110年 - 110 國立臺北科技大學_碩士班招生考試_機械工程系機電整合碩士班(乙組)：工程力學#103348

1. The large window shown in Fig. 1 is opened using a hydraulic cylinder AB. If the cylinder extends at a constant rate of 0.2 m/s, determine the angular velocity and angular acceleration of the window at the instant θ = 30°. (25%)

2. The ram R shown in Fig. 2 has a mass 200 kg and is released from rest 0.75 m from the top of a spring, A, that has a stiffness k_A = 12 kN/m. If a second spring B, having a stiffness k_B = 15 kN/m, is nested in A, determine the maximum displacement of A needed to stop the downward motion of the ram. The unstretched length of each spring is indicated in the Fig. 2. Neglect the mass of the springs. (25%)

3. The movable bracket shown may be placed at any height on the 3-in.-diameter pipe. If the coefficient of static friction between the pipe and bracket is 0.2, determine the minimum distance x at which the load W can be supported. Neglect the weight of the bracket. (25%)

4. A fixed crane has a mass of 2000 kg and is used to lift a 2400-kg crate. It is held in place by a pin at A and a rocket at B. The center of gravity of the crane is located at G. Determine the components of the reactions at A and B. (25%)