110年 - 110 國立臺灣大學_碩士班招生考試_工程科學及海洋工程學研究所乙組:工程力學(動力學及靜力學)#100701

1. 15pts   A hole having a radius r is to be drilled in the center of the homogeneous block. Determine the depth h of the hole so that the center of gravity G is as low as possible. Write your final answer in the form: (h=_________).

3. 20pts   If a force of F = 22.5 kg is applied to the pads at A and C, determine the smallest dimension d required for equilibrium if the spring has an unstretched length of 0.3 m. The elastic constant of the spring is k = 225 kg/m. Write your final answer in the form: ( d =__________)

4.20pts Two uniform rods AB and CE, each of mass 1.5 kg and length 600 mm, are welded to each other at their midpoints. Knowing that this assembly has an angular velocity of constant magnitude ω = 12 rad/s, determine the magnitude and direction of the angular momentumH_D = of the assembly about D. Write your final answer in the form: ( H_D=_______ ). (In vector form)

6. 5pts A solid steel sphere A of radius r and mass m is released from rest and rolls without slipping down an incline as shown. After traveling a distance d the sphere has a speed v. If a solid steel sphere of radius 2r is released from rest on the same incline, what will its speed be after rolling a distance d?