Statics problem. Is my work correct?

[Blugga]

Homework Statement

Homework Equations

ƩF=0
ƩM=0

The Attempt at a Solution

I have done parts 1-3 (parts 1-2 in image) and I think it's right. It's been a while since I've had statics and I'm not 100% sure it's right. For part 4, where the pulley meets the frame at F do I need a F_x and F_y? or F_x ,F_y, and M_F?

 

[PhanthomJay]

Your initial FBD of the system (the whole frame) is not correct. You seem to have cut the rope and identified the internal horizontal cable tension as 500 N to the right at C, but you left off the internal horizontal cable tension of 500 N that acts to the left at the top of the pulley.
Don't cut the rope yet, and focus instead on the whole system and identify the external forces acting on it. The external forces are the applied vertical load of 500 N down on the rope, and the reaction forces at A and E. The horizontal cable tension is internal to the system and thus is not an external force, so it does not come into play when looking at the FBD of the system. Now sum moments and forces equal to 0. You will find perhaps a surprising result for the reaction at E.

 

[Blugga]

Your initial FBD of the system (the whole frame) is not correct. You seem to have cut the rope and identified the internal horizontal cable tension as 500 N to the right at C, but you left off the internal horizontal cable tension of 500 N that acts to the left at the top of the pulley.
Don't cut the rope yet, and focus instead on the whole system and identify the external forces acting on it. The external forces are the applied vertical load of 500 N down on the rope, and the reaction forces at A and E. The horizontal cable tension is internal to the system and thus is not an external force, so it does not come into play when looking at the FBD of the system. Now sum moments and forces equal to 0. You will find perhaps a surprising result for the reaction at E.

Yes, I did figure it out. I left out the force to the left on top of the pulley. That gave me new answers. E_x turned out to equal 0.

Thanks for the help.