Question

A solid sphere rolls up a plane inclined at 45° to the horizontal. If the speed of its centre of mass at the bottom of the plane is 5 m/s, find how far the sphere travels up the plane.

Answer 1

Data : v = 5 m/s, θ = 45°, g = 9.8 m/s² 

The total energy of the sphere at the bottom of the plane is

E = \(\frac7{10}\)Mv²

where M is the mass of the sphere. In rolling up the incline through a vertical height h, it travels a distance L along the plane. Then,

By conservation of energy.

The sphere travels 2.526 m up the plane.