First slide

Elastic Modulie

Question

Two wires are made of the same material and have the same volume. However wire l has cross-sectional area A and wire 2 has cross-sectional area 3A. If the length of wire 1 increases by $∆ x$ . on applying force F, how much force is needed to Stretch wire 2 by the same amount?

Moderate

A

F
B

4F
C

6F
D

9F

Solution

For same volume AL=constant
$F = \frac{AY}{L} ∆ l \Rightarrow F \infty \frac{A}{L} \infty A^{2} \frac{F_{2}}{F_{1}} = {(\frac{A_{2}}{A_{1}})}^{2} = {(\frac{3 A}{A})}^{2} \Rightarrow F_{2} = 9 F$

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