00:01
In this video, i'm going to be working with conservation laws, namely the laws of conservation of mechanical energy and conservation of momentum.
00:09
Okay, and we're going to be looking at a collision and using these laws to answer some questions.
00:15
Right, so let me show you our setup.
00:17
Okay, so we have this semi -circular kind of ramp.
00:21
All right, and we've got two blocks.
00:23
They're each held at the same height at rest.
00:26
Okay, we're going to release them from rest.
00:28
They're going to travel down these frictionless ramps.
00:31
So this whole track is frictionless, so we won't have to worry about that factor.
00:35
But anyway, they're going to travel down the ramp.
00:38
They're going to collide in a perfectly elastic collision, bounce back.
00:43
Okay.
00:43
And what we want to find is the velocity of each block before the collision, the velocity of the blocks after the collision, and then the maximum height that each block rebounds to you after it clides and then moves back up the ramp.
00:57
Right, so let me get you some numbers so we can start working on this.
01:02
I have the masses of my blocks.
01:05
So mass 1 equals 1 .83 kilograms.
01:08
Mass 2 is 4 .84 kilograms.
01:12
And each block starts at a height h above the origin.
01:16
Okay, i'm going to call this level the origin.
01:19
Also, this is going to be my positive direction.
01:21
This will be my negative direction.
01:23
All right, so let's just go over quickly what our conservation laws are.
01:27
That says that a quantity is conserved, so it does not change over time.
01:33
So that means for momentum, my initial momentum equals my final momentum.
01:39
Okay, so this is for a closed system with no outside forces acting, and that is what we have here in this ramp system.
01:46
And then the same thing for the conservation of mechanical energy.
01:49
That is also constant.
01:50
And we know mechanical energy equals kinetic energy plus potential energy.
01:58
Energy.
02:00
All right.
02:01
So let's look at the speed of each block before the collision, right? so after they've been released from rest and just before they collide.
02:11
Okay.
02:11
And for this, i'm going to use the concept of conservation of energy.
02:15
Okay, so let's look at block one first.
02:18
Right? initially, it's at rest.
02:20
So it's mechanical energy will be all potential.
02:23
So it's going to be potential energy, and that equals m, g, h, where g is the acceleration due to gravity, and h is the height that we're at.
02:34
Mass, of course, is the mass of the block.
02:36
Right.
02:37
Just before the collision, it's at the origin.
02:40
It has no more potential energy.
02:42
The energy is all kinetic.
02:44
Okay, so kinetic energy equals one -half mass times a velocity squared.
02:50
That's mass of one.
02:51
All right, we can see that the two energies are going to be, equal.
02:57
So we're going to have m1gh equals 1 1�m1v squared...