Question

When a piece of wood is pressed against a spring and compresses the spring by 2.00 cm , the wood gains a maximum kinetic energy K when it is released. How much kinetic energy (in terms of K) would the piece of wood gain if the spring were compressed 10.0 cm instead?

Answer 1

If, S = spring constant of the spring.

x = compression of the spring

Then the maximum kinetic energy of the wood = potential energy stored in the spring = (1/2)*S*x^2

So, in the first case -

K = (1/2)*S*2.00^2-------------------------------------------------(i)

Suppose, in the second case, maximum kinetic energy of the wood = K'

So, K' = (1/2)*S*10.00^2-----------------------------------------------(ii)

Do (ii)/(i) -

K'/K = [(1/2)*S*10.00^2] / [(1/2)*S*2.00^2] = 10.00^2 / 2.00^2 = 100 / 4 = 25

Hence, K' = 25*K (Answer)