Minimum coefficient of friction to prevent slipping - torque

[ph123]

A hollow, spherical shell with mass 1.95 rolls without slipping down a slope angled at 30.0. Find the minimum coefficient of friction needed to prevent slipping.

I have already calculated the acceleration of the sphere and the magnitude of the friction force on the sphere in previous parts. I used torque and Newton's laws to find the acceleration and friction. They are:
a = 2.94 m/s^2
f = 3.82 N

I used the following equation for the sum of forces in the x-direction, which I oriented along the slope of the incline, with the positive direction down the incline. I didn't think I needed to use torque here, because I got the same answer that way as well.

(sum)Fx = mgsin(theta) - f = ma
= mgsin(theta) - (mu)mgsin(theta) = ma
mu = [a - gsin(theta)] / [-gsin(theta)]
mu = (-1.96 m/s^2) / (-4.9 m/s^2)
= 0.4

This coefficient of friction isn't right, but I'm sure I included all of the forces. Anyone know where I messed up? Thanks.

 

[AlephZero]

(sum)Fx = mgsin(theta) - f = ma
= mgsin(theta) - (mu)mgsin(theta) = ma

The friction force is mu times the normal force on the plane

f = (mu)mg COS(theta).

You don't need the rest of your equation. You already found f = 3.82N so just plug the numbers into that equation.