110年 - 110 國立臺灣大學_碩士班招生考試_應用力學研究所甲組:動力學(B)#100852

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.