(i) The moment of inertia of the ball is 2mr²/5. Please derive it. (10%)

(i) Please find the angular acceleration of the bar AB. (12%)

(ii) Find the angular acceleration of the bar BC. (13%)

(ii) Determine the height h at which the ball must be struck so that no frictional force develops between it and the table at A. Assume that the cue C only exerts a horizontal force P on the ball.(15%)

3. (25%) A homogeneous sphere of mass m and radius r falls without rotation upon a fixed and perfectly rough surface inclined at an angle o to the horizontal plane. The vertical velocity before impact is Vo, and the coefficient of restitution for the collision is e. Determine the angular velocity of the sphere, the velocity, and the direction of motion of the center of mass of the sphere after the impact. (The moment of inertia of the sphere is )

4. (25%) A cannon in a fort at height h from the sea level overlooking the ocean fires a shell of mass m at an angle of θand muzzle velocity vo. See the figure below. At the highest point the shell explodes, with additional energy Ea, into two fragments with equal mass, travelling in the original horizontal direction. Neglect the air drag. Find the distance separating the two fragments when they land into the ocean.

(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.

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