36. A small block of mass m rests on the sloping side of a triangular block of mass M which itself rests on a horizontal table as shown in the figure below. Assuming all surfaces are frictionless, determine the magnitude of the force F that must be applied to M so that m remains in a fixed position relative to M. Hint: 1. Take x and y axes horizontal and vertical. 2. Focus at the object m.

(A) mg sinθ 
(B) mg tanθ 
(C) (m+M)g tanθ
(D) (m+M)g sinθ
(E) None of these

32. A part of the square that has sides of length L is removed from one corner. The center of mass of the remainder moves from C to C'. The displacement of the x coordinate of the center of mass (from C to C') is ______. (A) (2/3)L (B) (1/6)L (C) (1/8)L (D) (1/10)L (E) (1/12)L

複選題33. The string and the pulley are massless, and the coefficient of static and kinetic frictions are 0.2 and 0.1, respectively, for both table 1 (T1) and 2 (T2). If m1 = 2 kg, m2 = 3 kg, and m = 1.5 kg, find the acceleration of m. (Gravitational acceleration g = 10 m/s2 )  (AB) 7.7 m2 /s (AC) 8.7 m2 /s (AD) 9.7 m2 /s (AE) 10.7 m2 /s (BC) 11.7 m2 /s (BD)一律送分

34. Aluminum Rod #1 has a length L and a diameter d. Aluminum Rod #2 has a length 2L and a diameter 2d. If Rod #1 is under tension T and Rod #2 is under tension 2T, how do the changes in length of the two rods compare? (A) They are the same. (B) Rod #1 has double the change in length that Rod #2 has. (C) Rod #2 has double the change in length that Rod #1 has. (D) Rod #1 has quadruple the change in length that Rod #2 has. (E) Rod #2 has quadruple the change in length that Rod #1 has.

35. A toy car is running on a banked circular track of radius 10 m, as shown below. If the car weighs 5 kg and on wet ice, find the maximum velocity for the car to keep on the track without skid. (Gravitational acceleration g = 10 m/s2 , cos30° = 0.87, cos60° = 0.5)  (A) 5.4 m/s (B) 7.6 m/s (C) 9.4 m/s (D) 12.6 m/s (E) 15.7 m/s

37. The four tires of an automobile are inflated to a gauge pressure of 2.0 × 105 N/m2 (29 psi). Each of the four tires has an area of 0.024 m2 that is in contact with the ground. Determine the weight of the auto. (A) 4.80 × 103N (B) 1.92 × 104N (C) 7.68 × 104N (D) 8.33 × 106N (E) 2.08 × 107N

38. A 2-kg block slides down a frictionless incline from point A to point B. A force (magnitude P = 3 N) acts on the block between A and B, as shown in the figure Points A and B are 2 m apart. If the kinetic energy of the block at A is 10 J, what is the kinetic energy of the block at B? (Gravitational acceleration g = 10 m/s2 ) (A) 17 J (B) 20 J (C) 24 J (D) 27 J (E) 37 J

39. On a bridge, a man (weight = 70 kg) plays bungee jumping by tying himself to one end of an elastic rope. The rope has a length of 100 m, and the height of the bridge is 500 m. After jumping, the man begins to bounce back 10 seconds later. What is the effective weight of the man at the bouncing point? (Gravitational acceleration g = 10 m/s2 ) (A) 83 kg (B) 95 kg (C) 102 kg (D) 117 kg (E) 127 kg

40. How much energy is required to move a mass m object from the Earth’s surface to an altitude twice the Earth’s radius RE? (A) (-1/2)mgRE (B) (1/2)mgRE (C) (-2/3)mgRE (D) (2/3)mgRE (E) (1/4)mgRE

41. A styrofoam container used as a picnic cooler contains a block of ice at 0°C. If 225 g of ice melts in 1 hour, how much heat energy (Joule) per second is passing through the walls of the container? (The heat of fusion of ice is 3.33 × 105 J/kg). (A) 20.8 (B) 124.8 (C) 1800.0 (D) 7492.5 (E) 749250.0

42. How much is the internal energy change of a gas that expands from i to f as indicated in the figure if there is also a frictional heat loss of 10 J? (A) -34.5 J (B) 22.5 J (C) -18.5 J (D) -28.5 J (E) 36.5 J