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

ID: 1324157 • Letter: A

Question

A hollow spherical shell with mass 1.80kg rolls without slipping down a slope that makes an angle of 34.0? with the horizontal.

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 .

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

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

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

m a = m g sin theta - F

I * dw / dt = F R

A spherical shell of mass m has moment of inertia I = 2/3 m R2

a = R dw/dt

m a = m g sin theta - F

2/3 m a = F

Substituting F , m a = m g sin theta - 2/3 m a

a = 3/5 * g * sin theta

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a) a = 3/5 * 9.81 * sin(34.0)

= 3.29 m/s2

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F = 2/3 m 3/5 g sin theta

F = 2/5 m g sin theta

F = 2/5 * 1.80 kg * 9.81 * sin(34.0)

= 3.946 N

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