A ball with a mass of #2 kg# moving at #3 m/s# hits a still ball with a mass of #10 kg#. If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?

Question

15549 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-05T12:52:06

The second ball moves at #0.6ms^-1#.

#7.2J# or #80%# of the original kinetic energy is lost.

Conservation of momentum says that momentum before a reaction and momentum after a reaction must be equal.

Momentum is the product of mass and velocity, so

#(mv)_1 = (mv)_2#

Only moving objects have momentum, so all the momentum beforehand is in the moving ball, so

#(mv)_1 = 2kg xx 3ms^-1 = 6Ns#

This ball stops moving, and now only the #10kg# ball moves, so momentum after the reaction is

#(mv)_2 = 10kg xx vms^-1#

We know that this is equal to the momentum before, so

#10 xx v = 6 -> v = 0.6ms^-1#

Now for the second part. Calculating kinetic energy is done by the equation

#E = 1/2mv^2#

which, before the reaction, is

#E = 1/2 xx 2 xx 3^2 = 9J#

after the reaction, it will be

#E = 1/2 xx 10 xx 0.6^2 = 1.8J#

Overall, then, the kinetic energy lost is

#DeltaE = 9 - 1.8 = 7.2J#

or, as a percentage,

#(9-1.8)/9 xx 100% = 80%# of the kinetic energy is lost.