physics question

Question

At an amusement park, a 96 kg bumper car moving with a speed of 1.24 m/s bounces elastically off a 135 kg bumper car that is initial at rest. Find the final velocities of the two cars.

Answer 1

Hi Ashy A.,

1) find motion of the center of mass (CM)

2) calculate velocity of approach of each mass to the CM at collision site (from difference of velocities)

3) this velocity is reversed for each mass after the collision, in the frame of reference of the CM

4) transform relative to CM velocities (after collision) into absolute velocities (after collision). The CM movement continues unaltered, since it has (effectively) all the momentum of the system, considered as a total mass. That's what makes the CM so useful -- it's as if it were a rock-solid, bouncy point. Everything coming at it, leaves at the same momentum, reversed (as CM frame of reference). That also ensures that kinetic energy is conserved in elastic collisions. If a collision is not elastic, the CM still has the same properties, but the individual object momenta and kinetic energies coming out have changed (generally, decreased). The momenta will still stay balanced (conserved), but the kinetic energy generally turns into other things -- heat, rotation energy, sound, light, ...

-- Cheers, -Mr. d.