00:01
In this problem, we have two smooth spheres, a and b, with identical mass.
00:07
A is given a velocity of v -0 while b is at rest.
00:10
We want to determine the velocity of b just after it strikes the wall.
00:16
Now, for the first impact, this occurs when sphere a strikes sphere b.
00:21
When this occurs, the linear momentum of the system is conserved along the x axis, along the line of impact.
00:27
So if we take the right direction as positive, and we use the conservation of momentum, this tells us that the mass of a times its initial velocity va plus the mass of b times its initial velocity before the collision is equal to ma, va, va, 1 after the collision, plus mbb1 after the collision.
01:01
So putting our values in here, this is m v0 plus 0, ball b is at rest, so it has no momentum.
01:10
And this is equal to the mass of a, which is simply m, times va1, plus m vb1.
01:25
And so if you divide both sides by m, we get that va1 plus vb1 is equal to the initial velocity v0.
01:38
So assuming we know v0, we have only two unknowns in this problem, va and vb.
01:47
Now, if we choose again the right direction as possible, and now use the definition for the coefficient of restitution.
01:56
E, remember e is equal to vb1 minus va1, that's the relationship between the velocities after the impact over v0 minus, we'll write down the relationship first, that's va minus vb, the initial velocities.
02:22
So this is actually vb1 minus va1, both of which are unknown over v0 minus 0...