Spring question

Question

A long spring is stretched by 2cm. Its
potential energy is V. If the spring is stretched
by 10cm, its potential energy would be______

Answer 1

The force due to a stretched spring is F = kx, where k is a constant and x is the amount of stretch.  The potential, P, is:

 

P = k∫x dx = (1/2)kx²

 

When x = 2, P = V:

 

V = (1/2) k 2²

V = 2k

V/2 = k

 

So P = (1/2)(V/2)x² = (V/4)x².  For x = 10 cm:

 

P = (V/4)(10²) = 100V/4 = 25V