How much potential energy does it store, when stretched by 1.0 cm?

Question

A spring is characterized by a spring constant of 60 N/m. How much potential energy does it store, when stretched by 1.0 cm?

Answer 1

From the conservation of energy, the spring will contain as much potential energy PE as the work energy WE put into stretching it.  That is, PE = WE = FdX; where F = f/2 = kdX/2 is the average force in moving the spring dX = .01 m.  k = 60 N/m, the spring constant.

Thus we have PE = WE = (1/2)kdX^2 = (1/2)60(.01)^2...you can do the arithmetic.

The physics is this.  The work function is FdX, which is the average force times the distance the force acts over.  That work has to go somewhere because, according to the conservation of energy law, energy is neither created nor destroyed; that somewhere is into the potential energy of the spring.  That is, the work energy is converted into potential energy of the spring.