A certain wire stretches 0.90 cm when outward forces with magnitude F are applied to each end.The same forces are applied to a wire of the same material but with three times the diameter and three times the length.The second wire stretches:
A)0.10 cm
B)0.30 cm
C)0.90 cm
D)2.7 cm
E)8.1 cm

Question

Quizplus · Accepted Answer

The stretch of a wire under a force is given by the formula $ \Delta L = \frac{1}{Y} \cdot \frac{F}{A} \cdot L $, where $ \Delta L $ is the change in length, $ Y $ is Young's modulus (a property of the material), $ F $ is the force applied, $ A $ is the cross-sectional area, and $ L $ is the original length of the wire. When the diameter is tripled, the area ($ A = \pi r^2 $) becomes 9 times larger because the radius is doubled (area is proportional to the square of the radius). When the length is tripled, the effect of the increased length is to triple the stretch. However, because the area is 9 times larger, the stretch due to the force is reduced by a factor of 9. Therefore, the overall effect is to reduce the stretch by a factor of 3 (triple the length but divide the stretch by 9 due to the increased area), making the stretch $ \frac{0.90 \, \text{cm}}{3} = 0.30 \, \text{cm} $.

A Certain Wire Stretches 0