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Equilibrium with Torques on a Cylinder on an Inclined Plane

A unifom cylinder, mass M= 15 kg, rests on a plane inclined at angle b=30°, held stationary by a cord attached to the plane at angle a= 50° which applies tangential force C to the cylinder. A mass m= 5 kg is suspended on a cable which is wrapped on the surface of the cyiinder. The radius R is unknown.
See the attachment for a diagram with all knowns.
a. Find the force C in the cord.
b. Find the friction force at the cylinder/plane contact.


Solution Preview

Equilibrium requires that 'net torque=0' about any axis chosen. Before making your choice of axis location, you need to show as arrows on the diagram, all existing forces on the cylinder, including components of Mg parallel and perpendicular to the plane, mg, C, normal force N, and friction force F.
Then, since F is unknown, use the fact that if the axis is chosen on the line of action of any force, then that ...