# Friction force on a rolling ball

1. Dec 2, 2008

### jimbo71

1. The problem statement, all variables and given/known data
A uniform hollow spherical ball of mass 1.75kg and radius 40.0cm rolls without slipping up a ramp that rises 30 degrees above the horizontal. The speed of the ball at the base of the ramp is 2.63m/s. while the ball is moving up the ramp, find the acceleration of its center of mass and the friction force acting on it due to the surface of the ramp.

2. Relevant equations
I=2/5MR^2
K=1/2mv^2
U=mgh

3. The attempt at a solution
I think I want to start out with K1 - Wf= U1+K2. However the problem doesn't state anything about how far the ball travels up the ramp or what its speed is at a certain point on the ramp.

2. Dec 2, 2008

### mgb_phys

Not sure you have enough information here.
You have the total energy at the start of the ramp (ke = rotational ke)
As the ball goes up the ramp this is lost to pe and the ball slows down.

Without the coeff of friction, or the the energy lost I don't see how you can calculate the frictional force?

3. Dec 2, 2008

### nasu

The key here is that it moves without slipping.
This condition determines the friction force required. (if it's more than miu*N it will slip)
You just write Newton's law for the center of mass (translation) and for rotation.

m*g*sin(alpha)-F_friction=m*a_cm
For rotation you need to pick a point (axis)
For the contact point,
m*g*sin(alpha)=I*a_cm/R

(the moment of inertia is then 2/5MR^2+MR^2)
You'll have two equations with two unknowns (F_friction and a)