Question

A body is released from rest at the top of a plane inclined at 30° to the horizontal and 4.0m high.
If the coefficient of the friction between the body and the plane is 0.3 , calculate the time the body takes to reach the bottom of the plane

Answer 1

$$l=\frac{h}{\sin{30}}=\frac{4}{\sin{30}}=8\ m$$

$$F=ma=mg\sin{30}-\mu mg\cos{30}$$

$$a=g(\sin{30}-\mu \cos{30})=\frac{2l}{t^2}$$

$$9.8(\sin{30}-0.3 \cos{30})=\frac{2(8)}{t^2}$$

$$t=2.6\ s$$