00:01
So in this problem, we're going to be looking at torques, also called moments.
00:05
I'll try to keep it torques like the problem says though.
00:09
So in our first situation here, we have a beam of four meters total, which means each side would be, of course, half of that, or two meters.
00:22
And so we have some forces acting on it.
00:27
Let's not do that in blue, though, because that's the dimension color.
00:37
0 .63 newtons upwards on the right here, 11 newtons upwards on the left here, and then 9 newtons, and this is 0 .5 meters from the end, which means from the center would be 1 .5 meters to match the 2.
00:58
And so for all these problems, we're going to set our axis at the fulcrum here, x and y, and that's where we're going to take our torques about.
01:09
So, of course, we can take the of all twerks and we'll pick counterclockwise to be positive because of course we need a direction.
01:15
So we know that a torque is a force times a distance.
01:20
And so whatever force on the fulcrum doesn't matter because that distance is zero.
01:23
And here we all have perpendicular forces and the direction, so it doesn't really matter to add the angle yet.
01:32
And so if we look at this 11 newton force tends to rotate clockwise around our fulcrum, so it's going to be a negative moment.
01:41
And so the sum of twerks here is a number.
01:43
Equal to negative 11 and what distance is it away from the center? well, it's at the end, so two meters, because that's one half.
01:51
The nine newtons tends to be the same way around.
01:55
So it's also a negative moment 1 .5 meters away from the dimensions we set, and are 0 .63, the other direction, so positive now, also two meters away.
02:06
So we add that all up to get the sum of torques equal to negative 34 .24 and newton meters as the unit.
02:15
That just means our torque is overall clockwise here because we picked counterclockwise to be positive.
02:21
That's the convention, but as long as you're consistent, you can do problems with either direction.
02:25
So the same kind of process for all of our situations.
02:30
Here we have a 2 .4 meter total beam, so it's 1 .2 meters on each side, 7 newtons downwards on one end, and this 0 .63 newton force downwards, but it's towards the left, and it is 10 degrees.
02:48
From the horizontal.
02:50
Now we can break this force down into two components, a vertical force, so we can call it say force in the y and force in the x.
02:59
Now if we look back at our definition of torque, it's based, it's multiplied by a distance.
03:03
So fx here goes along the beam axis and we know our axes are right here.
03:09
And so what that means is the x component of this force makes no moment because its distance is zero.
03:15
So we only want to consider the f y component.
03:17
Now we can also draw it here, we see it's opposite the angle, so it's going to be the sign part of the force.
03:27
So, summa torcs, oh, and there's also a 2 newton force here, which is 0 .2 meters away from this end, so it means it's 1 meter from the fulcrum...