Confusion about springs and hooke's law

[ehabmozart]

There is a statement in my book i can't really understand. "To stretch a spring, we must do work. We apply equal and opposite forces to the ends of a spring and gradually increase the forces. We hold the left end stationary, so the force we apply at this end does no work.The force at the moving end does do work" ... How is it we apply force on both ends of a spring. Doesn't hook's law apply for the end we actually stretch. F=kx? Kindly Clarify.. Thanks!

 

[K^2]

If you apply force to only one end of the spring, the entire spring will simply accelerate. F=ma still works. If you want to stretch or compress the spring, something or someone must hold the other end of the spring stationary. In other words, the net force on the spring needs to be zero.

 

[ehabmozart]

But then if it is stationary, how does the spring produce a force on the wall = -Fx??

 

[K^2]

Because x is not just displacement of an end point. It's displacement relative to the other end of the spring. If you displace one end by x, it's the same as displacing the other end by -x in terms of Hooke's Law.

 

[Doc Al]

Think of the x in Hooke's law as the amount by which the spring is stretched (from its unstretched length). As K^2 explains, the restoring force is exerted at both ends of the spring.