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00:00:00,980 --> 00:00:04,140
I'm going to do a couple more
moment and force problems,

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00:00:04,140 --> 00:00:06,320
especially because I think
I might have bungled the

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00:00:06,320 --> 00:00:08,680
terminology in the previous
video because I kept confusing

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00:00:08,680 --> 00:00:11,120
clockwise with counterclockwise.

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This time I'll try to
be more consistent.

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Let me draw my lever again.

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My seesaw.

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00:00:20,590 --> 00:00:27,680
So that's my seesaw, and that is
my axis of rotation, or my

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00:00:27,680 --> 00:00:30,270
fulcrum, or my pivot point,
whatever you want to call it.

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And let me throw a bunch
of forces on there.

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So let's say that I have a
10-Newton force and it is at a

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distance of 10, so distance
is equal to 10.

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The moment arm distance is 10.

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Let's say that I have a
50-Newton force and its moment

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arm distance is equal to 8.

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Let's say that I have a 5-Newton
force, and its moment

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arm distance is 4.

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The distance is equal to 4.

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That's enough for that side.

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And let's say I have a I'm
going to switch colors.

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Actually, no, I'm going to keep
it all the same color and

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then we'll use colors to
differentiate between

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clockwise and counterclockwise
so I don't bungle

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everything up again.

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So let's say I have a 10-Newton
force here.

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And, of course, these vectors
aren't proportional to

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actually what I drew.

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50 Newtons would be huge if
these were the actual vectors.

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And let's say that that moment
arm distance is 3.

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Let me do a couple more.

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And let's say I have a moment
arm distance of 8.

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I have a clockwise force of 20
Newtons, And let's say at a

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distance of 10 again, so
distance is equal to 10, I

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have my mystery force.

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It's going to act in a
counterclockwise direction and

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I want to know what
it needs to be.

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So whenever you do any of
these moment of force

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problems, and you say, well,
what does the force need to be

40
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in order for this see
saw to not rotate?

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You just say, well, all the
clockwise moments have to

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equal all of the
counterclockwise moments, So

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clockwise moments equal
counterclockwise.

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I'll do them in different
colors.

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So what are all the
clockwise moments?

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Well, clockwise is this
direction, right?

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That's the way a clock goes.

49
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So this is clockwise,
that is clockwise.

50
00:03:04,052 --> 00:03:06,290
I want to go in this
direction.

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And so this is clockwise.

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What are all the clockwise
moments?

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It's 10 Newtons times its
moment arm distance 10.

54
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So 10 times 10 plus 5 Newtons
times this moment arm distance

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4, plus 5 times 4, plus 20
Newtons times its moment arm

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distance of 8, plus 20 times 8,
and that's going to equal

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the counterclockwise moments,
and so the leftover ones are

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counterclockwise.

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So we have 50 Newtons acting
downward here, and that's

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counterclockwise, and it's at
a distance of 8 from the

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moment arm, so 50 times 8.

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Let's see, we don't
have any other

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counterclockwise on that side.

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This is counterclockwise,
right?

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00:03:48,600 --> 00:03:51,290
We have 10 Newtons acting
in the counterclockwise

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direction, and its moment arm
distance is 3, plus 10 times

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3, and we're assuming our
mystery force, which is at a

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distance of 10, is also
counterclockwise,

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plus force times 10.

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And now we simplify.

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00:04:06,120 --> 00:04:08,630
And I'll just go to a neutral
color because this

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is just math now.

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100 plus 20 plus 160 is equal
to-- what's 50 times 8?

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That's 400 plus 30 plus 10F.

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What is this?

76
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2, 50 times 8.

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Right, that's 400.

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OK, this is 120 plus
a 160 is 280.

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280 is equal to 430-- this is
a good example-- plus 10F, I

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just realized.

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00:04:42,550 --> 00:04:45,390
Subtract 430 from both sides.

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So what's 430 minus 280?

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It's 150.

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So it's minus 150
is equal to 10F.

85
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So F is equal to minus
15 Newtons in the

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counterclockwise direction.

87
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So F is minus 15 Newtons
in the counterclockwise

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direction, or it means that
it is 15 Newtons.

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00:05:15,830 --> 00:05:17,620
We assumed that it was in the
counterclockwise direction,

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but when we did the math,
we got a minus number.

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[SNEEZE]

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Excuse me.

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I apologize if I blew out your
speakers with that sneeze.

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But anyway, we assume it was
going in the counterclockwise

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direction, but when we did the
math, we got a negative

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number, so that means it's
actually operating in the

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clockwise direction at 15
Newtons at a distance of 10

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from the moment arm.

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Hopefully, that one was less
confusing than the last one.

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So let me do another problem,
and these actually used to

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confuse me when I first learned
about moments, but in

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some ways, they're the
most useful ones.

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So let's say that I have
some type of table.

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I'll draw it in wood.

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It's a wood table.

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That's my table.

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And I have a leg here,
I have a leg here.

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Let's say that the center
of mass of the top of

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the table is here.

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It's at the center.

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And let's say that
it has a weight.

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It has a weight going down.

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What's a reasonable weight?

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Let's say 20 Newtons.

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It has a weight of 20 Newtons.

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Let's say that I place some
textbooks on top of this

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table, or box, just to make
the drawing simpler.

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Let's say I place a box there.

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Let's say the box weighs 10
kilograms, which would be

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about 100 Newtons.

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So let's say it weighs
about 100 Newtons.

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So what I want to figure out,
what I need to figure out, is

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how much weight is being
put onto each of

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the legs of the table?

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And this might not have even
been obviously a moment

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problem, but you'll see in
a second it really is.

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So how do we know that?

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Well, both of these legs are
supporting the table, right?

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Whatever the table is exerting
downwards, the leg is exerting

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upwards, so that's the amount of
force that each of the legs

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are holding.

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So what we do is we pick-- so
let's just pick this leg, just

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because I'm picking
it arbitrarily.

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Let's pick this leg,
and let's pick an

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arbitrary axis of rotation.

140
00:07:55,340 --> 00:07:58,920
Well, let's pick this is as
our axis of rotation.

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Why do I pick that as the
axis of rotation?

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Because think of it this way.

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If this leg started pushing more
than it needed to, the

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whole table would rotate in the

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counterclockwise direction.

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Or the other way, if this leg
started to weaken and started

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to buckle and couldn't hold
its force, the table would

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rotate down this way, and it
would rotate around the other

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leg, assuming that the other
leg doesn't fail.

150
00:08:20,760 --> 00:08:24,740
We're assuming that this leg
is just going to do its job

151
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and it's not going to move
one way or the other.

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But this leg, that's why we're
thinking about it that way.

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If it was too weak, the whole
table would rotate in the

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clockwise direction, and if it
was somehow exerting extra

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force, which we know a leg
can't, but let's say if it was

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a spring or something like that,
then the whole table

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would rotate in the
counterclockwise direction.

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So once we set that up, we can
actually set this up as a

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moment problem.

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So what is the force
of the leg?

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So the whole table is exerting
some type of-- if this leg

162
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wasn't here, the whole table
would have a net clockwise

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moment, right?

164
00:08:59,550 --> 00:09:02,690
The whole table would tilt down
and fall down like that.

165
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So the leg must be exerting a
counterclockwise moment in

166
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order to keep it stationary.

167
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So the leg must be exerting
a force upward right here.

168
00:09:12,640 --> 00:09:13,850
The force of the leg, right?

169
00:09:13,850 --> 00:09:14,400
We know that.

170
00:09:14,400 --> 00:09:16,190
We know that from
basic physics.

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There's some force coming down
here and the leg is doing an

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equal opposite force upwards.

173
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So what is that force
of that leg?

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And one thing I should
have told you

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is all of the distances.

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Let's say that this distance
between this leg and the book

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is 1 meter-- or the box.

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Let's say that this distance
between the leg and the center

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00:09:42,550 --> 00:09:46,980
of mass is 2 meters, and so
this is also 2 meters.

180
00:09:46,980 --> 00:09:50,390
OK, so we can now set this
up as a moment problem.

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So remember, all of the
clockwise moments have to

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00:09:53,430 --> 00:09:56,090
equal all of the
counterclockwise moments.

183
00:09:56,090 --> 00:09:57,930
So what are all of the
clockwise moments?

184
00:09:57,930 --> 00:10:01,060
What are all of the things that
want to make the table

185
00:10:01,060 --> 00:10:06,790
rotate this way or this way?

186
00:10:06,790 --> 00:10:08,920
Well, the leg is the
only thing keeping

187
00:10:08,920 --> 00:10:09,400
it from doing that.

188
00:10:09,400 --> 00:10:10,290
So everything else is

189
00:10:10,290 --> 00:10:11,840
essentially a clockwise moment.

190
00:10:11,840 --> 00:10:15,780
So we have this 100 Newtons,
and it is 1 meter away.

191
00:10:15,780 --> 00:10:17,270
Its moment arm distance is 1.

192
00:10:17,270 --> 00:10:22,500
So these are all the clockwise
moments, 100 times 1, right?

193
00:10:22,500 --> 00:10:25,320
It's 100 Newtons acting
downwards in the clockwise

194
00:10:25,320 --> 00:10:31,710
direction, clockwise moment, and
it's 1 meter away, plus we

195
00:10:31,710 --> 00:10:34,230
have the center of mass at the
top of the table, which is 20

196
00:10:34,230 --> 00:10:38,670
Newtons, plus 20 Newtons, and
that is 2 meters away from our

197
00:10:38,670 --> 00:10:44,250
designated axis,
so 20 times 2.

198
00:10:44,250 --> 00:10:46,950
And you might say, well, isn't
this leg exerting some force?

199
00:10:46,950 --> 00:10:49,780
Well, sure it is, but its
distance from our designated

200
00:10:49,780 --> 00:10:53,780
axis is zero, so its moment
of force is zero.

201
00:10:53,780 --> 00:10:56,420
Even if it is exerting a million
pounds or a million

202
00:10:56,420 --> 00:11:00,510
Newtons, its moment of force,
or its torque, would be zero

203
00:11:00,510 --> 00:11:03,470
because its moment arm distance
is zero, so we can

204
00:11:03,470 --> 00:11:05,330
ignore it, which makes
things simple.

205
00:11:05,330 --> 00:11:08,610
So those were the only
clockwise moments.

206
00:11:08,610 --> 00:11:10,490
And what's the counterclockwise
moment?

207
00:11:10,490 --> 00:11:13,350
Well, that's going to be the
force exerted by this leg.

208
00:11:13,350 --> 00:11:15,680
That's what's keeping the whole
thing from rotating.

209
00:11:15,680 --> 00:11:19,480
So it's the force of
the leg times its

210
00:11:19,480 --> 00:11:21,370
distance from our axis.

211
00:11:21,370 --> 00:11:23,770
Well, this is a total of 4
meters, which we've said here,

212
00:11:23,770 --> 00:11:25,020
times 4 meters.

213
00:11:25,020 --> 00:11:28,330


214
00:11:28,330 --> 00:11:30,180
And so we can just solve.

215
00:11:30,180 --> 00:11:34,870
We get 100 plus 40, so we get
140 is equal to the force of

216
00:11:34,870 --> 00:11:37,110
the leg times 4.

217
00:11:37,110 --> 00:11:48,040
So what's 140-- 4 goes
into 140 35 times?

218
00:11:48,040 --> 00:11:50,430
My math is not so good.

219
00:11:50,430 --> 00:11:50,940
Is that right?

220
00:11:50,940 --> 00:11:53,730
4 times 30 is 120.

221
00:11:53,730 --> 00:11:55,690
120 plus 20.

222
00:11:55,690 --> 00:11:59,370
So the force of the leg
is 35 Newtons upwards.

223
00:11:59,370 --> 00:12:02,040
And since this isn't moving,
we know that the downward

224
00:12:02,040 --> 00:12:05,130
force right here must
be 35 Newtons.

225
00:12:05,130 --> 00:12:07,630
And so there's a couple of ways
we can think about it.

226
00:12:07,630 --> 00:12:14,950
If this leg is supporting 35
Newtons and we have a total

227
00:12:14,950 --> 00:12:18,850
weight here of 120 Newtons, our
total weight, the weight

228
00:12:18,850 --> 00:12:20,180
at the top of the
table plus the

229
00:12:20,180 --> 00:12:22,270
bookshelf, that's 120 Newtons.

230
00:12:22,270 --> 00:12:25,120
So the balance of this
must be supported by

231
00:12:25,120 --> 00:12:26,820
something or someone.

232
00:12:26,820 --> 00:12:28,060
So the balance of this
is going to be

233
00:12:28,060 --> 00:12:29,830
supported by this leg.

234
00:12:29,830 --> 00:12:33,810
So it's 120 minus 35 is what?

235
00:12:33,810 --> 00:12:34,120
[PHONE RINGS]

236
00:12:34,120 --> 00:12:36,640
Oh, my phone is ringing.

237
00:12:36,640 --> 00:12:39,010
120 minus 35 is what?

238
00:12:39,010 --> 00:12:41,710
120 minus 30 is 90.

239
00:12:41,710 --> 00:12:46,720
And then 90 minus
5 is 85 Newtons.

240
00:12:46,720 --> 00:12:49,540
It's so disconcerting
when my phone rings.

241
00:12:49,540 --> 00:12:51,340
I have trouble focusing.

242
00:12:51,340 --> 00:12:54,000
Anyway, it's probably because
my phone sounds

243
00:12:54,000 --> 00:12:56,160
like a freight train.

244
00:12:56,160 --> 00:12:58,940
Anyway, so there you go.

245
00:12:58,940 --> 00:13:01,800
This type of problem is actually
key to, as you can

246
00:13:01,800 --> 00:13:06,660
imagine, bridge builders, or
furniture manufacturers, or

247
00:13:06,660 --> 00:13:09,730
civil engineers who are bridge
builders, or architects,

248
00:13:09,730 --> 00:13:12,160
because you actually have to
figure out, well, if I design

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something a certain way, I have
to figure out how much

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weight each of the supporting
structures

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will have to support.

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And as you can imagine,
why is this one

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supporting more weight?

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Why is this leg supporting more
weight than that leg?

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Well, because this book, which
is 100 Newtons, which is a

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significant amount of the total
weight, is much closer

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to this leg than it
is to this leg.

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If we put it to the center, they
would balance, and then

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if we push it further to the
right, then this leg would

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start bearing more
of the weight.

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Anyway, hopefully you found
that interesting, and

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hopefully, I didn't
confuse you.

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And I will see you
in future videos.

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