Finding the Axle Force on a Pulley System

[needphyshelp]

Homework Statement

A 12.0kg box resting on a horizontal, frictionless surface is attached to a 5.00 kg weight by a thin, light wire that passes over a frictionless pulley. The pulley has the shape of a uniform solid disk of mass 2.00 kg and diameter 0.500 m. After the system is released, find the horizontal and vertical components of the force that the axle exerts on the pulley.

Homework Equations

F=ma (?)

The Attempt at a Solution

I have already calculated the tension in the wire on both sides of the pulley (x =32.6N and y=35.4 N) and the linear acceleration which equals 2.72 m/s². I know that this question has been asked previously, but I still don't understand what the force exerted on the pulley by the axle is.

Am I just trying to find Fx=m (alphax) and Fy=m(alpha y)?

 

[Doc Al]

Hint: Since the center of mass of the pulley doesn't move, the net force on the pulley must be zero.

 

[needphyshelp]

But how would I calculate the components of the force acting on the pulley? I know nothing about the axle, and it can't be just the tensions on each side because their net force is not zero.

 

[Doc Al]

All you have to know is that the force that the axle exerts on the pulley must exactly balance the tension forces on the pulley. It's not the tensions that add to zero, it's the tensions plus the axle force that must add to zero. And if the net force is zero, all components of the net force must be zero.