I'm going to do a couple more moment and force problems,
especially because I think I might have bungled the
terminology in the previous video because I kept confusing
clockwise with counterclockwise.
This time I'll try to be more consistent.
Let me draw my lever again.
My seesaw.
So that's my seesaw, and that is my axis of rotation, or my
fulcrum, or my pivot point, whatever you want to call it.
And let me throw a bunch of forces on there.
So let's say that I have a 10-Newton force and it is at a
distance of 10, so distance is equal to 10.
The moment arm distance is 10.
Let's say that I have a 50-Newton force and its moment
arm distance is equal to 8.
Let's say that I have a 5-Newton force, and its moment
arm distance is 4.
The distance is equal to 4.
That's enough for that side.
And let's say I have a I'm going to switch colors.
Actually, no, I'm going to keep it all the same color and
then we'll use colors to differentiate between
clockwise and counterclockwise so I don't bungle
everything up again.
So let's say I have a 10-Newton force here.
And, of course, these vectors aren't proportional to
actually what I drew.
50 Newtons would be huge if these were the actual vectors.
And let's say that that moment arm distance is 3.
Let me do a couple more.
And let's say I have a moment arm distance of 8.
I have a clockwise force of 20 Newtons, And let's say at a
distance of 10 again, so distance is equal to 10, I
have my mystery force.
It's going to act in a counterclockwise direction and
I want to know what it needs to be.
So whenever you do any of these moment of force
problems, and you say, well, what does the force need to be
in order for this see saw to not rotate?
You just say, well, all the clockwise moments have to
equal all of the counterclockwise moments, So
clockwise moments equal counterclockwise.
I'll do them in different colors.
So what are all the clockwise moments?
Well, clockwise is this direction, right?
That's the way a clock goes.
So this is clockwise, that is clockwise.
I want to go in this direction.
And so this is clockwise.
What are all the clockwise moments?
It's 10 Newtons times its moment arm distance 10.
So 10 times 10 plus 5 Newtons times this moment arm distance
4, plus 5 times 4, plus 20 Newtons times its moment arm
distance of 8, plus 20 times 8, and that's going to equal
the counterclockwise moments, and so the leftover ones are
counterclockwise.
So we have 50 Newtons acting downward here, and that's
counterclockwise, and it's at a distance of 8 from the
moment arm, so 50 times 8.
Let's see, we don't have any other
counterclockwise on that side.
This is counterclockwise, right?
We have 10 Newtons acting in the counterclockwise
direction, and its moment arm distance is 3, plus 10 times
3, and we're assuming our mystery force, which is at a
distance of 10, is also counterclockwise,
plus force times 10.
And now we simplify.
And I'll just go to a neutral color because this
is just math now.
100 plus 20 plus 160 is equal to-- what's 50 times 8?
That's 400 plus 30 plus 10F.
What is this?
2, 50 times 8.
Right, that's 400.
OK, this is 120 plus a 160 is 280.
280 is equal to 430-- this is a good example-- plus 10F, I
just realized.
Subtract 430 from both sides.
So what's 430 minus 280?
It's 150.
So it's minus 150 is equal to 10F.
So F is equal to minus 15 Newtons in the
counterclockwise direction.
So F is minus 15 Newtons in the counterclockwise
direction, or it means that it is 15 Newtons.
We assumed that it was in the counterclockwise direction,
but when we did the math, we got a minus number.
[SNEEZE]
Excuse me.
I apologize if I blew out your speakers with that sneeze.
But anyway, we assume it was going in the counterclockwise
direction, but when we did the math, we got a negative
number, so that means it's actually operating in the
clockwise direction at 15 Newtons at a distance of 10
from the moment arm.
Hopefully, that one was less confusing than the last one.
So let me do another problem, and these actually used to
confuse me when I first learned about moments, but in
some ways, they're the most useful ones.
So let's say that I have some type of table.
I'll draw it in wood.
It's a wood table.
That's my table.
And I have a leg here, I have a leg here.
Let's say that the center of mass of the top of
the table is here.
It's at the center.
And let's say that it has a weight.
It has a weight going down.
What's a reasonable weight?
Let's say 20 Newtons.
It has a weight of 20 Newtons.
Let's say that I place some textbooks on top of this
table, or box, just to make the drawing simpler.
Let's say I place a box there.
Let's say the box weighs 10 kilograms, which would be
about 100 Newtons.
So let's say it weighs about 100 Newtons.
So what I want to figure out, what I need to figure out, is
how much weight is being put onto each of
the legs of the table?
And this might not have even been obviously a moment
problem, but you'll see in a second it really is.
So how do we know that?
Well, both of these legs are supporting the table, right?
Whatever the table is exerting downwards, the leg is exerting
upwards, so that's the amount of force that each of the legs
are holding.
So what we do is we pick-- so let's just pick this leg, just
because I'm picking it arbitrarily.
Let's pick this leg, and let's pick an
arbitrary axis of rotation.
Well, let's pick this is as our axis of rotation.
Why do I pick that as the axis of rotation?
Because think of it this way.
If this leg started pushing more than it needed to, the
whole table would rotate in the
counterclockwise direction.
Or the other way, if this leg started to weaken and started
to buckle and couldn't hold its force, the table would
rotate down this way, and it would rotate around the other
leg, assuming that the other leg doesn't fail.
We're assuming that this leg is just going to do its job
and it's not going to move one way or the other.
But this leg, that's why we're thinking about it that way.
If it was too weak, the whole table would rotate in the
clockwise direction, and if it was somehow exerting extra
force, which we know a leg can't, but let's say if it was
a spring or something like that, then the whole table
would rotate in the counterclockwise direction.
So once we set that up, we can actually set this up as a
moment problem.
So what is the force of the leg?
So the whole table is exerting some type of-- if this leg
wasn't here, the whole table would have a net clockwise
moment, right?
The whole table would tilt down and fall down like that.
So the leg must be exerting a counterclockwise moment in
order to keep it stationary.
So the leg must be exerting a force upward right here.
The force of the leg, right?
We know that.
We know that from basic physics.
There's some force coming down here and the leg is doing an
equal opposite force upwards.
So what is that force of that leg?
And one thing I should have told you
is all of the distances.
Let's say that this distance between this leg and the book
is 1 meter-- or the box.
Let's say that this distance between the leg and the center
of mass is 2 meters, and so this is also 2 meters.
OK, so we can now set this up as a moment problem.
So remember, all of the clockwise moments have to
equal all of the counterclockwise moments.
So what are all of the clockwise moments?
What are all of the things that want to make the table
rotate this way or this way?
Well, the leg is the only thing keeping
it from doing that.
So everything else is
essentially a clockwise moment.
So we have this 100 Newtons, and it is 1 meter away.
Its moment arm distance is 1.
So these are all the clockwise moments, 100 times 1, right?
It's 100 Newtons acting downwards in the clockwise
direction, clockwise moment, and it's 1 meter away, plus we
have the center of mass at the top of the table, which is 20
Newtons, plus 20 Newtons, and that is 2 meters away from our
designated axis, so 20 times 2.
And you might say, well, isn't this leg exerting some force?
Well, sure it is, but its distance from our designated
axis is zero, so its moment of force is zero.
Even if it is exerting a million pounds or a million
Newtons, its moment of force, or its torque, would be zero
because its moment arm distance is zero, so we can
ignore it, which makes things simple.
So those were the only clockwise moments.
And what's the counterclockwise moment?
Well, that's going to be the force exerted by this leg.
That's what's keeping the whole thing from rotating.
So it's the force of the leg times its
distance from our axis.
Well, this is a total of 4 meters, which we've said here,
times 4 meters.
And so we can just solve.
We get 100 plus 40, so we get 140 is equal to the force of
the leg times 4.
So what's 140-- 4 goes into 140 35 times?
My math is not so good.
Is that right?
4 times 30 is 120.
120 plus 20.
So the force of the leg is 35 Newtons upwards.
And since this isn't moving, we know that the downward
force right here must be 35 Newtons.
And so there's a couple of ways we can think about it.
If this leg is supporting 35 Newtons and we have a total
weight here of 120 Newtons, our total weight, the weight
at the top of the table plus the
bookshelf, that's 120 Newtons.
So the balance of this must be supported by
something or someone.
So the balance of this is going to be
supported by this leg.
So it's 120 minus 35 is what?
[PHONE RINGS]
Oh, my phone is ringing.
120 minus 35 is what?
120 minus 30 is 90.
And then 90 minus 5 is 85 Newtons.
It's so disconcerting when my phone rings.
I have trouble focusing.
Anyway, it's probably because my phone sounds
like a freight train.
Anyway, so there you go.
This type of problem is actually key to, as you can
imagine, bridge builders, or furniture manufacturers, or
civil engineers who are bridge builders, or architects,
because you actually have to figure out, well, if I design
something a certain way, I have to figure out how much
weight each of the supporting structures
will have to support.
And as you can imagine, why is this one
supporting more weight?
Why is this leg supporting more weight than that leg?
Well, because this book, which is 100 Newtons, which is a
significant amount of the total weight, is much closer
to this leg than it is to this leg.
If we put it to the center, they would balance, and then
if we push it further to the right, then this leg would
start bearing more of the weight.
Anyway, hopefully you found that interesting, and
hopefully, I didn't confuse you.
And I will see you in future videos.