30. Which of the following species needs resonance to adequately describe its structure?
(A) H₂O
(B) CO₃ ^2–
(C) NH₃
(D) HCN
(E) NH₄ ⁺

31. An object of mass m is sliding with speed v at some instant across a level tabletop, with which its coefficient of kinetic friction is µ. It then moves through a distance d and comes to rest. Which of the following equations for the speed v is reasonable? (Gravitational acceleration is g) (A) (2μgd) 1/2 (B) (mgd) 1/2 (C) (2μmgd) 1/2 (D) (2μgd) -1/2 (E) (2μd) 1/2

32. A force acting on an object moving along the x axis is given by Fx = (14x − 3x2 ) N, where x is in m. How much work is done by this force as the object moves from x = −1 m to x = +2 m? (A) +12 J (B) +28 J (C) +40 J (D) +42 J (E) −28 J

33. The block shown in the figure is released from rest when the spring is stretched a distance d. If k = 75 N/m, m = 0.5 kg, d =10 cm, and the coefficient of kinetic friction between the block and the horizontal surface is equal to 0.25, what is the speed of the block when it first passes through the position for which the spring is unstretched. (Gravitational acceleration g = 10 m/s2 )(A) 0.53 m/s (B) 0.92 m/s (C) 1.00 m/s (D) 1.22 m/s (E) 1.44 m/s k 

34. A police crime lab is trying to determine whether someone was murdered or died as a result of an accident. The victim was struck in the temple by a 4 kg sculpture that is alleged to have fallen off a bookcase. The sculpture presumably fell a distance of 20 m and the corner that struck him had an area of 0.25 cm2 . If the time for the sculpture to stop was 1 ms, the pressure on his temple, in N/m2 , was ______. (Gravitational acceleration g = 10 m/s2 ) (A) 3.2 × 105 (B) 1.6 × 106 (C) 3.2 × 106 (D) 1.6 × 109 (E) 3.2 × 109

35. A 3 kg particle moves to the right at 4 m/s as shown in the figure. The magnitude of its angular momentum in (kg ● m2 /s) about the point O is ______.  (A) 0 (B) 48 (C) 72 (D) 144 (E) 1728

36. A particle moves in the xy plane, starting from the origin at t = 0 with an initial velocity having an x component of 20 m/s and a y component of −15 m/s. The particle experiences an acceleration in the x direction, given by ax = 4 m/s2 . What is the total velocity at any time? (A)(B)(C)(D)(E)

37. A grindstone increases in an angular speed from 4 rad/s to 12 rad/s in 4 s. Through what angle does it turn during that time interval if the angular acceleration is constant? (A) 8 rad (B) 12 rad (C) 16 rad (D) 32 rad (E) 64 rad

38. A 1 kg copper block and a 6 kg steel block are connected by a light string over a frictionless pulley. The two blocks are allowed to move on a fixed steel block wedge (θ = 60°) as shown in the figure. If the coefficients of friction of the copper-steel and steel-steel are 0.4 and 0.6, respectively, what is the acceleration of the two blocks? (Gravitational acceleration g = 10 m/s2 )(A) 5.28 m/s2 (B) 5.08 m/s2 (C) 4.88 m/s2 (D) 4.68 m/s2 (E) 4.28 m/s2

40. A 5 kg ball is held in the hand as shown in the figure, with the arm horizontal and 40 cm from the elbow joint. The forearm mass is 2 kg and the center of gravity is 18 cm from the joint. The biceps connect to the arm at 5 cm from the joint. How much force (FM) must the biceps exert to hold the ball in place? (Gravitational acceleration g = 10 m/s2 )(A) 472 N (B) 236 N (C) 118 N (D) 59 N (E) 30 N

41. If middle C (262 Hz) and C# (277 Hz) are played together, it would cause interference beats. What the beat frequency would be if each is played one octave lower (each frequency reduced by a factor of 2)? (A) 30 Hz (B) 15 Hz (C) 7.5 Hz (D) 3.75 Hz (E) None of the above.

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