Firing a ball from a cart at rest on air track

This is the classical recoil experiment where the change in internal energy comes from explosion of lighter gas. This seemingly more complex event is also fully accounted for by simply recognizing that the linear momentum and the total energy of the system cannot change. This time we do not know exactly how large the change in internal energy will be but by observing the recoil we will determine this energy, . If is the recoil velocity of the cart then because linear momentum must be conserved the velocity of the ball with respect to the ground is

With this velocity the ball should fly a distance

before hitting the floor and we can put in numbers to see if it looks sensible. We can also determine from energy conservation:

we put in numbers and obtain in kJ.