Question

One side of a double inclined plane makes an angle of 30𝑜 with the horizontal, and the other makes an angle of 53𝑜 . A 100 𝑙𝑏 weight and a 50 𝑙𝑏 weight are attached to the ends of the string, which passes over a pulley at the top of the smooth double plane with the 50 𝑙𝑏 load on the steeper side. Find the velocity of the 50 𝑙𝑏 load when it reaches the bottom of the plane. The length of the steeper plane is 16.4 𝑓𝑡. 

Answer 1

By Newton's second law:

$$-ma=T-mg\sin53°,\\ -Ma=-T+Mg\sin30°.\\\space\\ a=-2.15\text{ ft/s}^2,\\ T=1385.2\text{ lbf}.$$

The time it will take to pass the length of the plane is

$$t=\sqrt{2d/a}=3.9\text{ s}.$$