Physics C Mechanics Exam 2024

Section I: Multiple-Choice Questions 5.0 m =0 P 1. k = 0.20 A block is released from rest and slides down a track with negligible friction, descending a vertical distance of 5.0 m from its initial position to Point P, as shown in the figure. The block then slides on a horizontal surface where the coefficient of kinetic friction µ k between the block and the horizontal surface is 0.20. How far does the block slide on the horizontal surface before coming to rest? (A) 1.0 m (B) 5.0 m (C) 10 m (D) 25 m Velocity P Q T R U Time O S 2. The velocity as a function of time for an object moving along a straight line is shown in the graph. For which of the following sections of the graph is the acceleration constant and nonzero? (A) QR only (B) PQ and TU only (C) RS and ST only (D) PQ, RS, ST and TU only 2024 4. The net force F exerted on an object that moves along a straight line is given as a function of time t by F (t ) = At 2 + B, where A =1 N/s 2 and B =1 N. What is the change in momentum of the object from t = 0 to t = 3 s? (A) 6 kg·m/s (B) 12 kg·m/s (C) 17 kg·m/s (D) 30 kg·m/s A spherical star spinning at an initial angular velocity ω suddenly collapses to half of its original radius without any loss of mass. Assume the star has uniform density before and uniform density after the collapse. What is the angular velocity of the star after the collapse? (C) 2ω (B) ω / 2 (D) 4ω A pendulum is constructed by attaching a 1 kg sphere to the end of a light string that is fixed to a ceiling. A second 1 kg sphere is attached the end of a spring, which is also fixed to the ceiling. The pendulum and spring have the same length when in equilibrium, as shown in the figure. Both spheres are displaced from equilibrium in the directions shown and oscillate with the same period. If the 1 kg spheres are replaced with 2 kg spheres and the amplitudes of oscillations are unchanged, which of the following is true about each of their resulting periods of oscillation? Period of pendulum A Remains the same B Remains the same C Increases D Increases Period of spring Remains the same Increases Remains the same Increases (B) B (C) C (D) D (A) A 5. (A) ω / 4 3. 2024 M A heavy sign of mass M is held at rest by two supporting wires between two buildings, with each wire making an angle θ with the vertical, as shown in the figure. What is the tension in each wire? Mg Mg (A) (B) 2sinθ 2cosθ (C) Mg sinθ (D) 6. Mg cosθ Mass ( kg ) Area (cm 2 ) Coefficient of Static Friction (µ s ) Block 1 0.75 75 0.20 Block 2 3.0 100 0.40 7. In an experiment, two blocks made of different materials are placed on the same wooden board, which is initially horizontal. The table shown provides three values for each block: the mass, the area of the side of the block in contact with the board, and the coefficient of static friction between the block and the board. One end of the board is then slowly raised. Which of the following correctly identifies the block that will start sliding down the board first, and includes appropriate reasoning? (A) Block 1, because it has less mass per unit area. (B) Block 1, because the coefficient of static friction is smaller. (C) Block 2, because it has greater mass. (D) Block 2, because the coefficient of static friction is larger. 2024 Energy 0 8. Energy 0 UG K Energy at t = t0 UG K Energy at t = tf A student lifts a ball straight upward at a constant speed. The energy bar diagrams represent the gravitational potential energy U G of the ball-Earth system and the kinetic energy K of the ball at a time t = t0 and at a later time t = t f . Which of the following energy bar diagrams correctly represents the change in mechanical energy ∆E of the ball-Earth system for the time interval ∆t = t f − t0? (A) (B) Energy Energy 0 0 E (D) Energy (C) Energy 0 E E 0 E 2024 Block Pivot Beam A uniform beam of length 0.60 m and mass 4.0 kg is fixed to a wall by a pivot. The beam is held horizontally by a string fixed to the beam and wall. A block of mass 1.0 kg is attached at the end of the beam, as shown. Which of the following is nearest to the magnitude of the torque about the pivot exerted by the weight of the block? (A) 0 (B) 6 N·m 9. (C) 10 N ⋅ m (D) 18 N·m m T2 T1 m2 m1 10. Two blocks of mass m1 and m2 are connected by a thin string that passes over a circular wheel of mass m, as shown. The wheel is attached to a vertical stand and rotates freely about its center. The string does not slip on the wheel and exerts forces T1 and T2 on the blocks. When the wheel is released from rest in the position shown, it undergoes an angular acceleration and rotates clockwise. Which of the following statements about the magnitudes of T1 and T2 is correct? (A) T1 = T2 because the tension in the string must always be constant within the string. (B) T1 = T2 because both blocks have the same acceleration. (C) T1 < T2 because m1 is farther from the wheel than m2 (D) T1 < T2 because an unbalanced clockwise torque is needed to accelerate the wheel clockwise. 2024 11. Two small, identical blocks, Block 1 and Block 2, are dropped from rest at different heights above a horizontal floor. Block 1 has speed v1 immediately before hitting the floor, and Block 2 has speed 2v1 immediately before hitting the floor. The work done by gravity on Block 1 as it falls is W1. What is the work done by gravity on Block 2 as it falls? 1 W1 4 (C) 2W1 (B) 1 W1 2 (D) 4W1 (A) y t 12. A block is hung vertically from an ideal spring. The block is pulled down, released, and allowed to oscillate. The vertical position y of the block as a function of time t is shown in the graph. Which of the following graphs best represents the corresponding acceleration a of the block as a function of time? (B) (A) a a t (C) t (D) a a t t 13. A small rock is launched from the surface of a planet with no atmosphere. The initial speed of the rock is 2vesc , where vesc is the escape speed of the planet. What is the speed of the rock when it is very far from the surface of the planet? 1 (B) vesc (A) Zero 2 (C) 2vesc (D) 3vesc 2024 R Disk B M 2R Disk A M 0 14. Two uniform disks, A and B, each of mass M, have radii 2R and R, respectively. 1 2 The rotational inertia of a uniform disk of mass m and radius r is mr . Disk A 2 rotates in a horizontal plane about its center with angular velocity ω0 and Disk B is initially held at rest. Disk B is then released and falls onto the center of Disk A such that both disks spin together about their centers without slipping. What is the angular velocity ω f of the two-disk system? (C) 4 ω0 5 (B) 1 ω0 2 2 ω0 3 (D) (A) mS 2 ω0 5 mT Leaving Sand F0 15. A truck of mass mT is initially at rest with a load of sand of initial mass ms . At time t = 0, the truck is pushed forward by a constant force F0 and the sand begins to leave the truck, as shown. The mass of sand that has left the truck as a function of time t is given by Ct, where C is a positive constant with appropriate units. At time t1 there is no sand left in the truck. Which of the following graphs most nearly shows the velocity v T of the truck as a function of time? (A) (B) vT t1 (C) vT t t1 t (D) vT vT t1 t t1 t 2024