Question

A string in a double inclined plane connects two bodies. If the 6.0 𝑘𝑔 mass starts from the top of the plane and the length is 8 m. Find the velocity of the 6 𝑘𝑔 body when it reaches the bottom of the plane. 

Answer 1

Assume the mass of the second body is M>m=6 kg. Assume the plane with the 6-kg body is vertical and the plane on which the other body rests is θ above the horizontal.

Applying Newton's second law for both bodies, we have

$$-ma=T-mg,\\ Ma=T-Mg\sin\theta.\\\space\\ Ma=mg-ma-Mg\sin\theta,\\ a(M+m)=g(m-M\sin\theta),\\\space\\ a=\frac{g(m-M\sin\theta)}{M+m}.$$

The velocity near the ground is

$$v=\sqrt{2gh\frac{(m-M\sin\theta)}{(M+m)}}.$$