3. 2.5 U(J) MAMMA Time (s) A 2.00 kg block is attached to a horizontal ideal spring with a spring constant k = 100. The block-spring system is set on a horizontal surface with negligible friction. A graph of the potential energy ( as a function of time t for this system is shown. The maximum displacement Myx of the block from its equilibrium position and the maximum speed Umar of the block during the motion represented by the graph are most nearly (A) TMAX = 2.0 m and VMAX = 1.4 (B) "MAX = 1.4 and VMAX = 0.20% (C) @MAX = 0.20 m and VMAX = 1.4 (D) EMAX = 0.40 m and VMAX = 1.4 (E) TMAX = 0.04 m and VMAX = 2.0% 4. A block is released from rest at the top of a hill of height h. If there is negligible friction between the block and the hill, the block arrives at the bottom of the hill with speed v. The block is released from rest at the top of another hill with a rough surface and height h. If one-half of the initial mechanical energy of the block-Earth system is lost due to friction as the block descends the hill, the block will reach the bottom of the hill with a speed of (A) TU I(B) 20 (C) (D) V2v (E)A conservative force has the potential energy function O (@), indicated by the graph shown. A particle of mass 3 kg moving in one dimension under the influence of this force has kinetic energy 9.5 J when it is at a position * = 10m. U(J) 1J+ - x (m) 5 10 15 18 20 -1J+ -2J+ 5. At which of the following positions does the object come to rest? (A) = = 4m B) = 10m (C) = = 5 mand x = 15 m Between 2 = 18 m and = = 20m (E) At no point on the graph does the object come to rest. 6. At @ = 15m, the speed of the particle is most nearly (A) 0m (B) 2.24 I (C) 2.74- (D) 5 m (E) 7.5 mBlock 2 Block 1 Two blocks of equal mass are connected by a string that passes over a pulley, as shown in the figure. Block 1 hangs from the string, and block 2 can slide on a table. The system is released from rest. Using conservation of energy, a student derives an expression for the speed v of block I when it has fallen a distance h after the system has been released from rest and obtains the equation u = v gh. 7. The experiment is performed and both h and v are measured, but the measured value of v is larger than the calculated value using the student'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. (B) The mass of block 2 is actually greater than the mass of block 1. (C) Air resistance is not negligible. (D) There is friction between the rim of the pulley disk and the string. (E) The table is not horizontal.8. 1.0 m 201 - 0.20 kg A simple pendulum consisting of a 1.0 m long string and a 0.20 kg bob is pulled to the side so that the string makes an angle of 20" with the vertical. If the gravitational potential energy of the bob-Earth system is zero at the lowest point of the pendulum's arc, the angle at which the gravitational potential energy of the bob-Earth system is equal to the kinetic energy of the bob is most nearly (A) 6.9" (B) 9.8 (C) 10' (D) 14" (E) 19'M L- 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