Question

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!

Answer 1

m*g*sin20-f=m*a
and the rotational frame
f*r=I*a/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
f*r^2/I=g*sin20-f/m
or
f=g*sin20/(r^2/I+1/m)

I=2*m*r^2/5
therefore
f=2*m*g*sin20/7