Acceleration and Friction of a Rolling Cylinder

[hm8]

Homework Statement

A lawn roller in the form of a thin-walled, hollow cylinder with mass M is pulled horizontally with a constant horizontal force F applied by a handle attached to the axle.

a)If it rolls without slipping, find the acceleration.

b)If it rolls without slipping, find the friction force.

Homework Equations

$I_{Hollow Cylinder} = MR^{2}$

$\sum \tau = f_{friction}R = I\alpha = MR^{2}\alpha$

$\sum F = F - f_{friction} = F = Ma$

The Attempt at a Solution

I'm really not sure...it seems like I have too many unknowns (R, a, alpha, friction)

 

[hm8]

Ok, so I just remembered that because its not slipping, I can change $\alpha$ to $\frac{a}{r}$

so I get $f_{friction}R = MR^{2}*\frac{a}{R}$

which cancels down to $f_{friction} = Ma$

But when I plug that back into the other equation I just get F - ma = ma...

where did I go wrong?

 

[hm8]

Any help, guys?