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PtichkaEL [24]
3 years ago
8

A hollow spherical shell with mass 1.95 kg rolls without slipping down a slope that makes an angle of 39.0 ∘ with the horizontal

. Find the minimum coefficient of friction μ needed to prevent the spherical shell from slipping as it rolls down the slope.
Physics
1 answer:
irinina [24]3 years ago
4 0

Answer:0.323

Explanation:

mass of spherical shell=1.95 kg

inclination \theta =39^{\circ}

Friction(f_r) will oppose the motion of shell

mgsin\theta -f_r=ma

where a=acceleration

a is given by

a=\frac{gsin\theta }{1+\frac{I}{mr^2}}

I=moment of inertia =\fac{2mr^2}{3}

a=\frac{3gsin\theta }{5}

f_r=mg\sin \theta -\frac{3mgsin\theta }{5}

f_r=\frac{2mgsin\theta }{5}

and f_r=\mu N

f_r=\mu mg\cos \theta

\mu mg\cos \theta =\frac{2mgsin\theta }{5}

\mu =\frac{2}{5}\times \tan \theta

\mu =0.323

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