A solid sphere of uniform density starts from rest and rolls without slipping do

Question

A solid sphere of uniform density starts from rest and rolls without slipping down an inclined plane with angle ? = 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 ? = 0.64.

What is the magnitude of the frictional force on the sphere?

Can someone please carefully explain the steps on how to solve this?

A solid sphere of uniform density starts from rest and rolls without slipping down an inclined plane with angle ? = 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 ? = 0.64. What is the magnitude of the frictional force on the sphere? Can someone please carefully explain the steps on how to solve this?

Explanation / Answer

using torque f*R=I*alpha alpha=a/r due to rolling f*0.19=0.4*8*0.19^2*a/0.19 mgsint-f=ma 8*9.81*0.5-f=8*(f*0.19/(0.4*8*0.19)) f=11.21 N

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