Vector Components: Equal Force of Two Wires Suspending 500N Sign

In summary, two wires are used to suspend a sign weighing 500N and making an angle of 100 degrees between each other. Each wire exerts an equal force, and by drawing a free body diagram and using trigonometry to calculate the vertical components of the forces, it can be determined that each wire exerts a force of 389N.
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Homework Statement


two wires are used to suspend a sign that weighs 500N. the two wires make an angle of 100 degrees between each other. If each wire is exerting an equal amount of force, how much force does each wire exert?


Homework Equations





The Attempt at a Solution


The answer is 389.. but I don't understand how to get that.. Can someone please explain. Thanks
 
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Draw a free body diagram for the sign. What are ALL the forces that act on it? Since the sign is not moving, what must be true about the vector sum of these forces? Now pay attention to the vertical components of those forces...how would you use trigonometry to figure out what these are?
 
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  • #3
Also note, that both wires are exerting equal force. Exploit symmetry.
 

1. What is the purpose of determining the vector components of equal force for two wires suspending a 500N sign?

The purpose of determining the vector components is to understand the forces acting on the sign and ensure that it is being safely supported by the wires.

2. How do you calculate the vector components for each wire?

The vector components can be calculated by breaking down the force of 500N into its horizontal and vertical components. This can be done using trigonometric functions such as sine and cosine.

3. What is the significance of the equal force of the two wires?

The equal force of the two wires ensures that the sign is being held in place with balanced tension. If the forces were not equal, the sign could tilt or become unstable.

4. Can the angle of the wires affect the equal force of the vector components?

Yes, the angle of the wires can affect the equal force of the vector components. If the wires are not positioned at equal angles, the forces acting on the sign may not be balanced and could lead to instability.

5. How can the vector components be used to determine the strength of the wires?

The vector components can be used to determine the strength of the wires by calculating the tension in each wire. This can be done by dividing the force of 500N by the sine of the angle of the wire.

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