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## Homework Statement

A hollow spherical shell with mass 2.50 kg rolls without slipping down a slope that makes an angle of 32.0 degrees with the horizontal.

a. Find the magnitude of the acceleration [tex] a_c[/tex] of the center of mass of the spherical shell.

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

c. Find the minimum coefficient of friction [tex] \mu [/tex] needed to prevent the spherical shell from slipping as it rolls down the slope.

## Homework Equations

For part a.

Since its pure roll, [tex] a_c = \alpha * R

\alpha = a_c/R [/tex]

[tex] \tau = R*Friction = I (moment-of-inertia) * \alpha [/tex]

[tex]Friction = (I*\alpha)/R = (I*a_c)/R^2 [/tex]

[tex]Ma_c = Mgsin(\theta)-Friction[/tex]

[tex]Ma_c = Mgsin(\theta)-Ia_c/R^2[/tex]

[tex]a_c = (MR^2*g*sin(\theta))/(MR^2+I)[/tex]

## The Attempt at a Solution

I for sphere =[tex] 2/3 MR^2[/tex]

so, [tex]a_c = (MR^2*g*sin(\theta))/(MR^2+2/3*MR^2)[/tex]

MR^2 cancels..

[tex]a_c = 3/5*g*sin(\theta)[/tex]

for a_c i got [tex]a_c = 3.12m/s^2[/tex] i think im right unless i made a mathematical error some where.

and substituting a_c, in [tex]Ma_c = Mgsin(\theta)-Friction[/tex]

i got Friction = 5.19 N.

And c,

this where I'm kind of stuck. I'm assuming since they are asking for minimum [tex]\mu[/tex] Friction is 0 in [tex] Ma_c = Mgsin(\theta)-Friction [\tex]

[tex]a_c = gsin(\theta) [/tex].

[tex]Friction = (I*\alpha)/R = (I*a_c)/R^2 [/tex], and

[tex] Friction = \mu*mg*sin(\theta) [/tex]

[tex] /mu= ((I*a_c)/R^2)/mg*sin(\theta)

idk if I'm right in assuming Friction is 0 in one part and not in other.. Any hints/guides and help would greatly be appreciated.

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