Answer to Question #264133 in Electricity and Magnetism for Melly

Question

4. Angelo was choosing springs to use their door. He noticed that spring A was stiffer than spring B; that is ka> ka. Which spring will have more elastic potential energy stored if (a) they are compressed the same distance and (b) if the same force is applied on them?

Answer 1

Given,

Spring constant of sprint A $=K_a$

Spring constant of spring B $=K_b$

As we know that spring A is stiffer than spring B, so $K_a>K_b$

If same force(F) applied on both the spring then the elongation in the spring be $x_a$ and $x_b$

$x_a=\frac{F}{K_a}$ and $x_b=\frac{F}{K_b}$

Now, potential energy stored in the spring

$E_a=\frac{k_a F^2}{2K_a^2}$

$E_b=\frac{k_b F^2}{2K_b^2}$

Now, $\frac{E_a}{E_b}=\frac{k_b}{k_a}$