A solid sphere of uniform density starts from rest and rolls without slipping down an inclined plane with angle θ = 30o. The sphere has mass M = 8 kg and radius R = 0.19 m . The coefficient of static friction between the sphere and the plane is μ = 0.64. What is the magnitude of the frictional force on the sphere?

I got 21.168N and the computer told me I was wrong because I was trying to find force of the max static instead of the actual static force. Please help!

Verified Answer :

mgsin20-f=ma 
and the rotational frame 
f
r=Ia/r 
where f is the force of friction, a is the translational acceleration and I is the moment of inertia of the sphere 

combine and solve for f 
a=g
sin20-f/m 
and 
fr^2/I=gsin20-f/m 
or 
f=gsin20/(r^2/I+1/m) 

I=2
mr^2/5 
therefore 
f=2
mgsin20/7