Calculating total work using kinetic-work theorem

[tjw137]

1. 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 as shown above. What is the total work done by the children.



2. KE=1/2(mv^2)



3. I was thinking of adding the kinetic energies together. For the girl, I was thinking mv^2 and 1/2 mv^2 for the boy. This would give me 3/2(mv^2), but the correct answer should be 3mv^2. I need help understanding this concept, and how you would arrive to this conclusion. Thanks!

 

[Doc Al]

You are given that the speed of the girl is v, so how her KE be mv^2?

But first things first. How can you figure out the speed of the boy?

 

[tjw137]

By conservation of momentum! Thanks for pointing me in the right direction.

 

[Doc Al]

You are given that the speed of the girl is v, so how her KE be mv^2?

But you were correct about that! (Her mass is 2m, not m. )

By conservation of momentum!

Exactly!

 

[tjw137]

I had written her mass in terms of the boys mass. I was not clear on that in my initial post. Sorry about that. I should have used subscripts.