# Hollow sphere rolling down a slope

## Homework Statement

A hollow, spherical shell with mass 2.50kg rolls without slipping down a slope angled at 35.0 degrees.
i) Find the acceleration
ii) Find the friction force
iii) Find the minimum coefficient of friction to prevent slipping

## Homework Equations

$F=ma$

$I=\frac{2MR^2}{3}$

Energy must stay constant:
$E_{p}+E_{kr}+E_{k} = E_{p}+E_{kr}+E_{k}$

$mgh+\frac{1}{2}Iw^{2}+\frac{1}{2}mv^{2}=mgh+\frac{1}{2}Iw^{2}+\frac{1}{2}mv^{2}$

## The Attempt at a Solution

I really have no idea where to start, because a radius is not given, so I cannot find the moment of inertia. I was thinking if I used the energies, and said that

$mgh=\frac{1}{2}mv^{2}+\frac{1}{2}Iw^{2}$

$mgh=\frac{1}{2}mv^{2}+\frac{1}{2}((\frac{2}{3}mR^2)w^{2}$

because we could use a pretend example, say that the sphere starts at rest at the top of the ramp, and in the end, all the energy is kinetic. But from here, I'm not really sure where to go. Thanks!

Delphi51
Homework Helper
Who knows, maybe it will turn out that the radius doesn't matter! If not, then an R in the answers will be expected. Go ahead and do it with an R and see. You will need v = r*ω, too.

You energy approach looks good. No doubt it could also be done with force, acceleration, etc.

Simon Bridge