Elasticity,stress, and strain questions

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SUMMARY

This discussion focuses on the concepts of elasticity, stress, and strain in metal rods, specifically addressing calculations related to stretching and strain energy. The first question confirms that a rod with double the cross-sectional area will stretch half as much under the same force, resulting in a 0.2 mm elongation. The second question successfully applies the formula for strain energy, F²L/2AY, to calculate energy stored in an aluminum wire under tension. The third question involves calculating Young’s modulus and stress from given strain energy per unit volume and elongation percentage, with participants confirming correct answers throughout.

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1. A 3.0-mm2 cross sectional area metal rod is stretched by 0.4 mm when a certain stretching force is applied to it. Another rod of the same length and metal but of a cross sectional of twice as large is stretched by the same amount of force. Calculate the stretching in the second wire.

the answer is 0.2mm? half stretch than the first rod?

2.Compute the strain energy stored in an aluminium wire of 2.0 m long, 1.0 mm diameter subjected to a 25.0-N tension. [Y-aluminium = 7.0 x 10^10 Nm-2].
i just have to use this formula right?
F^2L/2AY

3.A stretched wire has strain energy per unit volume of 4.00 x 10^3 Jm-3. Find the Young’s modulus and the stress in the wire if the wire elongates 0.5% of its original length.
i have no idea about this
1/2Y(strain)^2 ?
 
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(1) Excellent work, defdek. Your answer on question 1 is correct.

(2) Nice work on question 2. That is correct.

(3) <standing ovation. crowd roars.> Nice job on question 3. That is correct.
 

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