Tension on a wire with equal angles

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SUMMARY

The tension in the wires supporting a 100N light suspended from a beam, with both wires making angles of 40 degrees with the beam, is calculated to be 77.8N for each wire (T1 and T2). The equations used are based on the equilibrium of forces, specifically the sum of horizontal (Fx) and vertical (Fy) components. Changing the angle of the wires affects the tension values, as a smaller angle results in a reduced vertical component of tension, leading to different numerical outcomes for the tensions.

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nicolette2413
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1. A 100N light is suspended from a beam with two wires. Both wires make angles of 40 degrees with the beam.

2. What is the tension in the wires?

3. Ok here's what I have so far...
Sum Fx: T2(cos 40)-T1(cos 40)=0
so T2=T1

Sum Fy: T2 (sin 40)+T1(sin 40+(-100)=0
so T2(sin 40)+T1(sin 40)=100

With subsitutions...
T1(sin 40)+T1(sin 40)=100

And T1=77.8N, T2=77.8N, and T3=100N
Is this correct? And does changing the angle change the final breakdown? Such as if the angle was 30 degrees vice 40 degrees??
 
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That looks correct to me. If the angles both changed to 30 degrees, the equations would be exactly the same, except the tensions would have different numerical answers compared to if the angles were 40 degrees. This is because there is a smaller y component of tension.
 
Thank you ! This has been getting me for about 2 weeks now.
 

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