Suppose that 2J of work is needed to stretch a spring from its natural length of 30cm to a length of 42cm
how much work is needed to stretch the spring from 35 to 40cm
The work done on the spring is equal to the elastic potential energy of a spring. We look at Hooke's law, which states that the force needed to stretch a spring is proportional to the displacement of the spring.
F = -kx W = (integral) Fdx W = (integral) -kx dx W = kΔx²/2 20 = k(42 - 30) / 2 k = 10/3
