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丙組:動力學(C)#100778

1. (20%)

The motorcycle travels along the elliptical track at a constant speed ν . Determine its smallest acceleration if a > b.

2. (20%)

If blocks A and B of mass 0 kg and 6 kg, respectively. are placed on the inclined plane and released. determine the force

developed in the link. The coetticients of kinetic friction between the blocks and the inelined plane are μ_A. =0.1 μ_B= 0.3. Neglect the mass of the link.

3. (20%)

If the 75-kg crate starts from rest at A. determine its speed when it reaches point B. The cable is subjected to a constant force

of F=300N. Neelect friction and the size of the pulley.

4.(20%) The boat has a mass of I 80 kg and is traveling forward on a river with a constant velocity of 70 kn/h. measured relative to the river. The river is flowing in the opposite direction at 5 km/h. If a tube is placed in the water, as shown, and it collects 40 kg of water in the boat in 80 s, determine the horizontal thrust T on the tube that is required to overcome the resistance due to the water collection and yet maintain the constant speed of the boat. ( Pw = 1 Mg/m³) 

5.(20%) A car of mass m is traveling at a slow velocity vo. If it is subjected to the drag resistance of the wind. which is proportional to its velocity. F_D = ky. where k is a known propotional constant. Determine the distance and the time the car will travel before its velocity becomes 0.5vo. Assume no other frictional forces act on the car.