00:01
Here we're going to look at the condition for equilibrium that the sum of forces on an object must be equal to zero.
00:16
And usually it is best to start with a force diagram and show all the forces and then work out components.
00:27
And then add up the x components and the y components and see how they can.
00:34
Can be equal to zero.
00:37
There is a second condition of equilibrium that says the sum of the torques on an extended object is equal to zero.
00:46
And ordinarily, you would have to use this with something like the forearm that we're going to discuss.
00:53
However, they do not give enough position information in order to figure out exactly where the forces are acting, so we can take torques.
01:04
But we're doing the sample with a forearm, which we are going to model as just a stick.
01:12
And we are told some things about the forces on this stick, namely that the weight of the forearm, which we'll call w, is 20 .5 newton's by itself.
01:26
But the person is also holding a weight in their hand as part of their exercise, and that's 120 newtons down.
01:37
I know those aren't quite to scale.
01:39
Let me scale them a little bit.
01:42
We're also told that we have a situation where the slant of the stick, and i don't have it quite drawn right, is a 43 degree angle to the horizontal.
02:01
Okay, so i'll have to draw it a little bit more slanted like so.
02:07
43 degree angle.
02:10
That may not be the best picture, but it will work.
02:14
And then we are told that the biceps muscle is perpendicular to the arm, no matter how the arm is oriented.
02:25
And at this particular angle makes an angle of 232 newtons.
02:30
And there is one last force, which is working at the elbow.
02:35
I will call that the e -force, and we don't know anything about it, so we'll just leave it as e -question mark.
02:43
And of course, that is what we are going to try to solve for.
02:47
So the next thing that i try to do is write up a little table.
02:52
For each force, we want to set the table up so we can calculate the x and y components.
03:02
And let's see, we'll call this.
03:06
Hand weight, hw for hand weight.
03:11
And the two weights, of course, are the easiest to create because they both point straight down, which we'll call negative y, we'll call positive y up, and to the right, positive x.
03:26
So the hand weight has two components, zero in the x, minus 112 newtons in the y.
03:36
And we'll just assume newtons from now on.
03:39
And of course, the weight of the forearm is similar to minus 20 .5 downwards.
03:50
The what to call that, the biceps, we'll call that b for bicep.
03:57
It would be nice to know what angle it's making to the horizontal.
04:02
And we can use a little bit of logic.
04:05
If it's making a right angle to the arm and the arm is at a 43 degree angle.
04:13
We are left with the complement of that angle in the second quadrant.
04:19
So the biceps force will have a negative 22 cosine of 47 and a positive to 32 sign of 47.
04:39
The arrow is pointing up and to the left...