(4) (Please see Fig. 4) As shown in Fig. 4, the crank AB rotates with a constant angular velocity of 600 rpm clockwise. Please determine:
(1) the angular velocity of the connecting rod BD (10%); (2) the angular acceleration of the connecting rod BD (10%); (3) the acceleration of point D on the piston. (5%)

(a) At an instant after it passes B, the normal force exerted by the road on the car drop to one-third of the normal force at point A. Please determine the θ. (15%)

(b) If the car speed is variable, what is the minimum speed that will cause the car to lose contact with the road at the highest point C ? (10%)

(2) (Please see Fig. 2) Three identical small spheres, each of mass 1 kg, can slide freely on a horizontal frictionless surface. Spheres B and C are connected by a light rod and are at rest in the position shown when sphere B is struck squarely by sphere A which is moving to the right with a velocityVo= 2.4 m/s. Knowing that θ = 45°and that the velocities of spheres A and B immediately after the impact are and ， determine (a) (9%); and (b) the velocity of sphere C immediately after impact. (16%)

(3) (Please sce Fig. 3) The homogeneous sphere of mass m and radius r is projected along the incline of angleθ with an initial speed v0 and no angular velocity (ω0 = 0). If the coefficients of static and kinetic friction are μs and  μk, respectively, determine the time duration t of the period of slipping (10%). In addition, find the velocity v of the mass center G and the angular velocity ω at the end of the period of slipping.(7% and 8%, respectively)

(D) Species C is adsorbed on the catalyst at 700 K:(1) Ture, (2) False), (3) Cannot tell (3%)

(C)Species C is adsorbed on the catalyst surface at 400 K:(1) Ture,(2) False), (3) Cannot tell (3%)

(B) The reaction is endothermic: (1) Ture, (2) False), (3) Cannot tell (3%)

(A) The reaction is exothermic: (1) Ture, (2) False), (3) Cannot tell (3%)

7. (11%) In an ammonia decomposition reaction to generate N2 and H2 on a Platinum catalyst (2NH3 → N2 + 3H2) the rate can be expressed as -r = kKAPA/KHPH, where k is the rate constant, PA and PH indicate the pressures of ammonia and hydrogen, and KA and KH are the adsorption constants for ammonia and hydrogen. Suggest a mechanism and the assumptions consistent with the rate equation and prove it.

(c) Would you expect to have temperature variations within the pellet or across the gas film?(5%) 

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