Question

When two forces of equal magnitude are applied on the two ends of a string , what is the energy stored in the spring ?

I can't make out whether net force on spring is 0 or 2F , Vectorially it adds up to zero , but when I imagine it I feel its 2F . Please help !

Answer 1

Imagine pulling on one end of a spring - there has to be an equal and opposite force applied at the other end of the spring somehow, otherwise the spring would not extend, it would just start to accelerate as a whole under the unbalanced force.

When a spring is stretched by pulling on each end with a force F (same size but opposite directions), the tension in the spring is equal to the magnitude of F.

But your question concerns another aspect, the energy stored in the spring - do you know any expressions for the energy stored in a spring ?

Answer 2

Thanks a lot for helping me out :)
I understood what you have written ,so in the case when force is applied on only one end of a spring , as you said it will accelerate as a whole , so tension would be zero , right ?
Oh , Yes , energy stored is 1/2 kx^2 ..and since tension in it is F =kx here , it would give me 1/2kx^2 on integration , I think so :)

Answer 3

You're right to suppose the tension would be zero in the first circumstance.

Yes, you can write the energy stored in an extended spring as 1/2 kx^2.

But what if we want to express the energy in terms of F rather than x, as the question implies - can you rewrite the expression for the energy using F instead of x ?

Answer 4

Oh , Since F=kx , F/k=x , hence it becomes 1/2(k)(F/k)^2= (F^2)/2k ..thanks a lot !