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What effect does doubling the diameter and length of a wire have on elongation (\Delta L) if...

Question:

What effect does doubling the diameter and length of a wire have on elongation ({eq}\Delta L {/eq}) if everything else is kept constant?

A. {eq}\Delta L/2 {/eq}

B. {eq}\Delta L {/eq} does not change.

C. {eq}\Delta L/4 {/eq}

D. {eq}\Delta L/8 {/eq}

E. {eq}2 \Delta L {/eq}

Hooke's Law:

The Hooke's Law says that within the elastic limit, the strain produced in a body is proportional to the stress developed in the body. The relation between the applied force, the area of cross-section of the specimen, the lenght, and change in lenght of the specimen is given by the following formula:

{eq}\begin{align} \frac{F} {A} &= E \frac{\Delta L} {L} \\ \end{align} {/eq}

Where E is the material constant known as the Young's Modulus.

Answer and Explanation:

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{eq}\begin{align} \frac{F} {A} &= E \frac{\Delta L} {L} \\ \Rightarrow \Delta L &= \frac{FL} {AE} \\ \Rightarrow \Delta L &= \frac{FL}...

See full answer below.


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Hooke's Law & the Spring Constant: Definition & Equation

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Chapter 4 / Lesson 19
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After watching this video, you will be able to explain what Hooke's Law is and use the equation for Hooke's Law to solve problems. A short quiz will follow.


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