Answer to Question #150399 in Mechanics | Relativity for Ziad Abdou

Question

If a spring is doubled in length, then the potential energy stored in the spring will be

Answer 1

Let`s solve this question:

we need to define K if length of spring is doubled:

$k=E\times \frac{S}{l}$, E - young modules, S- area of spring and l-length of spring, So if we doubled length:

$k1=E\times \frac{S}{2\times l}$=$\frac{k}{2}$, k decreases twice than first vaue.

Potential energy: $E=\frac{k1\times l^2}{2}$ if we put k and l:

$E(final)=\frac{\frac{k}{2}\times (2\times l)^2}{2}=2\times E$ this means if doubled length of spring, then its potential energy also doubled.