Sol'n: Find Force P to Balance Weight of Blocks A and B

[Melawrghk]

This is just a problem from my midterm, and I was wondering if I did it correctly

Homework Statement

Weight of block B is 15kN, weight of block A is 25kN. Find force P that has to be applied to keep the system in equilibrium in tension in the cable

Homework Equations

$$\sum$$Fx=0
$$\sum$$Fy=0

The Attempt at a Solution

So first I figured I'd draw a FBD around block B (FBD1 on the image). I also decided I would use a different axis (x' and y'). From this I was able to write the equilibrium equations:
$$\sum$$Fx=3T-15*cos(60)=0, from which T=2.5kN
(I also wrote the Fy equation, but I won't post it because it serves no real point)

Next, I drew a FBD around block A (FBD2 on the image). I used a different axis once again. And I got:
$$\sum$$Fx=-25*cos(60)+P(cos30)+2.5kN=0, from which P=11.55kN

Is that correct? It makes sense in my head, but then again that wouldn't be the first time my gut feeling is wrong.Thanks!

 

[PhanthomJay]

...but this time, your gut feeling is right.