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 F_a 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.

Homework Equations

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

 

[BigJDubs]

! The correct answer is option 1. The force on the pulley is equal to the frictional force on the belt. This is because the friction between the belt and the pulley is what provides the torque that causes the pulley to rotate. Therefore, the force on the pulley must be equal to the friction on the belt, since it is this friction that is causing the pulley to rotate.