00:01
Hi there.
00:01
So for this problem, we have two glitters with different masses that move to where it's shorter, and a frictionless air track, and undergo elastic glist.
00:10
So we need to find the velocity of each glitter after the collision.
00:15
So we are given the initial values.
00:19
So we have the mass and the speed of one.
00:26
We're going to call the initial speed of one.
00:28
And that is equal to two meters per second.
00:31
The initial speed of 2 that is equal to minus 2 meters per second.
00:38
And we also have the mass of 1, which is equal to 0 .5 kilograms at the mass of 2, that is equal to 0 .3 kilograms.
00:51
And what we need to find is the final speed for 1 and the final speed for 2.
00:58
So in this case, we are going to have two equations, and the first one comes from the conservation of momentum.
01:06
We know that the initial momentum should be equal to the final momentum.
01:09
So the initial momentum is going to be the mass m1 times its initial speed plus the mass m2 times its initial speed, and this should be equal to the mass m1 times its final speed, plus the mass m2 times its final speed.
01:26
And the other equation that we're going to have since the problem states that the glitters undergo an elastic collision.
01:35
That means that the sum of the initial speed one plus the final speed one is equal to the sum of initial speed two plus the final speed two.
01:47
So we have these two equations.
01:50
What we are going to do, first i'm going to move the initial speeds to one side.
01:58
So we're going to put all in this part, see this side of the equation, and the final twos in this side.
02:09
Okay, we have this.
02:11
Now, what we are going to do is to substitute the values that we know for the initial speeds and the masses in both equations.
02:20
So for the first one, we're going to call this just one and this two.
02:25
So for the first one, if we substitute the values, we are going to have the mass m1 which is 0 .5 kilograms times the mass m1 which is 0 .5 kilograms times the mass at the speed the initial speed 1 which is 2 meters per second and this plus the mass 2 which is 0 .3 kilograms and this times minus 2 meters per second which is the initial speed 2.
03:03
And this is equal to the mass m1, which is 0 .5 kilograms, times the final speed 1, and this plus 0 .3 kilograms times the final speed 2.
03:22
So we have that, and what we are going to do now is to substitute, when we solve this in here, we are going to obtain it that is 0 .4.
03:36
I'm going to leave it without the units for now.
03:39
And this is equal to 0 .5 times the initial speed, the final speed of 1 plus 0 .3 times the final speed of 2.
03:49
Now, what we can do to get this a better sense of what we are doing in here is to multiply all of this by 10...