110年 - 110 國立中山大學碩士暨碩士專班招生考試_機電系碩士班/丁組:動力學#104255

1. As shown in Figure 1, a ball is thrown so that the motion is defined by the equations x = 3t and y= 2 + 6t - 3t², where x and y are expressed in meters and t is expressed in seconds. Determine (a) the velocity at t = 2s, (b) the horizontal distance the ball travels before hitting the ground. (20%)

2. In Figure 2, as the truck shown begins to back up with a constant acceleration of 0.6 m/s², the outer section B of its boom starts to retract with a constant acceleration of 0.24 m/s² relative to the truck. Determine (a) the acceleration of section B, (b) the velocity of section B when t = 4 s. (20%)

3.Two rods AB and DE are connected as shown in Figure 3. Knowing that Point B moves downward with a velocity of 500 mm/s, determine (a) the angular velocity of each rod, (b) the velocity of Point E. (20%)

4. A beam AB of length L and mass M is supported by two cables as shown in Figure 4. If cable BD breaks, determine at that instant the tension in the remaining cable as a function of its initial angular orientation θ.(20%)

5.As shown in Figure 5, a 1-kg block A is pushed up against a spring compressing it a distance x. The block is then released from rest and slides down the 20° incline until it strikes a 1-kg sphere B which is suspended from a 1-m inextensible rope. The spring constant k =800 N/m, the coefficient of friction between A and the ground is 0.2, the distance A slides from the unstretched length of the spring d =1.5 m and the coeficient of restitution between A and B is 0.8. Knowing the tension in the rope is 20 N when a = 20° , determine initial compression x of the spring. (20%)