Yet another static equilibrium problem.

[akan]

The figure shows a wheel on a slope with inclination angle 16 degrees, where the coefficient of friction is adequate to prevent the wheel from slipping; however, it might still roll. The wheel is a uniform disk of mass 1.35 kg, and it is weighted at one point on the rim with an additional 0.960 kg mass. Find the angle PHI shown in the figure such that the wheel will be in static equilibrium.

http://img181.imageshack.us/img181/9085/rw1261xj2.jpg
http://g.imageshack.us/img181/rw1261xj2.jpg/1/

I understand this:
m sin(phi) R = M sin(theta) R

However, this does not give me the right answer. So how do I solve this?

 

[tiny-tim]

Hi akan!

Hint: you don't want the wheel to turn …

so take moments about a suitable point (to find the torques of the forces), and put that equal to zero.

 

[akan]

What would be a suitable pivot point here? Thanks.

 

[tiny-tim]

moments of forces

What would be a suitable pivot point here? Thanks.

oh come on!

I can only see two possible pivot points …

choose one of them, and see if it works!

 

[akan]

Sorry, I suck with pivot points. If I put it at the center, then gravity is acting parallel to the level arm, so that ain't going to work. If I put it at the circumference, then the whole thing is just going to be weird. So where do I place it?

 

[tiny-tim]

Sorry, I suck with pivot points. If I put it at the center, then gravity is acting parallel to the level arm, so that ain't going to work. If I put it at the circumference, then the whole thing is just going to be weird. So where do I place it?

Place it at the point of contact (between the wheel and the slope).

There, the torque of the reaction and friction forces will be zero (that's why you're choosing it ), so you just have m and M to balance … like a see-saw!