Question

a spring of mass m and spring constant k is extended by a distance x with velocity V. What is the work done by the external force
​

Answer 1

Given :-

Mass of Spring = m

Spring Constant = k

Distance of extension = x

Velocity of extension = v

As we know that By Work-Energy Theorem that, Work done by all the forces on the body is equal to the change in its kinetic energy.

Work done by Spring = Change in Kinetic Energy

1/2 kx² = 1/2 mv² - 1/2 mu²

As the body doesn't have initial Kinetic energy because initial velocity is zero.

1/2 kx² = 1/2 mv²

Now,

Work done by External Force,

W = Work done by Spring Force + Change in Kinetic energy

W = 1/2 kx² + 1/2 mv²

W = 1/2(kx² + mv²) J