h Students set up an experiment with a small block on an ramp. The block of mass M = 3.0 kg is released from rest at the top of the curved ramp. The length of the ramp as measured along the curve is _ = 3.0 m, and the height is h = 1.5 m, as shown. There is negligible friction between the small block and the ramp. 9. The speed of the block at the bottom of the ramp is most nearly (A) 0 (B) 5.5 m/s (C) 7.7 m/s (D) 9.5 m/s (E) 13 m/s Ap CallegsBoard Test Booklet Unit 3.3 Conservation of Energy 10 Daily 10. U (J) 3 00808080 Motion Sensor Students perform an experiment to test the conservation of mechanical energy of a vertical block-spring system, as shown in the figure. The position 2 = 0 is the point where the block of mass m hangs at equilibrium. The weight of the block and the stretch of the spring to this equilibrium position are used to determine the value of the spring constant k. The block is pulled down and released from rest. A motion sensor collects data for the position z and velocity u of the block. These data are used to create the graph of potential energy U of the spring-block system, kinetic energy K of the block, and total energy E of the spring-block system as functions of 2 shown. Which of the following is the most likely source of error to describe the variance in the total energy of the block-spring system indicated in the graph? (A) Air resistance is a nonconservative force that is significantly reducing the total energy of the system. (B) Internal friction of the spring is generating a small but significant amount of thermal energy. (C) The motion of the spring has been neglected and omitted from consideration. (D) The value of g is assumed constant, but it has a notable variation as the height of the block changes. (E) The graph omits a small but significant amount of gravitational potential energy: U = mgh.Block 2 Block 1 Two blocks of equal mass are connected by a string that passes over a pulley. as shown in the gure. Block I hangs from the string, derives an and block 2 can slide on a table. The system is released from rest. Using conservation of energy, a smdent expression for the speed 1: of block I when it has fallen a distance it. after the system has been released from resl and obtains the equation 1.! = u" 9h. 7. The experiment is perfonned and both h. and u are measured, but the measured value of 1.! is larger than the calculated value using the stLtdent's equation. Which of the following sources of experimental error could have caused the discrepancy? (A) Friction between the table and block 2 is not negligible. (3) (C) The mass ofbloek 2 is aemallv greater than the mass of block 1. Air resistance is not negligible. [D] There is friction between the rim ofthe pulleyr disk and the string. (13} The table is not horizontal. Test Hwklel Unit 3.3 Conservation of Energy ll] Daily 0.20 kg A simple pendulum consisting of a 1.0 In long string and a 0.20 kg bob is pulled to the side so that the string makes lowest an angle of 20 with the vertical; If the gravitational potential energy.r of the bob-Earth system is zero at the point of the pendulum's are, the angle at which the gravitational potential Energy of the bobEarth system is equal to the kinetic energy ot'the bob is most nearly (M {B} (Q (D) (E) 6.9' 9.8' 10' 14 l9" Unit 3.4 Power 10 Daily 1. Power (KW) 2 8 Time ( S ) The graph above shows the power output as a function of time for a pump motor. The work done by the motor during the time interval 0 to 8 s is (A) 24KJ (B) 30kJ (C) 36kJ (D) 42kJ (E) 48 k.J 2. During a certain time interval, a constant force delivers an average power of 4 watts to an object. If the object has an average speed of 2 meters per second and the force acts in the direction of motion of the object, the magnitude of the force is (A) 1 (B) 8 N (C) 6 N 4N (E)