A hollow spherical shell with mass 1.80kg rolls without slipping down a slope th

Question

A hollow spherical shell with mass 1.80kg rolls without slipping down a slope that makes an angle of 40.0? with the horizontal.

Part A)

Find the magnitude of the accelerationacm of the center of mass of the spherical shell.

Take the free-fall acceleration to be g = 9.80m/s2 .

Part B)

Find the magnitude of the frictional force acting on the spherical shell.

Take the free-fall acceleration to be g = 9.80m/s2 .

Part C)

Find the minimum coefficient of friction ? needed to prevent the spherical shell from slipping as it rolls down the slope.

*** I already know the answer for Parts A and B, it is 3.78m/s^2 and 4.54N. I need help on how to figure out Part C. Thank you!

Explanation / Answer

Here ,

C)

as Normal force acting is N = mg*cos(40)

Now, maximum static friction ,

f = u*N

4.54 = u*(1.8 * 9.8 * cos(40))

u = 0.336

the minimum coeffiecient of friction is 0.336

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