and are the same because the acceleration is constant and therefore the kinetic energy is the (B) same at all times between and. (C) and are different because the object is moving in opposite directions at these times. (D) and are different because the object is moving with a constant acceleration between and. Answer A Correct. Kinetic energy is a scalar quantity, and therefore the magnitude of an object’s velocity is appropriate to use in calculating its kinetic energy. The slope of the graph has the same magnitude at the two times, so the speed of the object is the same at those times. AP Physics C: Mechanics Page 7 of 13  Scoring Guide Unit 3 Progress Check: MCQ 11. Sphere , with mass , is dropped from a cliff. Once Sphere has fallen distance , it has a kinetic energy. Sphere , with mass , is dropped from the same cliff. How much kinetic energy does Sphere have once it has fallen a distance of ? (A) (B) (C) (D) Answer C Correct. Applying the law conservation of energy, the change in the gravitational potential energy of the sphere-Earth system at the sphere’s initial and final positions is equal to into kinetic energy of the sphere. So, Sphere gains a kinetic energy. 12. A ball is dropped from the top of a very tall building and falls with negligible air resistance. The instantaneous power delivered to the ball by the force of gravity when the ball has a velocity of is. What is the power delivered to the ball when its velocity is ? (A) (B) (C) (D) Answer B Correct. The instantaneous power delivered to the ball by the force of gravity is equal to the force of gravity times the speed of the ball. Because the force of gravity is the same at both points, the change in power is only due to the change in the speed of the ball. Since the speed is now , the instantaneous power is. Page 8 of 13 AP Physics C: Mechanics  Scoring Guide Unit 3 Progress Check: MCQ 13. Block of mass is suspended vertically from Spring with spring constant. With the spring at its unstretched length, the block is released from rest. When the block stops momentarily after falling a distance , the Block -Spring system has mechanical energy. Block of mass is suspended by Spring with spring constant. The block is released from rest with the spring at its unstretched length. When the block stops momentarily after falling a distance , the Block -Spring system has mechanical energy. Which of the following, if any, correctly compare and ? (A) (B) (C) The comparison cannot be made without knowing the relative values of the block masses and spring (D) constants of the springs. Answer D Correct. For both systems, the total mechanical energy of the system when the block comes to rest is equal to the work done by the gravitational force on the system (because Earth is external to the system). However, the work done by the gravitational force depends on the masses of the blocks and the distances they fall, which also depend on the block masses as well as the spring constants. Therefore, the ratio of the masses and the ratio of the spring constants must be known to compare the total mechanical energies of the systems. 14. An object moves under the influence of a single force of constant magnitude. The object’s kinetic energy is constant throughout its motion. Which of the following statements is a correct claim about this force? (A) The directions of the force and velocity are the same as each other. (B) The directions of the force and velocity are opposite to each other. (C) The directions of the force and velocity are perpendicular to each other. (D) The directions of the force and velocity are neither parallel nor perpendicular to each other. Answer C Correct. A force acting perpendicular to the direction of motion does no work on the object, and therefore the object’s kinetic energy remains constant. AP Physics C: Mechanics Page 9 of 13  Scoring Guide Unit 3 Progress Check: MCQ Two particles of a certain type interact with each other with a repulsive conservative force with magnitude where is a constant and is the distance between the particles. A system of four such particles is held together to form a triangular pyramid with a distance between each pair of particles, as shown in the figure. 15. If the potential energy associated with is defined to be zero at infinite separation, what is the potential energy of the four-particle system while it is being held in the triangular pyramid arrangement shown? (A) (B) (C) (D) Answer B Correct. The equation for the change in potential energy for each object pair can be solved as:. There are 6 different object pairs therefore multiplying the energy per pair by 6 yields the answer. Page 10 of 13 AP Physics C: Mechanics  Scoring Guide Unit 3 Progress Check: MCQ 16. The four particles are simultaneously released from rest. Which of the following best describes the potential energy of the system and the magnitude of the acceleration of one of the particles after they are released? Potential Energy Acceleration A Decreasing Decreasing B Decreasing Increasing C Increasing Decreasing D Increasing Increasing (A) A (B) B (C) C (D) D Answer A Correct. The potential energy of the system of particles repelling each other has an initial positive value and approaches zero when the particles are infinitely far from each other, therefore the potential energy is decreasing as the particles move farther apart. The net force exerted on each particle is decreasing because the interaction described is inversely related to the distance cubed, therefore the acceleration also decreases. AP Physics C: Mechanics Page 11 of 13  Scoring Guide Unit 3 Progress Check: MCQ 17. A block slides down a rough ramp starting from rest at a height of and reaches a final speed of at the bottom of the ramp. Which of the following systems of objects experiences a decrease in energy and what reasoning justifies this answer? The block-ramp system, because the surface of the ramp does negative work on the block which reduces (A) the total energy of the system. The block-ramp system, because the Earth does negative work on the block which reduces the total (B) energy of the system. The block-Earth system. The component of the force exerted by the ramp's surface on the block parallel (C) to the ramp dissipates energy, reducing the mechanical energy of the system. The block-Earth system. The component of the force exerted by the ramp's surface on the block (D) perpendicular to the ramp dissipates energy, reducing the mechanical energy of the system. Answer C Correct. The component of the force exerted by the ramp's surface on the block parallel to the ramp is the frictional force exerted on the block by the ramp. Friction will dissipate mechanical energy from the block-Earth system. Page 12 of 13 AP Physics C: Mechanics  Scoring Guide Unit 3 Progress Check: MCQ 18. Two objects, and , of equal mass experience net forces that are graphed as functions of time in Figure. The velocities of the two objects are graphed as functions of time in Figure. A student claims that at time , the instantaneous power being delivered to Object is greater than the power being delivered to Object by the net forces acting on each object. Which of the following identifies whether the claim is correct or incorrect and provides appropriate evidence to support the claim? The claim is correct. At , the slope of the velocity curve for Object ’s is greater than the (A) slope of the velocity curve for Object. (B) The claim is correct. At , the net force on Object is greater than the net force on Object. The claim is correct. At , the product of the net force and velocity for Object is greater than (C) the product of the net force and velocity for Object. The claim is incorrect. The area under the force-time graph for Object from to is less (D) than the area for Object. Answer C Correct. Power is the product of force and velocity. AP Physics C: Mechanics Page 13 of 13