00:01
Okay, this one is a fun one.
00:03
The first thing to know is we're looking for the masses of a, b, c, and d.
00:11
This is in dynamic equilibrium.
00:13
And so that means our torques are balanced.
00:17
And if you think about it, a torque is going to be your force perpendicular times of distance.
00:22
And all of these masses are hanging at right angles.
00:26
And so i know that my force times distance, for part d is going to equal my force times distance for part c.
00:37
Now, as they're hanging, i'm going to bring these together with that idea.
00:46
But i am going to use that if my force times my distance is going to balance out the force times the distance on the left, the force we're talking about is the force of gravity.
00:59
And so force of gravity is just mass times gravity.
01:07
And so notice this is the left side, this is the right side.
01:11
So they're not the same masses, but the gravities will cancel.
01:14
So i am going to use the understanding that my mass times my distance on the left is going to balance with my mass times my distance on the right.
01:23
So i'm going to set up a few different equations.
01:26
I'm going to start at the bottom and kind of work my way up.
01:29
So on the bottom, i know that 17 .5 centimeters times d.
01:38
Is going to equal 5 centimeters times c.
01:45
Up here, i know that if i know d and c, that's what's hanging right here.
01:52
So i know 15 centimeters times d plus c is going to balance out with the 5 centimeters times b.
02:03
And then if i come all the way up here, i know that all three of these masses are hanging on this cable over here.
02:14
So i know to balance out with a, i have that 30 centimeters times a, and that's going to equal that 7 .5 times all of these masses that are hanging off of this side.
02:29
So d, b plus d plus c.
02:32
So say b, c, we'll just go alphabetical order.
02:37
One thing that we do know is that b is 0 .75 kilograms.
02:45
Okay, so i know 15 times d plus d plus c equals 5 times 0 .75.
03:01
So you get 3 .75 here.
03:07
This has d and c, so i'm going to use the pink equation and get it in terms of one or the other.
03:13
So i'm going to divide by 5 to get it in terms of c.
03:18
So i get c equals 3 .5d.
03:26
And then i'm going to use that information right here.
03:30
And i'm going to substitute it in right here...