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

[tex]\sum[/tex]Fx=0
[tex]\sum[/tex]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:
[tex]\sum[/tex]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:
[tex]\sum[/tex]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.

 

[baba89]

Hello,

Your solution looks correct to me. I agree with your equations and calculations. It's always a good idea to double check your work and make sure it makes sense logically. In this case, your solution aligns with what I would expect based on the given information. Great job!

 

[thomate1]

Your approach and calculations seem to be correct. It is important to draw accurate free body diagrams and use the correct equations for equilibrium in order to solve this type of problem. Good job!