- #1

- 188

- 3

## Homework Statement

Two spheres are placed side by side on an inclined plane and released at the same time. Both spheres roll down the inclined plane without slipping.

(a) Using FBD, explain what force provides the torque allowing the sphere to roll down the inclined plane.

(b) Which sphere reaches the bottom of the inclined plane first and why?

(c) How do the kinetic energies of the two spheres compare at the bottom of the inclined plane?

## Homework Equations

Tau = Fr sin theta

## The Attempt at a Solution

(a) Friction is the only force providing the torque. Fg is applied directly from the centre of mass of the spheres so it has r=0 and so cannot provide any torque. F_N is directed towards the centre of mass so it has sin theta = 0.

(b) Here's where I'm getting a little confused. I used energy to solve this. For the hollow sphere, most of the mass needs to be rotated, so it has more KE_rot than KE_trans. But for the solid sphere, most of the mass will effectively be sliding across, so it has more KE_trans than KE_rot. So with greater KE_trans the solid sphere will have a greater speed and so will reach the bottom first.

However, I'm pretty sure this isn't entirely right bc I'm ignoring the energy released by friction, but I'm not sure how to determine how much energy was lost to friction for each sphere.

(c) I think this is the same issue with what I found in (b). Without knowing how much loss of energy friction caused, how can I determine how much KE is left —I'm assuming they're talking about the total KE here.