3. When a certain rubber band is stretched a distance x, it exerts a restoring force F = ax + bx², where a and b are constants. The work done in stretching this rubber band from x = 0 to x = L is:
(A) aL²/2 + bL³/3
(B) aL+bL²/2
(C) a + 2bL
(D) aL + 2bL²
(E) aL² + bLx³.

 50. When a certain rubber band is stretched a distance x, it exerts a restoring force F = ax + bx2 , where a and b are constants. The work done in stretching this rubber band from x = 0 to x = L is: (A) aL2 + bLx3 (B) aL + 2bL2 (C) a + 2bL (D) bL (E) aL2 /2 + bL3 /3 

4. The potential energy of a 2.0-kg particle moving along the x axis is given by U(x)=5.0J/m²)x4 J.When the particle is at x = 1.0 m it is traveling in the positive x direction with a speed of 5.0 m/s. It next stops momentarily to turn around at about x = (A) 0 (B) 1.56 m (C) -1.56 m (D) 3.02 m (E) -3.02 m.

5. A sled loaded with sand, slides along a horizontal frictionless track. As the sled moves, sand trickles out at a constant mass-reduced rate through a hole in the back. The speed of the sled will: (A) decrease at a constant rate (B) increase at a constant rate (C) remain the same (D) decrease at a variable rate (E) increase at a variable rate.

6. When the speed of a rear-drive car is increasing on a horizontal road the direction of the frictional force on the tires is: (A) forward for all tires (B) backward for all tires (C) forward for the front tires and backward for the rear tires (D) backward for the front tires and forward for the rear tires (E) zero.

7. Two uniform cylinders have different masses and different rotational inertias. They simultaneously start from rest at the top of an inclined plane and roll without sliding down the plane. The cylinder that gets to the bottom first is: (A) the one with the larger mass (B) the one with the smaller mass (C) the one with the larger rotational inertia (D) the one with the smaller rotational inertia (E) neither (they arrive together).

8. A meter stick 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 = 0.5 m (B) a = 0.3 m (C) a = 0.2 m (D) a = 0.1 m (E) a = 0 m.

9. A quantity of an ideal gas is compressed to half its initial volume. The process may be adiabatic, isothermal or isobaric. Rank those three processes in order of the work required of an external agent, least to greatest. (A) adiabatic, isothermal, isobaric (B) adiabatic, isobaric, isothermal (C) isothermal, adiabatic, isobaric (D) isobaric, adiabatic, isothermal (E) isobaric, isothermal, adiabatic.

10. For all reversible processes involving a system and its environment: (A) the entropy of the system does not change. (B) the entropy of the system increases. (C) the total entropy of the system and its environment does not change. (D) the total entropy of the system and its environment increases. (E) none of the above (the provided information is not enough).

11. The figure shows two charged particles (q₁ = +6e, q2 = -2e) that are fixed in place and separated by distance d = 1.50 m. At what x coordinate (m) can a third charged particle be placed such that the net force on the third particle is zero?  (A) 0.35 (B) -3.96 (C) 3.55 (D) -0.54 (E) 7.10.

12. The figure shows six charged rods. Some have the same sign charge throughout and are uniformly charged. The rest have one sign on one half and the opposite sign on the other half, with each half uniformly charged. For each rod, a point P on a perpendicular bisector is indicated. In which situation is the net electric field at P in the positive direction of the y axis?(A) 2 and 5, (B) 2 and 6, (C) 4 and 5, (D) 1 and 4, (E) 3 and 5.

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