Question

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.

Answer 1

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 $f_r=\mu N$

$f_r=\mu mg\cos \theta$

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

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

$\mu =0.323$