Question

A boy of mass m and a girl of mass 2m are initially at rest at the center of a frozen pond. They push each other so that she slides to the left at speed v across the frictionless ice surface and he slides to the right. What is the total work done by the children?

Answer 1

Step-by-step explanation:

Given

mass of boy is m

mass of girl is 2 m

Speed of girl is v towards left

Let u be the speed of boy after push

Conserving momentum

0=2m(v)+mu

u=-2v

Kinetic Energy of girl after push
`=(2mv^2)/(2)=mv^2`

Kinetic Energy of boy after Push
`=(m(2v)^2)/(2)=2mv^2`

Total Kinetic Energy
`=3mv^2`

Thus Work done =total Kinetic Energy
`=3mv^2`