# Torque on Pulley sitting on moving belt

• cp51

## Homework Statement

There is a Pulley (or just a wheel) sitting on a moving belt being pulled with force Fa with some unknown friction between the pulley and the belt. The pulley rotates without slipping on the belt. Draw a freebody diagram of the pulley and the belt.

## The Attempt at a Solution

So I feel bad asking this question because it is so basic, but for some reason I am just stuck between two possibilities.

so for the belt my free body diagram looks like:
Friction to the left, the applied force to the right, and the weight of the belt down and normal force up.

Now for the Pulley:
Weight of the pulley down, normal force up.
Now, there is a Force to the right, which creates a torque on the pulley, due to the friction with the belt. My question is:

1) is the force to the right(on the pulley) = to the frictional force on the belt?

or

2) force to the right(on the pulley) = Force applied - Frictional force(both of the belt)

I believe the Torque on the pulley is only due to friction, so I would assume 1 is correct, but I've heard arguments for 2, and since 2 is a force to the right, since Fapplied > Ffriction, its been bugging me which is correct.

Thanks