Question

Spring P has force constant k and a little boy stretches it a distance ℓ. Spring Q has force constant 2 k and the same little boy stretches it a distance 2 ℓ. What is the ratio WQ WP of the work done by the boy?

Answer 1

Answer:

$\dfrac{W_Q}{W_P}={8}$

Explanation:

For spring P

Spring constant = k

Stretches length = l

The work done by boy

$W_P=\dfrac{1}{2}kl^2$

For spring Q

Spring constant = 2k

Stretches length =2 l

The work done by boy

$W_Q=\dfrac{1}{2}2k(2l)^2$

$W_Q=\dfrac{1}{2}\times 8kl^2$

From above equation we can say that

$\dfrac{W_P}{W_Q}=\dfrac{\dfrac{1}{2}kl^2}{\dfrac{1}{2}\times 8kl^2}$

$\dfrac{W_P}{W_Q}=\dfrac{1}{8}$

$\dfrac{W_Q}{W_P}={8}$