00:01
In this problem, we have a bar of negligible weight, and our goal is to find tension in this wire that supports it from c to b.
00:12
Also, the maximum position that this weight, w, could be put before the wire would snap.
00:21
So we've got a few things to do.
00:23
First thing in a problem like this, free by diagram.
00:29
So let's redraw it.
00:36
And we have now this is a pin here so in general we would have general an x and y component maybe one of them zero maybe they're both non -zero but we don't know so we just put we just write fx maybe it's to the left maybe it's to the right we don't know likewise with the y maybe it's up maybe it's down we're just being we're just giving representation of those forces and then we'll find them later through equations.
01:08
We have the weight w.
01:12
Technically what this is, we write it as w here, but we've got to be careful.
01:19
The weight itself gets a normal force up on it.
01:22
Third law says that that would be the force down on the bar.
01:27
Well, but in equilibrium, the normal force is equal to w.
01:31
So that's odd times professors, textbook writers, jump.
01:37
That step and just basically say well you're in equilibrium it's going to be the same so don't worry about it but technically technically there's a third law action reaction pair with the normal force up on w and normal force down from w on the bar okay and so we have those forces and then we have the tension along the string the wire and that's at the angle theta now that's make a little table here.
02:16
Force, moment arm, sign.
02:22
This is for the torques.
02:24
Because a torque for an individual force is plus or minus f are perpendicular.
02:30
The plus comes about if that force acting alone would cause the object to turn counterclockwise, minus if it would force it to turn clockwise.
02:39
F is the magnitude of the force.
02:41
R perpendicular is what is called the moment arm.
02:44
It's the perpendicular distance from the line of action of the force to the rotation.
02:47
Axis or equivalently the shortest distance if you're starting your to you're starting at the rotation axis the shortest distance to get from the rotation axis to the line of action equivalent definitions so we have four forces in our problem so let's do it fx f y w and t now let's do our torques around a why do we do that can we choose any point we want yes but we do it around a so that we basically have no contribution of these two unknowns.
03:25
Could we do it on this end? certainly.
03:28
But now you're getting yourself into coupled equations.
03:32
You're just adding mathematics for no physical reason.
03:37
There's no rationale physically that you have to do it that way.
03:40
Any point is as good as any other in this equilibrium situation.
03:44
So you must as choose one that reduces your equations to straightforward.
03:49
One equation gives you one unknown.
03:51
Instead of having a couple of equations.
03:54
So, line of actions.
03:56
Let me change colors so you can kind of see this a little better.
04:00
This would be the line of action.
04:01
It's an infinite line going through the force.
04:07
And so if you're at the rotation axis, what's the shortest walk between the point a and the red line for fy? you look down and you're standing on it.
04:18
Zero.
04:21
Likewise for, likewise for fx, no different.
04:25
You're standing at the rotation axis a, you look down, you're standing on it.
04:30
So it also be zero.
04:31
So those two guys do not appear in the torque equation, which is good.
04:37
Like i said, the idea, it's not a physical issue at this point.
04:43
Because physics says you can choose any point you want, you choose a point that makes your mathematics easier.
04:49
All right.
04:49
Now, for the weight that added mass, here is your line of action.
05:00
Now the shortest walk from a to this red line would be like here.
05:07
This would be the moment arm.
05:12
This is a moment arm for w.
05:15
Notice it makes a 9 degree angle, makes a 9 degree angle with a line of action.
05:20
But it is the shortest walk.
05:22
If you were to go from a to here or a to down here anywhere, isn't that longer than this? so that's the shortest walk...