What force do ropes exert on a sign

[ahrog]

Homework Statement

A sign that weights 648 N is suspended by two ropes that make an angle of 38^o with the horizontal. What force does each rope exert on the sign?

Homework Equations

A + B + W= 0
F_h= F cos x
F_v= F sin x

The Attempt at a Solution

This is how my textbook says to do it:

The direction of W is down, so the direction of A + B is up. The sum A+B has no horizontal components, so the horizontal components of A and B, A_h and B_h have equal magnitudes. Now, A_h = Acos38^o and B_h=Bcos38^o. Since A_h=B_h, the magnitudes of A and B must be equal. The magnitude of the sum of the vertical components of A and B equals the magnitude of the weight of the sign, 648 N. That is, A_v + B_v =648 N Since A_v = Asin38 and B_v = Bsin38 and A=B, A_v=B_v.
Thus,
A_v=B_v =1/2(648N)= 324N
And.. A=A_v/sin38 = x
B=A= x

They don't tell me what x should be, nor what the 324N is for. Please help

 

[stewartcs]

Homework Statement

A sign that weights 648 N is suspended by two ropes that make an angle of 38^o with the horizontal. What force does each rope exert on the sign?

Homework Equations

A + B + W= 0
F_h= F cos x
F_v= F sin x

The Attempt at a Solution

This is how my textbook says to do it:

The direction of W is down, so the direction of A + B is up. The sum A+B has no horizontal components, so the horizontal components of A and B, A_h and B_h have equal magnitudes. Now, A_h = Acos38^o and B_h=Bcos38^o. Since A_h=B_h, the magnitudes of A and B must be equal. The magnitude of the sum of the vertical components of A and B equals the magnitude of the weight of the sign, 648 N. That is, A_v + B_v =648 N Since A_v = Asin38 and B_v = Bsin38 and A=B, A_v=B_v.
Thus,
A_v=B_v =1/2(648N)= 324N
And.. A=A_v/sin38 = x
B=A= x

They don't tell me what x should be, nor what the 324N is for. Please help

Start by drawing a free body diagram (FBD). Then uses Newton's second law (Fnet = ma) in both the x and y directions. You'll end up with two equations that you can solve simultaneously.

HINT: The force that the ropes exert on the sign is equal to the tension in the ropes.

CS