Static equilibrium with Youn modulus

[Toranc3]

Homework Statement

In Figure, a 103 kg uniform log hangs by two steel wires, A and B, both of radiuses 1.20 mm. Initially, wire A was 2.50 m long and 2.00 mm shorter than wire B. The log is now horizontal. What are the magnitudes of the forces on it from Wire A, and Wire B?
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Homework Equations

Young Modulus = (F(perpendicular)/Area)/(ΔL/L(initial))

The Attempt at a Solution

This is static equilibrium
so

Summation of Forces:
F: Ta-Tb-Wb =0

Not sure where to take it from here. Can somebody give me a direction?

Homework Statement

Homework Equations

The Attempt at a Solution

 

[SteamKing]

For a wire under tension, what is the formula for the amount it stretches?

 

[Toranc3]

For a wire under tension, what is the formula for the amount it stretches?

Would it be tensile strain?

Tensile strain=ΔL/L

 

[SteamKing]

Yeah, but what is the formula for calculating delta L?

 

[Toranc3]

Yeah, but what is the formula for calculating delta L?

Lfinal minus Linitial right

 

[SteamKing]

Read your problem carefully. You have two wires, one of which is slightly shorter than the other when there is no load (no tension) applied. After the log is suspended, it is perfectly horizontal, suggesting that both wires under tension are now the same length. How would you use the equation for Young's Modulus to calculate the tension in each wire?

 

[Chestermiller]

If wire A had a length of L_0A = 2.5 meters before it was loaded, and wire A had a length 2 mm shorter than wire B before it was loaded, what was the length L_0B of wire B before it was loaded?

If F_A is the force in wire A, and F_B is the force in wire B, what is the equation for the strain ε_A and ε_B in each of these wires in terms of Young's modulus?

From this, and knowing the unloaded lengths of the two wires, write an equation for the loaded lengths of the two wires L_A and L_B. Since the log is horizontal, what does this tell you about the relationship between L_A and L_B? This should give you a single relationship between F_A and F_B.

How are F_A and F_B related to the weight of the log? This should give you your second relationship between the unknowns F_A and F_B.