Statics : find coefficient of static friction

[tranj10]

Homework Statement

Find coefficient of static friction if shell starts to slip at θ = 60°

known - θ
unknowns - P, r, Normal force, weight

Homework Equations

friction = μ * normal force

The Attempt at a Solution

I do not know where to start. It looks like the picture wants you to assume P is always horizontal so it has no effect on the normal force which means friction is constant. If friction were constant though why would it start to slip?

 

[RTW69]

I haven't done this problem but here is a place to start.

Find the centroid of the shell. The gravitational force will act through the centroid. P is horizontal. Do a free body diagram. Sum forces in X and Y direction. Sum the moments around the contact point. Hopefully everything falls out but Coefficient of static friction which is probably related somehow to the angle.

 

[RTW69]

Yep, the method I outlined above will give you the correct answer. Treat this as a statics problem.

 

[tranj10]

ah yes. Your method worked perfectly for me, thank you.