Question

A spring is stretched from x=0 to x=d, where x=0 is the equilibrium position of the spring. It is then compressed from x=0 to x=−d. What can be said about the energy required to stretch or compress the spring?

Answer 1

The energy stored in the later case is equal to the energy stored in the former case of the spring.

Step-by-step explanation:

For a spring we have the expression of kinetic energy as:

`\rm KE=(1)/(2) k.x^2`

where:

k= elastic constant of the spring

x= length of deflection of the spring from the mean position

Here we are given two cases:

CASE:1

x=d

`\therefore KE_1=(1)/(2) k.(d)^2`

CASE:2

x=-d

`\therefore KE_2=(1)/(2) k.(-d)^2`

`\therefore KE_2=(1)/(2) k.d^2`

So, we get

`KE_1=KE_2`

Just the difference in the two cases is that there is deflection of the spring in the opposite direction.