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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!

Respuesta :

MissPhiladelphia
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

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