00:01
In this problem, we have two disks of different masses which are moving toward each other with different velocities.
00:09
They strike each other with a given coefficient of restitution, and we wish to calculate the final velocities of either disk.
00:19
Now, the first thing we will do is use the conservation of linear momentum.
00:28
So the conservation of momentum tells us that the initial mass of disk a times its initial velocity, so m -a -1 plus the initial momentum of disk b, m -b -b -1, is equal to the final velocity at which disk a moves off m -a -2 plus the final momentum of disk b, which is m -b -b -2.
01:03
So if we take the right direction, as we see in our diagram, we take the right direction as positive, we get that the mass of a which is 2 times its velocity 5 meters per second plus the mass of b which is 4 times its velocity initially minus 2 meters per second is equal to 2 times the final velocity of v of a va plus 4 times the final velocity of b vb2.
01:39
So we have an equation here with two unknowns.
01:42
We'll call this equation 1.
01:45
Relating va and vb...