00:01
In this problem, two smooth disks a and b with the identical mass are moving with different velocities before they collide.
00:09
We want to calculate their final velocity just after the collision.
00:14
Let's first look at the horizontal components of the momentum.
00:21
And we know that these must be conserved.
00:23
So the conservation of momentum tells us that the initial momentum of the two disks before the collision must equal to the final momentum of the disks after the collision.
00:33
So initially, the disks have momentum, disk 1, its mass 0 .5 times its x component of its velocity, which is 4 cost theta, which is 4 times 3 over 5, minus the initial velocity of disk b, or disk a actually, is minus mass 0 .5, times the x component of its velocity, which is 5, which is 1 .5 ,000.
01:08
Simply six, six meters to second.
01:13
After the collision we have that disk b has momentum 0 .5 v v .2 in the x direction plus the momentum of block of disk a which is 0 .5 v .a, 2 in the x direction.
01:42
And so essentially we have an equation there with two unknowns.
01:47
So now that we've used the conservation of momentum, let's look at the definition of the coefficient of restitution.
01:55
The coefficient of restitution e is equal to va2, the velocity of a after the collision, minus the velocity of disk b after the collision over the initial velocity of disk b vb1, minus the initial velocity of disk a, va1...