4. A particle moves along the x axis. The net force on the particle, which is conservative, is given by F = (8 N/m³)x3. If the potential energy is taken to be zero for x = 0 then the potential energy as a function ofx is given by:
(A) (2 J/m⁴)x⁴
(B) (-2 J/m⁴)x⁴ 
(C) (24 J/m²)x⁴ 
(D) (-24 J/m²)x²
(E) (8 J/m²)x².

1. A jet plane in straight horizontal flight passes over your head. When the plane is directly above you, the sound seems to come from a point behind the plane in a direction 45° from the vertical. The speed of the sound is vs. The speed of the plane is about: (A) vs (B) 0.5vj (C) 0.7 Ivj (D) 1.41vj (E) 2vs.

2. A horizontal force of 10 N pushes a 0.5-kg block against a vertical wall. The book is initially at rest. If the static coefficient of friction (μs) is 0.6 and the kinetic coefficient of friction  (μk) is 0.4, which of the following is true? (A) The frictional force is 4.9 N (B) The frictional force is 6.0 N (C) The frictional force is 4.0 N (D) The normal force is 4.9 N (E) The normal force is 10.9 N.

3. An ideal spring is hung vertically from the ceiling. When a 2.0-kg mass hangs at rest from it, the spring is extended 5.0 cm from its relaxed length. A downward external force is now applied to the mass to extend the spring an additional 10 cm. While the spring is being extended by the force, the work done by the spring is about: (A) -3.92 J (B)-1.96 J (C) 0 J (D) 1.96 J (E) 3.92 J.

5. Bullets from two guns are fired with the same velocity. The bullet from gun #1 is twice as heavy as the bullet from gun #2, and gun #1 weighs three times as much as gun #2. The ratio of the momentum imparted to gun #1 to that imparted to gun #2 is: (A) 2:3 (B) 3:2 (C) 3:1 (D) 2:1 (E) 6:1.

6. A forward force acting on the axle accelerates a rolling wheel on a horizontal surface. If the wheel does not slide, the frictional force of the surface on the wheel is: (A) zero. (B) in the forward direction and does zero work on the wheel. (C) in the forward direction and does positive work on the wheel. (D) in the backward direction and does zero work on the wheel. (E) in the backward direction and does negative work on the wheel.

7. A 2.0-kg block starts from rest on the positive x axis 3.0 m from the origin and thereafter has an acceleration given by . The torque, relative to the origin, acting on it at the end of 2.0 s is: (A) (0 N●m) (B)(-18N●m) (C) (+24 N●m)  (D)(-I44N●m) (E) (+144 N● m) .

8. A stick of length 1.0 m is pivoted at a point a distance a from its center and swings as a physical pendulum. Of the following values for a, which results in the shortest period of oscillation? (A) a = 0.1 m (B) a = 0.2 m (C) a = 0.3 m (D) a = 0.4 m (E) a = 0.5 m.

9. The displacement of a string wave is given by: y(x,t) = ymsin(kx + ωt). The traveling wave velocity is: (A) +2πkω(B)-2πkω(C) +kω (D) +ω/k (E) -ω/k .

10. A hot object and a cold object are placed in thermal contact and the combination is isolated. They transfer energy until they reach a common temperature. The change △Sh in the entropy of the hot object, the change △Scin the entropy of the cold object, and the change△Sioiai in the entropy of the combination are: (A) △Sh > 0,△Sc>0, △Stotai ＞ 0 (B) △Sh<0，△Sc> 0, △Sioiai= 0 (C) △Sh ＞ 0, △Sci<0 ,△Sioiai=0 (D)△Sh> 0, △Sc<  0, △Sioiai>0(E) A△Sh＜0, △Sc＞ 0, △Sioiai＞ 0.

11. The units ofk= 1/(4πε0)are: (A) N2/C2, (B) N●m/C, (C) N2●m2/C2, (D) N●m2/C2, (E) m2/C2.