156k views
5 votes
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?

1 Answer

4 votes

Answer:

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.

User Tbhartman
by
8.6k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.