00:01
In this example, we're looking at a collision problem.
00:03
Okay, so right away we know we're going to be dealing with conservation of momentum and conservation of kinetic energy.
00:09
Okay, so what we have is a block sliding along a horizontal surface.
00:13
Okay, it's got some initial velocity, phi initial, and that's in the positive x direction.
00:20
Okay, it's going to collide with a pendulum of length l.
00:27
Okay, and we're going to look at this collision for two cases.
00:31
For the first case, we're looking at a completely elastic collision, so no kinetic energy is lost.
00:38
In the second case, we're looking at an elastic, completely inelastic collision, so the objects will stick together after the collision.
00:48
Okay, we want to find the angle that this pendulum bob makes with the vertical axis theta.
00:57
Okay, after the collision for each of those two cases.
01:01
Okay, so obviously the block for case one, the elastic collision, the block is going to come in, it's going to strike the bob, the bob's going to move up.
01:09
The block itself will either continue on its way in the positive x direction, or it will reverse direction and go back in the negative direction.
01:19
Okay, in the second case, we're going to have the block still coming in, hits the block, hits the bob, and now they're both going to swing up together as one object and reach some new angle above the, or with respect to the vertical axis.
01:35
Okay, so we've got some numbers here, and then we'll start solving.
01:38
I have the mass of the block equals three kilograms.
01:42
I have the mass of the pendulum bob equals five kilograms.
01:51
I have the length of the pendulum bob is two meters, not of the pendulum bob, of the pendulum itself, the whole pendulum.
02:00
I have the initial velocity of the block, and that's two meters per second in the positive x direction.
02:08
Okay, so let's look at the elastic case first, because this one will take us the longest time.
02:16
Okay, so elastic, i know my initial momentum equals my final momentum, and my initial kinetic energy equals my final kinetic energy, and i can use these two equations to solve for my velocities post -collision for both the bob and the block.
02:32
Okay, so my initial momentum equals the initial mass of the block times velocity of the block plus mass of the pendulum times velocity of the pendulum, that's just zero.
02:46
So that is gone.
02:48
So that equals my final momentum, and that's mass of the block times velocity of the block.
02:54
I'll call this prime post -collision, plus the mass of the pendulum times the velocity of the pendulum.
03:02
Okay, so this gives me one equation, but i have two unknowns, so i need another equation, and i'm going to use a conservation of kinetic energy.
03:09
So pre -collision, my kinetic energy is one half m block v block squared.
03:17
Post -collision, it's one half m block v prime squared plus one half m pendulum velocity of pendulum squared.
03:31
Okay, so now i can solve these two expressions for my velocities post -collision.
03:38
I don't have time to do that derivation because it is very tedious, so i'll give you the result, and i'll just give you the result for the velocity of the pendulum because we don't care about the block anymore.
03:47
We don't care about it after the collision, and that equals two times the mass of the block divided by the mass of the block plus the mass of the pendulum times the velocity of the block initial, and that equals 1 .5 meters per second...