00:01
Hi there.
00:01
So for this problem, we have two glitters with different masses, move toward a shorter on a frictionless air track and undergo elastic collision.
00:11
Now, we need to find the velocity of each glitter after the collision.
00:16
So that means that we need to find the final velocity one and the final velocity two.
00:23
And, well, in this case, we call it a and b.
00:27
Let's call it dot a and b.
00:33
Okay, so we are given some information in here.
00:38
We are given the initial speed of the glitter a, which is equal to 2 meters per second.
00:50
The mass of the glitter a is also given, and that is equal to 2.
00:56
Oh, sorry, a is equal to 0 .5 kilograms.
01:03
The initial speed of p is also given, and that is minus 2 meters per second, and the mass of p is also given, and that is 0 .3 kilograms.
01:25
So with this information, we can write some equations and find the final speeds.
01:32
So we are going to have two equations, because we have two incognit us.
01:38
Now, the first one comes from the conservation of momentum that we know that the initial momentum must be equal to the final momentum.
01:47
So with that said, we're going to obtain that.
01:50
The mass a times initial speed a plus the mass of b times the initial speed of b is equal to the same thing, but changing now the changing in here the initial speeds by the final speeds because we have that that is the final momentum.
02:18
So we're going to have this final and final.
02:22
Okay, so that's the first equation that we can obtain.
02:26
And the other equation is that since this and this problem states that it is elastic collision, that means that the initial speed a plus the initial the final speed a is equal to the initial speed of b plus the final speed b.
02:49
So that is another condition when, that's another equation that we have when the problem states that it is an elastic collision.
02:59
In this last one, what we can do is to pass the initial ones to one side and the final one to the other side.
03:07
So i'm going to pass this to this side.
03:09
So we're going to have the initial speed of a minus the initial speed of b is equal to, we pass this to the other side, the final speed of b minus the final speed of a.
03:22
So what we are going to do now is to substitute the values of the initial speeds and the masses, so we can obtain a numerical equation.
03:34
So from the first one, if we suppose, the left side, we're going to obtain the following.
03:42
We're going to obtain that this is equal to.
03:45
So we know that the mass a, the mass of a, let me just remembering here, the mass of a is equal to 0 .5 kilograms.
03:57
And the initial speed of a is 2 meters per second.
04:05
And this plus the mass of b, which is 0 .3 kilograms, times its, speed that we know is minus 2 meters per second.
04:15
So if we solve the left side of this, we are going to obtain a value of 0 .4 times the mass.
04:28
And now we are going to substitute also the mass in this other side...