Question

A spring is cut into two equal halves. how is the spring constant of each half

Answer 1

We know that force (F) is directly proportional to length(l).
i.e F=kl where k is the spring constant .

l'=l/2(given)
F=k'l/2
k'=2F/l......eqn 1
We know k=F/l
k'=2k (substituting in eqn 1)

Answer 2

When a spring is cut into two halves of equal length, the spring constant of each half doubles.

The product of spring constant and length remains constant. Thus K multiplied by length must be same .

K*L=K' *L/2

Thus, the new spring constant will be twice of the original spring constant.

This is because force is directly proportional to the effective length.