What force do ropes exert on a sign

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The discussion focuses on calculating the forces exerted by two ropes on a sign weighing 648 N, suspended at a 38-degree angle. The vertical components of the forces from the ropes must equal the weight of the sign, leading to the conclusion that each rope exerts a vertical force of 324 N. The horizontal components of the forces are equal, indicating that the tensions in both ropes are the same. The solution involves using free body diagrams and applying Newton's second law to derive the necessary equations. The key takeaway is that the tension in the ropes corresponds to the forces they exert on the sign.
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Homework Statement


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


Homework Equations


A + B + W= 0
Fh= F cos x
Fv= 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, Ah and Bh have equal magnitudes. Now, Ah = Acos38o and Bh=Bcos38o. Since Ah=Bh, 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, Av + Bv =648 N Since Av = Asin38 and Bv = Bsin38 and A=B, Av=Bv.
Thus,
Av=Bv =1/2(648N)= 324N
And.. A=Av/sin38 = x
B=A= x

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

Homework Statement


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


Homework Equations


A + B + W= 0
Fh= F cos x
Fv= 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, Ah and Bh have equal magnitudes. Now, Ah = Acos38o and Bh=Bcos38o. Since Ah=Bh, 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, Av + Bv =648 N Since Av = Asin38 and Bv = Bsin38 and A=B, Av=Bv.
Thus,
Av=Bv =1/2(648N)= 324N
And.. A=Av/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
 

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