00:02
So this question involves what is known as an at -width machine.
00:07
The first thing, according to the hint that gave us there, the first thing we need to do is determine the acceleration of this ad -with machine.
00:15
It says to determine the acceleration of lighter mass, but the acceleration of lighter mass is also going to be equal to, in magnitude, in any way, the acceleration of the heavier mass.
00:24
It's going to be going to be going to different directions, but because they're connected together by that cord, they're going to have the same acceleration amount.
00:31
Several ways to approach it.
00:33
Let's take the easiest one.
00:35
We will just write an equation for each of the masses.
00:42
That's called lighter mass m1 and the heavy mass m2.
00:47
And then the force is acting on the lighter mass will be the tension in the rope.
00:52
And then that's going to be going up and we'll say that the force of gravity on it is going down.
00:59
So we're going to say m1 times g and according to newton's second law that should equal m1 times the acceleration now let us consider the other mass but let's take as for the other mass let's take down as our positive direction that way when we're solving for its acceleration it'll be the same acceleration as the other mass because when one mass goes up it'll go down so the right hand side we're going to call the downward direction as positive which means that its weight m2 times g minus the tension going up are going to equal m2 times a.
01:44
And there's a way you can do this with just treating the whole thing as one single system that's accelerating, but this is another way to do it.
01:51
If we add these two equations together, then we get another two equation, which should be the t cancels out with its negative there.
02:01
So this is going to give us m2g minus m1g is equal to m1 plus m2 times a.
02:18
And therefore we can kind of rewrite this a little bit, meeting it up a little bit.
02:23
This is m2 minus m1 times g divided by m1 plus m2 is equal to the exalt.
02:40
So if you plug in all the numbers that we know, m2, m1, and g, what i'm using 9 .8 for g, you end up with 6 .38 meters per second as the acceleration of the system, which is the acceleration of both of the masses.
03:03
So now we know the acceleration.
03:05
And what we're saying is that it's going to undergo that acceleration over the displacement of 0 .3 meters.
03:14
That's how far the heavier mass is going to move down, is going to move down 0 .3 meters, which means that the lighter mass is going to be accelerated upwards by an amount of 0 .3 meters.
03:32
And so therefore, we can talk about the velocity that's going to have when it's accelerated upwards at 0 .3 meters.
03:39
Let's get its velocity.
03:41
Starts at rest.
03:42
And so its velocity when it gets to that launch position, as they've called it in there.
03:48
I'm going to call it vl.
03:50
That's this launch velocity.
03:51
So we don't get all these velocities confused.
03:53
We're going to say that the velocity it's going to have when the heavier mass has gone down a distance of 0 .3 meters and lighter mass has gone up a distance of 0 .3 meters is going to equal its initial velocity, which is at rest...