00:02
Okay, so for this problem, it's asking us to find the largest counterweight for a loaded car on an inclined plane.
00:09
So to start off, we want to find the mass of the car, which we do by dividing the weight 4 ,000, by gravity, giving us 124 .2 pounds mass.
00:22
So next, we want to calculate the moment of the system.
00:25
So generally, you can take the moment of the system about any point and should get the same answer no matter what.
00:30
But it's best to choose a point where a force is acting since taking the moment there means that you don't have to include it in your calculations since the moment caused by that force is zero, which simplifies things a lot.
00:42
So we should choose point b as indicated here by the little subscript.
00:48
And that will equal to 124 .2a times three.
00:54
And so the reason we multiply by three here is because it's three feet away from the center of mass of the complex.
01:00
And similarly for multiplying by three here and multiplying by two here, it's just the number of feet that the distance of the force is acting on.
01:12
And from that we get our first equation, which we're going to use later.
01:19
And we can simplify this down into t minus 372 .6 .7a.
01:28
And that's equal to negative 928 .2.
01:45
So that's our first important equation...