Name: Forces: Conservative and Non-conservative
Uploaded: 2019-07-19
Duration: 4 min 29 s
Description: In this video, let us define the conservative and non-conservative forces and determine which forces are conservative and which are not. Learn more.

Question

Calculate the potential energy stored in a spring when it is compressed.

Accepted Answer

Potential and kinetic energy is stored in a spring when you compress or stretch it. The work you do compressing or stretching the spring must go into the energy stored in the spring. That energy is called elastic potential energy and is equal to the force, F, times the distance, s:

$W = Fs$

Compress a spring, the force varies, but it varies in a linear way (because in Hooke’s law, force is proportional to the displacement).

The distance (or displacement), s, is just the difference in position, $x_{f} and x_{i}$ and the average force is $\frac{1}{2} (F_{f} + F_{i})$ . Therefore, you can rewrite the equation as follows:

$W = \frac{1}{2} (F_{f} + F_{i}) (x_{f} - x_{i})$

Hooke’s law says that $F = - kx$ .Therefore,

$W = \frac{1}{2} - (F_{f} + F_{i}) (x_{f} - x_{i})$

Distributing and simplifying the equation gives you the equation for work in terms of the spring constant and position:

$W = \frac{1}{2} k {x^{2}}_{i} - \frac{1}{2} k {x_{f}}^{2}$

The work done on the spring changes the potential energy stored in the spring. Here’s how you give that potential energy, or the elastic potential energy

$P . E = \frac{1}{2} {kx}^{2}$ .

Calculate the potential energy stored in a spring when it is compressed.

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