Question

a 0.16 kg mass at the top of a 0.8 m high (vertical) incline. if this mass were a uniform, solid sphere (radius .057 m, like a billiard ball) and it is allowed to roll (without slipping) down the incline, what will be its speed (in m/s) at the bottom of the incline?

Answer 1

Initially, sphere is at the top of the incline, initial height is h=0.8m. Initial potential energy of the sphere is

Assuming the sphere was initially at rest, initial kinetic energy of the sphere is zero

At the bottom of the incline, the height of the sphere is zero, h=0. Final potential energy of the sphere is zero

Let v be the speed of the sphere at the bottom, the kinetic energy of the sphere at the bottom is

K_trans is the translation kinetic energy of the center of mass of the sphere, K_rot is the rotational kinetic energy of the sphere about the center of mass.

For rolling without slipping motion,

Moment of inertia of the sphere is

Assuming the lost in mechanical energy of the sphere negligible