Physics 1 Algebra-Based Exam 2024

Section I: Multiple-Choice Questions A C 1. B Attachment Blocks A and B, of masses mA and mB , respectively, are at rest on a horizontal surface with negligible friction. Block A is attached to the table. Block C of mass mC is suspended by a string that is tied to Block B and passes over a pulley as shown. The blocks all remain at rest. Which of the following gives the magnitude of the force exerted by Block A on Block B? (A) mB g (B) mC g m m g (C) A C mA + mB mm g (D) B C mA + mB 2024 vy vx Time 2. Time An object is subject to multiple forces that result in the object having horizontal and vertical velocity components v x and v y , respectively as a function of time, as shown. Which of the following diagrams could represent the forces exerted on the object? (A) +y +y +y +y +x +x +x +x (B) +y +y +y +y +x +x +x +x (C) +y +y +y +y +x +x +x +x (D) +y +y +y +y +x +x +x +x 2024 Block F0 0 cm 3. 10 cm 20 cm 30 cm 40 cm 50 cm 60 cm 70 cm 80 cm 90 cm 100 cm A constant force F0 is exerted continuously on a block that is initially at rest on a horizontal surface. The change in kinetic energy of the block while the block is moved from position x = 0 to x = 50 cm is K1 , and the change in kinetic energy of the block as the block is moved from x = 50 cm to x =100 cm is K 2 . How does K1 compare to K 2 , and why? (A) because the velocity increases by the same amount between 0 cm to 50 cm and between 50 cm to 100 cm. (B) because the applied force does the same work on the block between 0 cm to 50 cm and between 50 cm to 100 cm. (C) because the block is moving faster on average between 50 cm to 100 cm than it is between 0 cm to 50 cm. (D) because the rate of change of kinetic energy is greater between 50 cm to 100 cm than it is between 0 cm to 50 cm. Questions 4 and 5 refer to the following. v (m/s) O 1 2 3 4 5 6 t (s) At time t = 0, a car is moving in the positive direction along a straight road. The graph represents the car’s velocity v as a function of time t. The car’s position at t = 0 is x = 0. 4. The position of the car at times 1 s, 2 s, and 3 s are x1 , x2, and x3, respectively. Which of the following correctly ranks x1 , x2, and x3 from greatest to least? (A) x1 > x 2 > x 3 (B) x 3 > x 2 > x1 (C) x 2 > x 3 > x1 (D) x1 > x 3 > x 2 2024 5. Which of the following graphs could represent the acceleration a of the car as a function of time t? (A) a (m/s2) O 1 2 3 4 5 2 3 4 5 2 3 4 5 2 3 4 5 t (s) (B) a (m/s2) O 1 t (s) 2 (C) a (m/s ) O 1 t (s) (D) a (m/s2) O 1 t (s) Pivot 30˚ L Wall Rod Floor 6. A uniform rod of mass M0 and length L is free to rotate about a pivot at its left end and is released from rest when the rod is 30° below the horizontal, as shown 1 in the figure. With respect to the pivot, the rod has rotational inertia I 0 = M 0 L2. 3 Which of the following expressions correctly represents the magnitude of the net torque exerted on the rod about the pivot at the moment the rod is released? (A) (B) (C) M 0 gLsin (30°) (D) 2024 Block 1 Wall M −d0 Equilibrium d0 Trial 1 Wall Floor M M −d0 Equilibrium d0 Trial 2 7. Floor In Trial 1 of an experiment, Block 1 of mass M is oscillating at the end of a spring. The other end of the spring is attached to a wall. Friction between the block and the floor is negligible. Block 1 oscillates with amplitude d0 . In Trial 2 of the experiment, a second identical block is attached to Block 1, and the two-block system oscillates with amplitude d0 . How do the maximum speeds and maximum kinetic energies in the two trials compare? Maximum Speed Maximum Kinetic Energy (A) Greater in Trial 1 Greater in Trial 1 (B) Greater in Trial 1 Equal in both trials (C) Equal in both trials Equal in both trials (D) Equal in both trials Greater in Trial 2 (A) A (B) B (C) C (D) D 2024 8. A small rock sits at the at the bottom of a cup filled with water. The upward force exerted by the water on the rock is F0 . The water is then poured out and replaced 3 by an oil that is as dense as water, and the rock again sits at the bottom of 4 the cup, completely under the oil. Which of the following expressions correctly represents the magnitude of the upward force exerted by the oil on the rock? (A) 3 F0 4 (B) F0 4 F0 3 (D) The answer cannot be determined without knowing the rock’s volume. (C) x (m) 6 5 4 3 2 1 0 9. t (s) 0 1 2 3 4 5 6 Two blocks move on a straight, level track, where friction between the blocks and the track is negligible. Block B of mass 4.0 kg is initially at rest. Block A of mass 2.0 kg slides to the right and collides with Block B at time t = 3 s. The figure shows the position x of Block A as a function of time t. Which of the following is most nearly the momentum of Block B after the collision? (A) 2.0 kg·m/s (B) 3.0 kg·m/s (C) 4.0 kg·m/s (D) 6.0 kg·m/s 2024 A B 10. Block A is initially held at rest on a horizontal table and is connected to a horizontal spring that is fixed to a wall. The spring is initially at its relaxed length. Block A is connected to Block B by a string passing over a pulley, as shown. There is friction between Block A and the table. When Block A is released, Block B moves downward, and Block A moves to the right along the surface of the table until the system returns to rest. How do the mechanical energies of the two-block – spring system and the two-block –spring – Earth system change from when Block A is held at rest to when the blocks return to rest? Two-Block-Spring System Two-Block-Spring-Earth System (A) Increases Decreases (B) Decreases Increases (C) Remains Constant Decreases (D) Remains Constant Remains Constant (A) A (B) B (C) C (D) D 2024 Block 2 Block 1 11. Block 1 slides across a horizontal surface where friction between Block 1 and the surface is negligible. Block 2 is then carefully dropped from a small height above Block 1, as shown in the figure. Block 2 sticks to Block 1 and the two-block system continues to slide horizontally together. Which of the following correctly describes the change in speed of Block 1 immediately after Block 2 sticks to Block 1 ? (A) The speed of Block 1 is less because of conservation of mechanical energy. (B) The speed of Block 1 is less because of conservation of linear momentum. (C) The speed of Block 1 is greater because of the conservation of mechanical energy. (D) The speed of Block 1 is greater because of the conservation of linear momentum. 12. Two systems, a simple pendulum and a mass hanging on an ideal spring, both have a period of 1 s when set into small oscillatory motion on Earth. They are then set into small oscillatory motion on Planet X, which has the same diameter as Earth but twice the mass. Which of the following statements is true about the periods of the two objects on Planet X compared to their periods on Earth? (A) Both periods of oscillation are shorter. (B) Both periods of oscillation are the same. (C) The period of the mass on the spring is shorter; the period of the pendulum is the same. (D) The period of the pendulum is shorter; the period of the mass on the spring is the same. 2024 3.0 kg 0.8 m 0.8 m 3.0 kg t=0 t = t1 13. An object of mass m = 3.0 kg is attached to one end of a string with negligible mass and length L = 0.80 m. The object is released from rest at time t = 0, when the string is horizontal. At time t = t1 the object is at the location shown in the figure, where the string is vertical. Which of the following is most nearly the magnitude of the tension in the string at time t = t1? (A) 4 N (B) 30 N (C) 60 N (D) 90 N 2024 20 15 Object A Object B 10 5 0 t (s) 0 1 2 3 4 5 14. Two disks, A and B, each experience a net external torque that varies over an interval of 5 seconds. Disk B has a rotational inertia that is twice that of Disk A. The graph shown represents the angular momentum of the two disks as functions of time between time t = 0 s and t = 5 s. The average magnitudes of the net torques exerted on disks A and B from t = 0 to t = 5 s are and respectively. Which of the following expressions correctly relates the magnitudes of the average torques? (A) (B) (C) (D) Wide Section Narrow Section R 2R 15. An fluid flows through the two sections of cylindrical pipe shown in the figure. The narrow section of the pipe has radius R and the wide section has radius 2R. What is the ratio of the fluid’s speed in the wide section of pipe to its speed in v the narrow section of pipe, wide ? v narrow 1 (A) 4 1 (B) 2 (C) 2 (D) 4 2024