Static Equilibrium components (pulleys, weights)

[fizzsucks]

Homework Statement

Component diagram:
include all forces, x & y, angles
compare x components (are they equal?)
do y-components equal 0?

Homework Equations

Fnet = ma = 0 = F + F + F...
SOHCAHTOA

The Attempt at a Solution

Attached is my diagram with components drawn in. There are two pulleys with a rope strung across them, with a weight on each end, and one tied in the middle. Weight on the left (100g), middle (120g), right (92g). I need to calculate the x and y components, and see how close they add up to equal 0.

Is the y-component for both vectors = (120g)(9.8)? I thought it should be, however if that's the case, the x-components won't be equal and opposite: (.120g)(9.8)tan54 vs (.120g)(9.8)tan50. And how do I account for the other two weights?

 

[kuruman]

Is the y-component for both vectors = (120g)(9.8)? I thought it should be, however if that's the case, the x-components won't be equal and opposite: (.120g)(9.8)tan54 vs (.120g)(9.8)tan50. And how do I account for the other two weights?

The sum of the two y-components is (120g)*9.8.

To account for the other two weights, note that pulleys change the direction of the tension but not its magnitude.

 

[kuruman]

Each hanging weight is exerting a force mg on the rope. This force is the tension in that particular rope.

 

[kuruman]

It is not correct. Remember, cos = adj/hyp and sin = opp/hyp.

 

[kuruman]

It is not a matter of dotting your t's and crossing your i's. The numbers for the components are incorrect because you use sine where you should have used cosine and vice versa.

Also F_net,y = F_1y + F_2y - mg, where mg is the hanging weight in the middle. The net force is the sum of all the forces and there are three forces at equilibrium in the middle.