1
0:00:02 --> 00:00:08
Last time we discussed
that an acceleration is caused

2
00:00:08 --> 00:00:14
by a push or by a pull.

3
00:00:10 --> 00:00:16
Today we will express this
more qualitatively

4
00:00:15 --> 00:00:21
in three laws which
are called Newton's Laws.

5
00:00:19 --> 00:00:25
The first law really goes back

6
00:00:22 --> 00:00:28
to the first part
of the 17th century.

7
00:00:26 --> 00:00:32
It was Galileo who expressed

8
00:00:29 --> 00:00:35
what he called
the law of inertia

9
00:00:31 --> 00:00:37
and I will read you his law.

10
00:00:36 --> 00:00:42
"A body at rest remains at rest

11
00:00:39 --> 00:00:45
"and a body in motion
continues to move

12
00:00:43 --> 00:00:49
"at constant velocity
along a straight line

13
00:00:47 --> 00:00:53
unless acted upon
by an external force."

14
00:00:52 --> 00:00:58
And now I will read to you

15
00:00:54 --> 00:01:00
Newton's own words
in his famous book,Principia.

16
00:00:59 --> 00:01:05
"Every body perseveres
in its state of rest

17
00:01:04 --> 00:01:10
"or of uniform motion
in a right line

18
00:01:09 --> 00:01:15
"unless it is compelled
to change that state

19
00:01:14 --> 00:01:20
by forces impressed upon it."

20
00:01:17 --> 00:01:23
Now, Newton's First Law

21
00:01:19 --> 00:01:25
is clearly against
our daily experiences.

22
00:01:23 --> 00:01:29
Things that move don't move
along a straight line

23
00:01:26 --> 00:01:32
and don't continue to move, and
the reason is, there's gravity.

24
00:01:30 --> 00:01:36
And there is another reason.

25
00:01:32 --> 00:01:38
Even if you remove gravity

26
00:01:34 --> 00:01:40
then there is friction,
there's air drag.

27
00:01:37 --> 00:01:43
And so things will
always come to a halt.

28
00:01:40 --> 00:01:46
But we believe, though, that
in the absence of any forces

29
00:01:44 --> 00:01:50
indeed an object, if it had
a certain velocity

30
00:01:48 --> 00:01:54
would continue along a straight
line forever and ever and ever.

31
00:01:53 --> 00:01:59
Now, this law,
this very fundamental law

32
00:01:56 --> 00:02:02
does not hold
in all reference frames.

33
00:01:59 --> 00:02:05
For instance, it doesn't hold
in a reference frame

34
00:02:04 --> 00:02:10
which itself is
being accelerated.

35
00:02:07 --> 00:02:13
Imagine that I accelerate
myself right here.

36
00:02:11 --> 00:02:17
Either I jump on my horse,
or I take my bicycle

37
00:02:15 --> 00:02:21
or my motorcycle or my car

38
00:02:17 --> 00:02:23
and you see me being accelerated
in this direction.

39
00:02:21 --> 00:02:27
And you sit there and you say,
"Aha, his velocity is changing.

40
00:02:26 --> 00:02:32
"Therefore, according
to the First Law,

41
00:02:29 --> 00:02:35
there must be a force on him."

42
00:02:31 --> 00:02:37
And you say, "Hey, there,
do you feel that force?"

43
00:02:33 --> 00:02:39
And I said, "Yeah, I do!

44
00:02:35 --> 00:02:41
"I really feel that,
I feel someone's pushing me."

45
00:02:37 --> 00:02:43
Consistent with the first law.

46
00:02:39 --> 00:02:45
Perfect, the First Law works
for you.

47
00:02:42 --> 00:02:48
Now I'm here.

48
00:02:43 --> 00:02:49
I'm being accelerated
in this direction

49
00:02:45 --> 00:02:51
and you all come towards me

50
00:02:47 --> 00:02:53
being accelerated
in this direction.

51
00:02:49 --> 00:02:55
I say, "Aha, the First Law
should work

52
00:02:52 --> 00:02:58
so these people
should feel a push."

53
00:02:55 --> 00:03:01
I say, "Hey, there!

54
00:02:56 --> 00:03:02
Do you feel the push?"

55
00:02:58 --> 00:03:04
And you say, "I feel nothing.

56
00:02:59 --> 00:03:05
There is no push,
there is no pull."

57
00:03:02 --> 00:03:08
Therefore, the First Law doesn't
work from my frame of reference

58
00:03:05 --> 00:03:11
if I'm being accelerated
towards you.

59
00:03:08 --> 00:03:14
So now comes the question,
when does the First Law work?

60
00:03:13 --> 00:03:19
Well, the First Law works
when the frame of reference

61
00:03:17 --> 00:03:23
is what we call an "inertial"
frame of reference.

62
00:03:21 --> 00:03:27
And an inertial frame
of reference would then be

63
00:03:25 --> 00:03:31
a frame in which there are
no accelerations of any kind.

64
00:03:29 --> 00:03:35
Is that possible?

65
00:03:31 --> 00:03:37
Is 26.100...
is this lecture hall

66
00:03:33 --> 00:03:39
an inertial reference frame?

67
00:03:36 --> 00:03:42
For one, the earth rotates
about its own axis

68
00:03:39 --> 00:03:45
and 26.100 goes with it.

69
00:03:40 --> 00:03:46
That gives you
a centripetal acceleration.

70
00:03:43 --> 00:03:49
Number two, the earth
goes around the sun.

71
00:03:49 --> 00:03:55
That gives it
a centripetal acceleration

72
00:03:50 --> 00:03:56
including the earth, including
you, including 26.100.

73
00:03:53 --> 00:03:59
The sun goes around the Milky
Way, and you can go on and on.

74
00:03:58 --> 00:04:04
So clearly 26.100 is not
an inertial reference frame.

75
00:04:03 --> 00:04:09

76
00:04:05 --> 00:04:11
We can try to make an estimate

77
00:04:08 --> 00:04:14
on how large
these accelerations are

78
00:04:10 --> 00:04:16
that we experience
here in 26.100

79
00:04:13 --> 00:04:19
and let's start with the one

80
00:04:15 --> 00:04:21
that is due
to the earth's rotation.

81
00:04:18 --> 00:04:24
So here's the earth... rotating
with angular velocity omega

82
00:04:25 --> 00:04:31
and here is the equator, and
the earth has a certain radius.

83
00:04:32 --> 00:04:38
The radius of the earth...
this is the symbol for earth.

84
00:04:36 --> 00:04:42
Now, I know that 26.100 is here

85
00:04:38 --> 00:04:44
but let's just take the worst
case that you're on the equator.

86
00:04:43 --> 00:04:49
You're... (no audio )

87
00:04:45 --> 00:04:51
You go around like this
and in order to do that

88
00:04:48 --> 00:04:54
you need a centripetal
acceleration, a c

89
00:04:51 --> 00:04:57
which, as we have seen last
time, equals omega squared R.

90
00:04:54 --> 00:05:00
How large is that one?

91
00:04:57 --> 00:05:03
Well, the period of rotation
for the earth

92
00:05:03 --> 00:05:09
is 24 hours times 3,600 seconds

93
00:05:07 --> 00:05:13
so omega equals two pi
divided by 24 times 3,600

94
00:05:12 --> 00:05:18
and that would then be
in radians per second.

95
00:05:16 --> 00:05:22
And so you can calculate now
what omega squared R earth is

96
00:05:21 --> 00:05:27
if you know that the radius
of the earth

97
00:05:25 --> 00:05:31
is about 6,400 kilometers.

98
00:05:27 --> 00:05:33
Make sure you convert this
to meters, of course.

99
00:05:32 --> 00:05:38
And you will find, then

100
00:05:34 --> 00:05:40
that the centripetal
acceleration at the equator

101
00:05:38 --> 00:05:44
which is the worst case--
it's less here--

102
00:05:41 --> 00:05:47
is 0.034 meters
per second squared.

103
00:05:45 --> 00:05:51
And this is way, way less--
this is 300 times smaller

104
00:05:49 --> 00:05:55
than the gravitational
acceleration

105
00:05:52 --> 00:05:58
that you experience
here on Earth.

106
00:05:54 --> 00:06:00
And if we take the motion
of the earth around the sun

107
00:05:57 --> 00:06:03
then it is an additional factor
of five times lower.

108
00:06:01 --> 00:06:07
In other words,
these accelerations

109
00:06:03 --> 00:06:09
even though they're real
and they can be measured easily

110
00:06:06 --> 00:06:12
with today's
high-tech instrumentation--

111
00:06:09 --> 00:06:15
they are much, much lower
than what we are used to

112
00:06:11 --> 00:06:17
which is
the gravitational acceleration.

113
00:06:14 --> 00:06:20
And therefore,
in spite of these accelerations

114
00:06:16 --> 00:06:22
we will accept this hall

115
00:06:19 --> 00:06:25
as a reasonably good
inertial frame of reference

116
00:06:24 --> 00:06:30
in which the First Law
then should hold.

117
00:06:28 --> 00:06:34
Can Newton's Law be proven?

118
00:06:31 --> 00:06:37
The answer is no, because
it's impossible to be sure

119
00:06:36 --> 00:06:42
that your reference frame
is without any accelerations.

120
00:06:41 --> 00:06:47
Do we believe in this?

121
00:06:42 --> 00:06:48
Yes, we do.

122
00:06:43 --> 00:06:49
We believe in it
since it is consistent

123
00:06:46 --> 00:06:52
within the uncertainty
of the measurements

124
00:06:49 --> 00:06:55
with all experiments
that have been done.

125
00:06:52 --> 00:06:58

126
00:06:54 --> 00:07:00
Now we come to the Second Law,
Newton's Second Law.

127
00:07:01 --> 00:07:07
I have a spring...

128
00:07:03 --> 00:07:09

129
00:07:07 --> 00:07:13
Forget gravity for now--

130
00:07:09 --> 00:07:15
you can do this somewhere
in outer space.

131
00:07:11 --> 00:07:17
This is the relaxed length
of the spring

132
00:07:14 --> 00:07:20
and I extend the spring.

133
00:07:15 --> 00:07:21
I extend it over a certain
amount, a certain distance--

134
00:07:20 --> 00:07:26
unimportant how much.

135
00:07:22 --> 00:07:28
And I know that I when I do that
that there will be a pull--

136
00:07:27 --> 00:07:33
non-negotiable.

137
00:07:30 --> 00:07:36
I put a mass, m1, here,
and I measure the acceleration

138
00:07:34 --> 00:07:40
that this pull causes
on this mass

139
00:07:36 --> 00:07:42
immediately after I release it.

140
00:07:39 --> 00:07:45
I can measure that.

141
00:07:40 --> 00:07:46
So I measure
an acceleration, a1.

142
00:07:43 --> 00:07:49
Now I replace this object
by mass m2

143
00:07:47 --> 00:07:53
but the extension is the same,
so the pull must be same.

144
00:07:52 --> 00:07:58
The spring doesn't know what the
mass is at the other end, right?

145
00:07:56 --> 00:08:02
So the pull is the same.

146
00:07:58 --> 00:08:04
I put m2 there, different mass

147
00:08:00 --> 00:08:06
and I measure
the new acceleration, a2.

148
00:08:05 --> 00:08:11
It is now an experimental fact
that m1 a1 equals m2 a2.

149
00:08:13 --> 00:08:19
And this product, ma,
we call the force.

150
00:08:19 --> 00:08:25
That is our definition
of force.

151
00:08:23 --> 00:08:29
So the same pull
on a ten times larger mass

152
00:08:27 --> 00:08:33
would give a ten times
lower acceleration.

153
00:08:31 --> 00:08:37

154
00:08:32 --> 00:08:38
The Second Law
I will read to you:

155
00:08:35 --> 00:08:41
"A force action on a body
gives it an acceleration

156
00:08:39 --> 00:08:45
which is in the direction
of the force..."

157
00:08:42 --> 00:08:48
That's also important--

158
00:08:44 --> 00:08:50
the acceleration is in
the direction of the force.

159
00:08:47 --> 00:08:53
"And has a magnitude
given by ma."

160
00:08:50 --> 00:08:56
ma is the magnitude

161
00:08:52 --> 00:08:58
and the direction is
the direction of the force.

162
00:08:56 --> 00:09:02
And so now we will write
this in all glorious detail.

163
00:09:01 --> 00:09:07
This is the Second Law by Newton

164
00:09:07 --> 00:09:13
perhaps the most important law
in all of physics

165
00:09:12 --> 00:09:18
but certainly in all of 801:

166
00:09:15 --> 00:09:21
F equals ma.

167
00:09:17 --> 00:09:23
The units of this force

168
00:09:20 --> 00:09:26
are kilograms times meters
per second squared.

169
00:09:27 --> 00:09:33
In honor of the great man,
we call that "one newton."

170
00:09:32 --> 00:09:38

171
00:09:34 --> 00:09:40
Like the First Law,
the Second Law only holds

172
00:09:37 --> 00:09:43
in inertial reference frames.

173
00:09:40 --> 00:09:46

174
00:09:41 --> 00:09:47
Can the Second Law be proven?

175
00:09:45 --> 00:09:51
No.

176
00:09:46 --> 00:09:52
Do we believe in it?

177
00:09:48 --> 00:09:54
Yes.

178
00:09:49 --> 00:09:55
Why do we believe in it?

179
00:09:51 --> 00:09:57
Because all experiments
and all measurements

180
00:09:54 --> 00:10:00
within the uncertainty
of the measurements

181
00:09:57 --> 00:10:03
are in agreement
with the Second Law.

182
00:10:00 --> 00:10:06

183
00:10:03 --> 00:10:09
Now you may object
and you may say

184
00:10:05 --> 00:10:11
"This is strange,
what you've been doing.

185
00:10:08 --> 00:10:14
"How can you
ever determine a mass

186
00:10:11 --> 00:10:17
"if there is no force somewhere?

187
00:10:13 --> 00:10:19
"Because if you want
to determine the mass

188
00:10:15 --> 00:10:21
"maybe you put it on a scale,

189
00:10:17 --> 00:10:23
"and when you put it on a scale
to determine the mass

190
00:10:19 --> 00:10:25
"you made use
of gravitational force

191
00:10:21 --> 00:10:27
"so isn't that some kind
of a circular argument

192
00:10:23 --> 00:10:29
that you're using?"

193
00:10:24 --> 00:10:30
And your answer is "No."

194
00:10:27 --> 00:10:33
I can be somewhere
in outer space

195
00:10:29 --> 00:10:35
where there is no gravity.

196
00:10:31 --> 00:10:37
I have two pieces of cheese; 
they are identical in size.

197
00:10:34 --> 00:10:40
This is cheese without holes,
by the way.

198
00:10:37 --> 00:10:43
They are identical in size.

199
00:10:39 --> 00:10:45
The sum of the two has
double the mass of one.

200
00:10:43 --> 00:10:49
Mass is determined
by how many molecules--

201
00:10:45 --> 00:10:51
how many atoms I have.

202
00:10:47 --> 00:10:53
I don't need gravity to have
a relative scale of masses

203
00:10:50 --> 00:10:56
so I can determine the relative
scale of these masses

204
00:10:53 --> 00:10:59
without ever using the force.

205
00:10:55 --> 00:11:01
So this is a very legitimate way

206
00:10:58 --> 00:11:04
of checking up
on the Second Law.

207
00:11:04 --> 00:11:10

208
00:11:09 --> 00:11:15
Since all objects in
this lecture hall and the earth

209
00:11:14 --> 00:11:20
fall with the constant
acceleration, which is g

210
00:11:18 --> 00:11:24
we can write down
that the gravitational force

211
00:11:23 --> 00:11:29
would be m times
this acceleration, g.

212
00:11:27 --> 00:11:33
Normally I write an "a" for it,
but I make an exception now

213
00:11:31 --> 00:11:37
because gravity, I call it
"gravitational force."

214
00:11:34 --> 00:11:40
And so you see
that the gravitational force

215
00:11:37 --> 00:11:43
due to the earth
on a particular mass

216
00:11:40 --> 00:11:46
is linearly proportional
with the mass.

217
00:11:43 --> 00:11:49
If the mass becomes
ten times larger

218
00:11:45 --> 00:11:51
then the force due to gravity
goes up by a factor of ten.

219
00:11:50 --> 00:11:56

220
00:11:53 --> 00:11:59
Suppose I have here
this softball in my hands.

221
00:11:57 --> 00:12:03
In the reference frame...

222
00:12:00 --> 00:12:06
26.100 we will accept to be
an inertial reference frame.

223
00:12:04 --> 00:12:10
It's not being accelerated
in our reference frame.

224
00:12:09 --> 00:12:15
That means the force on it
must be zero.

225
00:12:12 --> 00:12:18
So here is that ball.

226
00:12:14 --> 00:12:20
And we know if it has mass, m--

227
00:12:17 --> 00:12:23
which in this case
is about half a kilogram--

228
00:12:21 --> 00:12:27
that there must be
a force here, mg

229
00:12:24 --> 00:12:30
which is about five newtons,
or half a kilogram.

230
00:12:28 --> 00:12:34
But the net force is zero.

231
00:12:32 --> 00:12:38
Therefore it is very clear

232
00:12:34 --> 00:12:40
that I, Walter Lewin,
must push up with a force

233
00:12:39 --> 00:12:45
from my hand onto the ball,
which is about the same...

234
00:12:44 --> 00:12:50
which is exactly the same,
five newtons.

235
00:12:47 --> 00:12:53
Only now is
there no acceleration

236
00:12:51 --> 00:12:57
so I can write down
that force of Walter Lewin

237
00:12:57 --> 00:13:03
plus the force of gravity
equals zero.

238
00:13:01 --> 00:13:07
Because it's
a one-dimensional problem

239
00:13:06 --> 00:13:12
you could say that the force
of Walter Lewin equals minus mg.

240
00:13:10 --> 00:13:16

241
00:13:13 --> 00:13:19
F equals ma.

242
00:13:15 --> 00:13:21
Notice that there is
no statement made

243
00:13:21 --> 00:13:27
on velocity or speed.

244
00:13:23 --> 00:13:29
As long as you know f
and as long as you know m

245
00:13:27 --> 00:13:33
a is uniquely specified.

246
00:13:28 --> 00:13:34
No information is needed
on the speed.

247
00:13:31 --> 00:13:37
So that would mean,
if we take gravity

248
00:13:34 --> 00:13:40
and an object was falling down
with five meters per second

249
00:13:38 --> 00:13:44
that the law would hold.

250
00:13:39 --> 00:13:45
If it would fall down
with 5,000 meters per second

251
00:13:45 --> 00:13:51
it would also hold.

252
00:13:47 --> 00:13:53
Will it always hold?

253
00:13:50 --> 00:13:56
No.

254
00:13:52 --> 00:13:58
Once your speed approaches
the speed of light

255
00:13:55 --> 00:14:01
then Newtonian mechanics
no longer works.

256
00:13:58 --> 00:14:04
Then you have to use Einstein's
theory of special relativity.

257
00:14:02 --> 00:14:08
So this is only valid
as long as we have speeds

258
00:14:06 --> 00:14:12
that are substantially smaller,
say, than the speed of light.

259
00:14:12 --> 00:14:18
Now we come
to Newton's Third Law:

260
00:14:16 --> 00:14:22
"If one object exerts
a force on another

261
00:14:21 --> 00:14:27
"the other exerts the same force

262
00:14:25 --> 00:14:31
in opposite direction
on the one."

263
00:14:29 --> 00:14:35
I'll read it again.

264
00:14:31 --> 00:14:37
"If one object exerts
a force on another

265
00:14:35 --> 00:14:41
"the other exerts the same force

266
00:14:38 --> 00:14:44
in opposite direction
on the one."

267
00:14:41 --> 00:14:47
And I normally summarize that
as follows, the Third Law

268
00:14:51 --> 00:14:57
as "Action equals
minus reaction."

269
00:14:58 --> 00:15:04

270
00:14:59 --> 00:15:05
And the minus sign indicates,
then, that it opposes

271
00:15:03 --> 00:15:09
so you sit on your seats

272
00:15:06 --> 00:15:12
and you are pulled down on
your seats because of gravity

273
00:15:11 --> 00:15:17
and the seats will push back
on you with the same force.

274
00:15:16 --> 00:15:22
Action equals minus reaction.

275
00:15:18 --> 00:15:24
I held the baseball in my hand.

276
00:15:21 --> 00:15:27
The baseball pushes on my hand
with a certain force.

277
00:15:25 --> 00:15:31
I push on the baseball
with the same force.

278
00:15:28 --> 00:15:34
I push against the wall
with a certain force.

279
00:15:32 --> 00:15:38
The wall pushes back
in the opposite direction

280
00:15:35 --> 00:15:41
with exactly the same force.

281
00:15:38 --> 00:15:44
The Third Law always holds.

282
00:15:40 --> 00:15:46
Whether the objects
are moving or accelerated

283
00:15:43 --> 00:15:49
makes no difference.

284
00:15:44 --> 00:15:50
All moments in time, the force--

285
00:15:47 --> 00:15:53
we call it actually the "contact
force" between two objects--

286
00:15:52 --> 00:15:58
one on the other is always
the same as the other on one

287
00:15:56 --> 00:16:02
but in the opposite direction.

288
00:16:01 --> 00:16:07
Let us work out
a very simple example.

289
00:16:06 --> 00:16:12
We have an object
which has a mass, m1.

290
00:16:11 --> 00:16:17
We have object number one
and m1 is five kilograms.

291
00:16:17 --> 00:16:23
And here, attached to it,
is an object two

292
00:16:23 --> 00:16:29
and m2 equals 15 kilograms.

293
00:16:26 --> 00:16:32
There is a force

294
00:16:28 --> 00:16:34
and the force is coming in
from this direction.

295
00:16:32 --> 00:16:38
This is the force--

296
00:16:34 --> 00:16:40
and the magnitude
of the force is 20 newtons.

297
00:16:38 --> 00:16:44
What is the acceleration
of this system?

298
00:16:43 --> 00:16:49
F equals ma.

299
00:16:45 --> 00:16:51

300
00:16:47 --> 00:16:53
Clearly the mass is
the sum of the two--

301
00:16:52 --> 00:16:58
this force acts on both--

302
00:16:55 --> 00:17:01
so we get m1 plus m2 times a.

303
00:16:58 --> 00:17:04
This is 20, this is 20

304
00:17:01 --> 00:17:07
so a equals
one meters per second squared

305
00:17:05 --> 00:17:11
in the same direction as f.

306
00:17:08 --> 00:17:14
So the whole system
is being accelerated

307
00:17:10 --> 00:17:16
with one meters
per second squared.

308
00:17:13 --> 00:17:19
Now watch me closely.

309
00:17:14 --> 00:17:20
Now I single out this object--

310
00:17:17 --> 00:17:23
here it is... object number two.

311
00:17:24 --> 00:17:30
Object number one, while
this acceleration takes place

312
00:17:29 --> 00:17:35
must be pushing
on object number two.

313
00:17:31 --> 00:17:37
Otherwise object number two
could never be accelerated.

314
00:17:37 --> 00:17:43
I call that force f12

315
00:17:39 --> 00:17:45
the force
that one exerts on two.

316
00:17:42 --> 00:17:48
I know that number two
has an acceleration of one.

317
00:17:46 --> 00:17:52
That's a given already.

318
00:17:50 --> 00:17:56
So here comes f equals ma.

319
00:17:54 --> 00:18:00
f12 equals m2 times a.

320
00:17:57 --> 00:18:03
We know a is one,
we know m2 is 15

321
00:18:02 --> 00:18:08
so we see that the magnitude
of the force 12 is 15 newtons.

322
00:18:10 --> 00:18:16
This force is 15.

323
00:18:13 --> 00:18:19

324
00:18:16 --> 00:18:22
Now I'm going to isolate
number one out.

325
00:18:21 --> 00:18:27
Here is number one.

326
00:18:26 --> 00:18:32
Number one experiences
this force, f, which was the 20

327
00:18:32 --> 00:18:38
and it must experience
a contact force from number two.

328
00:18:37 --> 00:18:43
Somehow, number two must
be pushing on number one

329
00:18:44 --> 00:18:50
if one is pushing on number two.

330
00:18:46 --> 00:18:52
And I call that force "f21."

331
00:18:50 --> 00:18:56

332
00:18:52 --> 00:18:58
I know that number one
is being accelerated

333
00:18:54 --> 00:19:00
and I know the magnitude is
one meter per second squared.

334
00:18:57 --> 00:19:03
That's non-negotiable,

335
00:19:01 --> 00:19:07
and so we have that f,
this one, plus f21

336
00:19:09 --> 00:19:15
must be m1 times a.

337
00:19:12 --> 00:19:18
This is one, this is five,
this is 20

338
00:19:16 --> 00:19:22
and so this one, you can
already see, is minus 15.

339
00:19:22 --> 00:19:28
F21 is in this direction

340
00:19:24 --> 00:19:30
and the magnitude is exactly
the same as f12.

341
00:19:30 --> 00:19:36
So you see?

342
00:19:32 --> 00:19:38
One is pushing on two with
15 newtons in this direction.

343
00:19:36 --> 00:19:42
Two is pushing back on one
with 15 newtons

344
00:19:39 --> 00:19:45
and the whole system
is being accelerated

345
00:19:42 --> 00:19:48
with one meter
per second squared.

346
00:19:45 --> 00:19:51
Now, in these two examples--

347
00:19:48 --> 00:19:54
the one whereby I had
the baseball on my hand--

348
00:19:52 --> 00:19:58
you saw that it was consistent
with the Third Law.

349
00:19:56 --> 00:20:02
In this example, you also see

350
00:19:57 --> 00:20:03
that it's consistent
with the Third Law.

351
00:20:00 --> 00:20:06
The contact force
from one on the other

352
00:20:02 --> 00:20:08
is the same as
from the other on one

353
00:20:04 --> 00:20:10
but in opposite signs.

354
00:20:05 --> 00:20:11
Is this a proof?

355
00:20:07 --> 00:20:13
No.

356
00:20:08 --> 00:20:14
Can the Third Law be proven?

357
00:20:11 --> 00:20:17
No.

358
00:20:12 --> 00:20:18
Do we believe in it?

359
00:20:14 --> 00:20:20
Yes.

360
00:20:15 --> 00:20:21
Why do we believe in it?

361
00:20:17 --> 00:20:23
Because all measurements,
all experiments

362
00:20:20 --> 00:20:26
within the uncertainties are
consistent with the Third Law.

363
00:20:26 --> 00:20:32

364
00:20:28 --> 00:20:34
Action equals minus reaction.

365
00:20:31 --> 00:20:37
It is something
that you experience every day.

366
00:20:35 --> 00:20:41
I remember I had
a garden hose on the lawn

367
00:20:42 --> 00:20:48
and I would open the faucet

368
00:20:43 --> 00:20:49
and the garden hose would start
to snake backwards.

369
00:20:46 --> 00:20:52
Why?

370
00:20:47 --> 00:20:53
Water squirts out.

371
00:20:48 --> 00:20:54
The garden hose pushes onto
the water in this direction.

372
00:20:52 --> 00:20:58
The water pushes back onto the
garden hose and it snakes back.

373
00:20:55 --> 00:21:01
Action equals minus reaction.

374
00:20:59 --> 00:21:05
You take a balloon.

375
00:21:03 --> 00:21:09
You take a balloon
and you blow up the balloon

376
00:21:07 --> 00:21:13
and you let the air out.

377
00:21:09 --> 00:21:15
The balloon pushes onto the air.

378
00:21:11 --> 00:21:17
The air must push
onto the balloon.

379
00:21:13 --> 00:21:19
And therefore,
when you let it go

380
00:21:15 --> 00:21:21
the balloon will go
in this direction

381
00:21:17 --> 00:21:23
which is the basic idea
behind the rocket.

382
00:21:20 --> 00:21:26
(huffing and puffing )

383
00:21:25 --> 00:21:31
I love to play with balloons,
don't you?

384
00:21:30 --> 00:21:36
So, if I do it like this,
and I let it go

385
00:21:32 --> 00:21:38
the air will come out
in this direction

386
00:21:34 --> 00:21:40
and so then it means the balloon

387
00:21:36 --> 00:21:42
is pushing on the air
in this direction.

388
00:21:38 --> 00:21:44
the air must be pushing on
the balloon in this direction.

389
00:21:41 --> 00:21:47
There it goes.

390
00:21:42 --> 00:21:48
(whistles )

391
00:21:43 --> 00:21:49
It didn't make it to the moon

392
00:21:46 --> 00:21:52
but you saw the idea
of a rocket.

393
00:21:49 --> 00:21:55
Action equals minus reaction.

394
00:21:52 --> 00:21:58

395
00:21:55 --> 00:22:01
If you fire a gun, the gun
exerts a force on the bullet

396
00:22:00 --> 00:22:06
the bullet exerts
an equal force on the gun

397
00:22:03 --> 00:22:09
which is called the recoil.

398
00:22:06 --> 00:22:12
You feel that in your hands
and your shoulder.

399
00:22:09 --> 00:22:15
I have here a marvelous device

400
00:22:12 --> 00:22:18
which is a beautiful example of
"action equals minus reaction."

401
00:22:17 --> 00:22:23
I show you from above
what it looks like.

402
00:22:20 --> 00:22:26
You'll see more details later.

403
00:22:23 --> 00:22:29

404
00:22:24 --> 00:22:30
This rotates about this axis
rather freely--

405
00:22:27 --> 00:22:33
the axis is vertical--

406
00:22:29 --> 00:22:35
and we have here a reservoir
of water, which we will heat up.

407
00:22:33 --> 00:22:39
It turns into steam

408
00:22:34 --> 00:22:40
and these are hollow tubes
and the steam will squirt out.

409
00:22:38 --> 00:22:44
And so when the steam squirts
out in this direction

410
00:22:44 --> 00:22:50
the tube exerts a force
on the steam in this direction

411
00:22:48 --> 00:22:54
so the steam exerts an equal
force in the opposite direction

412
00:22:53 --> 00:22:59
and so the thing will start
to rotate like this.

413
00:22:57 --> 00:23:03
And I would like
to demonstrate that.

414
00:23:01 --> 00:23:07

415
00:23:11 --> 00:23:17
You can see it now there.

416
00:23:12 --> 00:23:18
With a little bit of luck,
there you see it.

417
00:23:14 --> 00:23:20
So we're going to heat it.

418
00:23:18 --> 00:23:24
(torch hissing )

419
00:23:23 --> 00:23:29
Walking.

420
00:23:25 --> 00:23:31
When you walk,
you push against the floor.

421
00:23:29 --> 00:23:35
The floor pushes back at you

422
00:23:31 --> 00:23:37
and if the floor
wouldn't push back at you

423
00:23:34 --> 00:23:40
you couldn't even walk,
you couldn't go forwards.

424
00:23:37 --> 00:23:43

425
00:23:39 --> 00:23:45
If you walk on ice,
very slippery--

426
00:23:42 --> 00:23:48
you can't go anywhere, because
you can't push on the ice

427
00:23:45 --> 00:23:51
so the ice won't push back
on you.

428
00:23:48 --> 00:23:54

429
00:23:50 --> 00:23:56
That's another example
where you see

430
00:23:51 --> 00:23:57
action equals minus reaction.

431
00:23:53 --> 00:23:59

432
00:23:55 --> 00:24:01
This engine is called
"Hero's engine."

433
00:23:59 --> 00:24:05
Hero, according
to the Greek legend

434
00:24:02 --> 00:24:08
was a priestess of Aphrodite.

435
00:24:07 --> 00:24:13
Let's first look at it.

436
00:24:11 --> 00:24:17

437
00:24:19 --> 00:24:25
She was a priestess of Aphrodite
and her lover, Leander

438
00:24:25 --> 00:24:31
would swim across the Hellespont
every night to be with her.

439
00:24:30 --> 00:24:36
And then one night
the poor guy drowned

440
00:24:33 --> 00:24:39
and Hero threw herself
into the sea.

441
00:24:36 --> 00:24:42
Very romantic thing to do

442
00:24:38 --> 00:24:44
but, of course, also
not a very smart thing to do.

443
00:24:42 --> 00:24:48
On the other hand, it must
have been a smart lady

444
00:24:46 --> 00:24:52
if she invented,
really, this engine.

445
00:24:49 --> 00:24:55
Yesterday, I looked
at the Web, "ask.com."

446
00:24:56 --> 00:25:02
It's wonderful--
you can ask any question.

447
00:24:58 --> 00:25:04
You can say, "How old am I?"

448
00:24:59 --> 00:25:05
Now, you may not get
the right answer

449
00:25:01 --> 00:25:07
but you can ask any question.

450
00:25:02 --> 00:25:08
And I typed in, "Hero's engine."

451
00:25:06 --> 00:25:12
And out popped a very nice high-
tech version of Hero's engine.

452
00:25:14 --> 00:25:20
A soda can-- you pop four holes
in the soda can at the bottom.

453
00:25:20 --> 00:25:26
So here's your soda can.

454
00:25:25 --> 00:25:31
You pop four holes in here,
but when you put a nail in there

455
00:25:28 --> 00:25:34
you bend every time
the nail to the same side

456
00:25:30 --> 00:25:36
so the holes are slanted.

457
00:25:32 --> 00:25:38
You put it in water

458
00:25:33 --> 00:25:39
you lift it out of water
and you have a Hero's engine.

459
00:25:38 --> 00:25:44
And I made it for you--
it took me only five minutes.

460
00:25:43 --> 00:25:49
I went to one of MIT's machines,
got myself a soda

461
00:25:47 --> 00:25:53
put the holes in it,
and here it is.

462
00:25:50 --> 00:25:56
It's in the water there.

463
00:25:52 --> 00:25:58
When I lift it out,
you will see the water squirts.

464
00:25:56 --> 00:26:02
There it goes.

465
00:25:57 --> 00:26:03
High-tech version
of Hero's engine.

466
00:26:00 --> 00:26:06

467
00:26:04 --> 00:26:10
Also makes a bit of a mess,
but okay.

468
00:26:08 --> 00:26:14
All right.

469
00:26:09 --> 00:26:15

470
00:26:13 --> 00:26:19
Try to make one-- it's fun
and it's very quick.

471
00:26:16 --> 00:26:22
It doesn't take
much time at all.

472
00:26:17 --> 00:26:23

473
00:26:26 --> 00:26:32
There are some bizarre
consequences of these laws.

474
00:26:33 --> 00:26:39
Imagine that an object
is falling towards the earth.

475
00:26:37 --> 00:26:43
An apple is falling
towards the earth

476
00:26:41 --> 00:26:47
from a height, say, of,
hmm, I'd say 100 meters.

477
00:26:45 --> 00:26:51
And let's calculate
how long it takes

478
00:26:48 --> 00:26:54
for this apple to hit the earth

479
00:26:51 --> 00:26:57
which should for you
be trivial, of course.

480
00:26:53 --> 00:26:59
So here's the earth...

481
00:26:59 --> 00:27:05
and the mass of the earth

482
00:27:02 --> 00:27:08
is about 6 times 10
to the 24 kilograms.

483
00:27:06 --> 00:27:12
And here at a distance, h--

484
00:27:10 --> 00:27:16
for which we will take
100 meters--

485
00:27:13 --> 00:27:19
is this apple, m, which, say,
has a mass of half a kilogram.

486
00:27:19 --> 00:27:25
There's a force
from the earth onto the apple

487
00:27:24 --> 00:27:30
and this is that force.

488
00:27:27 --> 00:27:33
And the magnitude of that force
is mg and that is 5 newton.

489
00:27:33 --> 00:27:39
I make g ten and
just round it off a little.

490
00:27:39 --> 00:27:45
Now, how long does it take
this object to hit the earth?

491
00:27:46 --> 00:27:52
So, we know that
1/2 gt squared equals h.

492
00:27:52 --> 00:27:58
It doesn't start with any
initial speed, so that is 100.

493
00:27:58 --> 00:28:04
G is 10, this is 5,
so t squared is 20.

494
00:28:01 --> 00:28:07
So t is about 4½ seconds.

495
00:28:04 --> 00:28:10
So after 4½ seconds, it hits
the earth-- so far, so good.

496
00:28:10 --> 00:28:16
But now, according
to the Third Law

497
00:28:13 --> 00:28:19
the earth must experience

498
00:28:15 --> 00:28:21
exactly the same force
as the apple does

499
00:28:19 --> 00:28:25
but in opposite direction.

500
00:28:22 --> 00:28:28
So therefore the earth will
experience this same force, f--

501
00:28:30 --> 00:28:36
5 newton, in this direction.

502
00:28:32 --> 00:28:38
What is the earth going to do?

503
00:28:34 --> 00:28:40
Well, the earth is going to fall
towards the apple-- f equals ma.

504
00:28:39 --> 00:28:45
So the force on the earth
is the mass of the earth

505
00:28:45 --> 00:28:51
times the acceleration
of the earth.

506
00:28:48 --> 00:28:54
The force, we know, is 5.

507
00:28:51 --> 00:28:57
We know the mass,
6 times 10 to the 24

508
00:28:55 --> 00:29:01
so the acceleration will be 5
divided by 6 times 10 to the 24

509
00:29:01 --> 00:29:07
which is about 8 times 10

510
00:29:04 --> 00:29:10
to the minus 25 meters
per second squared.

511
00:29:08 --> 00:29:14

512
00:29:11 --> 00:29:17
How long will the earth fall?

513
00:29:13 --> 00:29:19
Well, the earth will fall
roughly 4½ seconds

514
00:29:16 --> 00:29:22
before they collide.

515
00:29:18 --> 00:29:24
How far does the earth move
in the 4½ seconds?

516
00:29:23 --> 00:29:29
Well, it moves
one-half a earth t squared.

517
00:29:28 --> 00:29:34
That's the distance
that it moves.

518
00:29:31 --> 00:29:37
We know a and we know t squared,
which is 20.

519
00:29:35 --> 00:29:41
One-half times 20 is 10

520
00:29:38 --> 00:29:44
so that means this distance
becomes that number times 10.

521
00:29:42 --> 00:29:48
It's about 8 times 10
to the minus 24 meters.

522
00:29:45 --> 00:29:51
The earth moves 8 times 10
to the minus 24 meters.

523
00:29:51 --> 00:29:57
That, of course, is
impossible to measure.

524
00:29:56 --> 00:30:02
But just imagine what
a wonderful concept this is!

525
00:30:02 --> 00:30:08
When this ball falls back to me

526
00:30:06 --> 00:30:12
the earth and you and I and MIT
are falling towards the ball.

527
00:30:14 --> 00:30:20
Every time that the ball
comes down

528
00:30:16 --> 00:30:22
we're falling towards the ball.

529
00:30:18 --> 00:30:24
Imagine the power I have
over you and over the earth!

530
00:30:21 --> 00:30:27

531
00:30:23 --> 00:30:29
But you may want
to think about this--

532
00:30:26 --> 00:30:32
if I throw the ball up,
going to be away from the earth

533
00:30:30 --> 00:30:36
I'll bet you anything

534
00:30:32 --> 00:30:38
that the earth will also
go away from the ball.

535
00:30:36 --> 00:30:42
So as I do this,
casually playing--

536
00:30:38 --> 00:30:44
believe me, man,
what a glorious feeling it is--

537
00:30:41 --> 00:30:47
earth is going down, earth
is coming towards the ball.

538
00:30:44 --> 00:30:50
The earth is going down
and I'm part of the earth

539
00:30:48 --> 00:30:54
and I'm shaking this earth
up and down

540
00:30:50 --> 00:30:56
by simply playing
with this ball.

541
00:30:52 --> 00:30:58
That is the consequence
of Newton's Third Law

542
00:30:56 --> 00:31:02
even though the amount
by which the earth moves

543
00:31:00 --> 00:31:06
is, of course,
too small to be measured.

544
00:31:03 --> 00:31:09

545
00:31:06 --> 00:31:12
I now want to work out with you
a rather detailed example

546
00:31:11 --> 00:31:17
of something in which we combine
what we have learned today--

547
00:31:17 --> 00:31:23
a down-to-earth problem--

548
00:31:20 --> 00:31:26
the kind of a problem
that you might see

549
00:31:23 --> 00:31:29
on an exam
or on an assignment.

550
00:31:28 --> 00:31:34
We hang an object on two strings

551
00:31:36 --> 00:31:42
and one string makes an angle
of 60 degrees with the vertical

552
00:31:42 --> 00:31:48
and the other makes an angle
of 45 degrees with the vertical.

553
00:31:49 --> 00:31:55
So this is the one
that makes an angle...

554
00:31:53 --> 00:31:59
oh, 60 degrees with the horizon,
30 degrees with the vertical

555
00:31:59 --> 00:32:05
and this one, 45 degrees.

556
00:32:01 --> 00:32:07

557
00:32:04 --> 00:32:10
Let's assume that the strings
have negligible mass.

558
00:32:08 --> 00:32:14
So they are attached here
to the ceiling

559
00:32:12 --> 00:32:18
and I hang here an object, m.

560
00:32:15 --> 00:32:21
Well, if there's an object m

561
00:32:18 --> 00:32:24
for sure there will be
a force mg, gravitational force.

562
00:32:23 --> 00:32:29
This object is hanging there,
it's not being accelerated

563
00:32:29 --> 00:32:35
so the net acceleration
must be zero.

564
00:32:33 --> 00:32:39
And so one string must
be pulling in this direction

565
00:32:36 --> 00:32:42
and the other string must
be pulling in this direction

566
00:32:39 --> 00:32:45
so that the net force
on the system is zero.

567
00:32:41 --> 00:32:47

568
00:32:44 --> 00:32:50
Let's call this pull,
for now, "T1."

569
00:32:48 --> 00:32:54
We'll call that the tension
in the string

570
00:32:51 --> 00:32:57
and we call the tension
in this string "T2."

571
00:32:54 --> 00:33:00

572
00:32:57 --> 00:33:03
And the question now is how
large is T1 and how large is T2?

573
00:33:01 --> 00:33:07
There are various ways
you can do this.

574
00:33:05 --> 00:33:11
One way that always works--
pretty safe--

575
00:33:09 --> 00:33:15
you call this the x direction.

576
00:33:12 --> 00:33:18
You may choose which direction
you call "plus."

577
00:33:15 --> 00:33:21
I call this plus,
I call this negative.

578
00:33:18 --> 00:33:24
And you could call this
the y direction

579
00:33:21 --> 00:33:27
and you may call this plus
and this negative.

580
00:33:25 --> 00:33:31
I know, from Newton's
Second Law-- F equals ma--

581
00:33:36 --> 00:33:42
that there is no acceleration,
so this must be zero

582
00:33:40 --> 00:33:46
so the sum of all forces
on that mass must be zero.

583
00:33:44 --> 00:33:50
These three forces must eat
each other up, so to speak.
 

584
00:33:50 --> 00:33:56
Well, if that's the case,
then the sum of all forces

585
00:33:52 --> 00:33:58
in the x direction
must also be zero

586
00:33:54 --> 00:34:00
because there's no acceleration
in the x direction

587
00:33:57 --> 00:34:03
and the sum of all forces
in the y direction must be zero.

588
00:34:00 --> 00:34:06
And so I am going
to decompose them--

589
00:34:03 --> 00:34:09
something we have done before.

590
00:34:06 --> 00:34:12
I am going to decompose
the forces

591
00:34:08 --> 00:34:14
into an x and
into a y direction.

592
00:34:11 --> 00:34:17

593
00:34:13 --> 00:34:19
So here comes
the x component of T1

594
00:34:20 --> 00:34:26
and its magnitude is T1
times the cosine of 60 degrees.

595
00:34:28 --> 00:34:34

596
00:34:36 --> 00:34:42
Now I want to know
what this one is.

597
00:34:44 --> 00:34:50
This one is T1 times
the sine of 60 degrees.

598
00:34:55 --> 00:35:01
This projection, T2,
cosign 45 degrees

599
00:35:04 --> 00:35:10
and the y component,
T2 times the sine of 45 degrees.

600
00:35:13 --> 00:35:19
So we go into the x direction.

601
00:35:18 --> 00:35:24
In the x direction
I have T1 cosign 60 degrees

602
00:35:26 --> 00:35:32
minus T2 cosign 45 degrees
equals zero--

603
00:35:32 --> 00:35:38
that's one equation.

604
00:35:35 --> 00:35:41
The cosine of 60 degrees
is one-half

605
00:35:40 --> 00:35:46
and the cosine of 45 degrees
is one-half square root two.

606
00:35:46 --> 00:35:52
Now I go to the y direction.

607
00:35:50 --> 00:35:56
This is plus, this is minus,
so we get one component here

608
00:35:56 --> 00:36:02
which is T1 times
the sine of 60 degrees

609
00:36:00 --> 00:36:06
plus T2 times the sine
of 45 degreesminus mg.

610
00:36:06 --> 00:36:12
It's in the opposite direction--
must be zero.

611
00:36:11 --> 00:36:17
That's my second equation.

612
00:36:15 --> 00:36:21
The sine of 60 degrees equals
one-half the square root three

613
00:36:24 --> 00:36:30
and the sine of 45 degrees

614
00:36:27 --> 00:36:33
is the same as the cosine
one-half square root two.

615
00:36:30 --> 00:36:36

616
00:36:32 --> 00:36:38
Notice I have two equations
with two unknowns.

617
00:36:35 --> 00:36:41
If you tell me what m is

618
00:36:37 --> 00:36:43
I should be able to solve
for T1 and for T2.

619
00:36:39 --> 00:36:45
In fact, if we add them up

620
00:36:42 --> 00:36:48
it's going to be very easy
because we lose this

621
00:36:45 --> 00:36:51
because we have both
one-half square root two.

622
00:36:49 --> 00:36:55
And so you see immediately here
that one-half times T1

623
00:36:53 --> 00:36:59
plus one-half square root three
times T1 equals mg

624
00:37:02 --> 00:37:08
and so you find that
the tension 1 equals two mg

625
00:37:07 --> 00:37:13
divided by one
plus the square root of three.

626
00:37:13 --> 00:37:19

627
00:37:15 --> 00:37:21
I can go back now
to this equation--

628
00:37:20 --> 00:37:26
T1 times one-half

629
00:37:22 --> 00:37:28
equals T2 times one-half
square root of two.

630
00:37:28 --> 00:37:34
I lose my half

631
00:37:29 --> 00:37:35
and so T2 equals T1 divided
by the square root of two.

632
00:37:36 --> 00:37:42
So the bottom line is,
you tell me what m is

633
00:37:38 --> 00:37:44
I'll tell you what T1 is
and I'll tell you what T2 is.

634
00:37:42 --> 00:37:48
Suppose we take a mass
of four kilograms--

635
00:37:47 --> 00:37:53
m equals four kilograms,
so mg is about 40

636
00:37:51 --> 00:37:57
if we make g ten for simplicity.

637
00:37:55 --> 00:38:01
Then T1, if you put in
the numbers, is about 29.3

638
00:38:03 --> 00:38:09
and T2... 29.3 newtons

639
00:38:06 --> 00:38:12
and T2 is about 20.7 newtons,
I believe.

640
00:38:12 --> 00:38:18

641
00:38:15 --> 00:38:21
It's very difficult to rig
this up as an experiment

642
00:38:20 --> 00:38:26
but I've tried that.

643
00:38:21 --> 00:38:27
I'll show you in a minute.

644
00:38:24 --> 00:38:30
I want you to know
that there is another method

645
00:38:28 --> 00:38:34
which is perhaps
even more elegant

646
00:38:31 --> 00:38:37
and which you may consider

647
00:38:34 --> 00:38:40
in which there is
no decomposition

648
00:38:37 --> 00:38:43
in the two directions.

649
00:38:39 --> 00:38:45

650
00:38:42 --> 00:38:48
Here is mg-- that's a given.

651
00:38:45 --> 00:38:51
And we know that the other
directions are also given--

652
00:38:50 --> 00:38:56
this angle of 30 degrees here
and this angle of 45 degrees.

653
00:38:57 --> 00:39:03
If these two forces
must cancel out this one

654
00:39:00 --> 00:39:06
why don't I flip this one over?

655
00:39:03 --> 00:39:09
Here it comes.

656
00:39:05 --> 00:39:11

657
00:39:07 --> 00:39:13
I flip it over.

658
00:39:10 --> 00:39:16
There it is.

659
00:39:12 --> 00:39:18
T1 and T2 now, together,
must add up to this one.

660
00:39:15 --> 00:39:21
Then the problem is solved,
then the net force is zero.

661
00:39:20 --> 00:39:26
Well, that's easy-- I do this.

662
00:39:22 --> 00:39:28

663
00:39:28 --> 00:39:34
And now I have constructed

664
00:39:31 --> 00:39:37
a complete fair construction
of T1 and of T2.

665
00:39:37 --> 00:39:43
No physics anymore now,
it's all over.

666
00:39:39 --> 00:39:45
You know this angle here, 45
degrees, so this is 45 degrees.

667
00:39:43 --> 00:39:49
This is 30, this is 30.

668
00:39:44 --> 00:39:50
You know all the angles and
you know this magnitude is mg

669
00:39:47 --> 00:39:53
so it's a high school problem.

670
00:39:49 --> 00:39:55
You have a triangle with
all the angles and one side; 

671
00:39:52 --> 00:39:58
you can calculate
the other sides

672
00:39:54 --> 00:40:00
and you should find exactly
the same answer, of course.

673
00:39:57 --> 00:40:03

674
00:39:59 --> 00:40:05
We made an attempt to rig it up.

675
00:40:01 --> 00:40:07
How do we measure tension?

676
00:40:03 --> 00:40:09
Well, we put in these lines,
scales, tension meters

677
00:40:07 --> 00:40:13
and that is problematic,
believe me.

678
00:40:11 --> 00:40:17
We put in here a tension meter,
we put in here a tension meter

679
00:40:16 --> 00:40:22
and the bottom one, we hang on a
string with a tension meter

680
00:40:22 --> 00:40:28
and then here we put
four kilograms.

681
00:40:25 --> 00:40:31
These scales are not masses.

682
00:40:28 --> 00:40:34
That's already problematic.

683
00:40:30 --> 00:40:36
The scales are
not very accurate

684
00:40:33 --> 00:40:39
so we may not even come close
to these numbers.

685
00:40:37 --> 00:40:43
For sure,
if I put four kilograms here

686
00:40:40 --> 00:40:46
then I would like this one
to read 40 newtons

687
00:40:43 --> 00:40:49
or somewhere
in that neighborhood

688
00:40:46 --> 00:40:52
depending on
how accurate my meters are.

689
00:40:49 --> 00:40:55
These are springs,
and the springs extend

690
00:40:52 --> 00:40:58
and when the springs extend,
you see a handle... a hand go.

691
00:40:58 --> 00:41:04
You can clearly see
how that works

692
00:41:01 --> 00:41:07
because if there is a force
on that bottom scale

693
00:41:05 --> 00:41:11
in this direction, which is mg,
and it's not being accelerated

694
00:41:11 --> 00:41:17
then the string
must pull upwards

695
00:41:13 --> 00:41:19
and so... in order to make
the net force zero.

696
00:41:17 --> 00:41:23
And if you have a pull down here
and you have a pull up here

697
00:41:21 --> 00:41:27
and you have in here a spring

698
00:41:22 --> 00:41:28
then you see you have
a way of measuring that force.

699
00:41:25 --> 00:41:31
We often do that--

700
00:41:26 --> 00:41:32
we measure with springs
the tension in strings.

701
00:41:30 --> 00:41:36
For whatever it's worth, I will
show you what we rigged up.

702
00:41:34 --> 00:41:40
Now a measurement without
knowledge of uncertainties

703
00:41:38 --> 00:41:44
is meaningless--
I told you that.

704
00:41:41 --> 00:41:47
So maybe this is meaningless,
what I am going to do now.

705
00:41:45 --> 00:41:51
Let me do something meaningless
for once.

706
00:41:48 --> 00:41:54
And remember, when I show it,
you can always close your eyes

707
00:41:52 --> 00:41:58
so that you haven't seen it.

708
00:41:54 --> 00:42:00
So we have here something
that approaches this 60 degrees

709
00:41:58 --> 00:42:04
and this approaches
the 45 degrees

710
00:42:02 --> 00:42:08
and we're going to hang
four kilograms at the bottom.

711
00:42:04 --> 00:42:10

712
00:42:08 --> 00:42:14
There it is, and here it is.

713
00:42:10 --> 00:42:16
All right, this one--
it's not too far from 40.

714
00:42:14 --> 00:42:20
It's not an embarrassment.

715
00:42:15 --> 00:42:21
This one is not too far
from 20.7.

716
00:42:17 --> 00:42:23
This one is a bit
on the low side.

717
00:42:19 --> 00:42:25
Maybe I can push it up a little.

718
00:42:21 --> 00:42:27
I think that's close to 30;
it's not bad.

719
00:42:24 --> 00:42:30
So you see, it's very difficult
to get these angles right

720
00:42:28 --> 00:42:34
but it's not too far off.

721
00:42:30 --> 00:42:36
So let's remove this again

722
00:42:32 --> 00:42:38
because this will block
your view.

723
00:42:35 --> 00:42:41
These scales were calibrated
in newtons, as you could see.

724
00:42:40 --> 00:42:46

725
00:42:45 --> 00:42:51
Now we come
to something very delicate.

726
00:42:49 --> 00:42:55
Now I need your alertness
and I need your help.

727
00:42:55 --> 00:43:01

728
00:42:58 --> 00:43:04
I have a block--
you see it there--

729
00:43:01 --> 00:43:07
and that block weighs
two kilograms.

730
00:43:05 --> 00:43:11
A red block.

731
00:43:07 --> 00:43:13
So here it is.

732
00:43:09 --> 00:43:15
It's red.

733
00:43:12 --> 00:43:18
And I have two strings.

734
00:43:13 --> 00:43:19
It's hanging from a black string
here and a black string there.

735
00:43:18 --> 00:43:24
Ignore that red string,
that is just a safety.

736
00:43:21 --> 00:43:27
But it's avery thin thread
here and here.

737
00:43:24 --> 00:43:30
And they are as close
as we can make them the same.

738
00:43:28 --> 00:43:34
They come from the same batch.

739
00:43:30 --> 00:43:36

740
00:43:33 --> 00:43:39
This one has a mass
of two kilograms

741
00:43:36 --> 00:43:42
and this string has no mass.

742
00:43:39 --> 00:43:45
This is two kilograms.

743
00:43:41 --> 00:43:47
So what will be the tension
in the upper string

744
00:43:45 --> 00:43:51
which is string number one?

745
00:43:47 --> 00:43:53
This is string number two.

746
00:43:49 --> 00:43:55
Well, this string must be able
to carry this two kilograms

747
00:43:53 --> 00:43:59
so the tension has to be
20 newtons.

748
00:43:56 --> 00:44:02
So you will find here
the tension-- call it T1--

749
00:43:59 --> 00:44:05
which is about 20 newtons.

750
00:44:03 --> 00:44:09
So it's pulling
up on this object.

751
00:44:07 --> 00:44:13
It's also pulling down
from the ceiling, by the way.

752
00:44:13 --> 00:44:19
Think about it, it's pulling
from the ceiling.

753
00:44:17 --> 00:44:23
The tension is here, 20 newtons.

754
00:44:20 --> 00:44:26
We could put in here
one of these scales

755
00:44:23 --> 00:44:29
and you would see
approximately 20 newtons.

756
00:44:25 --> 00:44:31
What is the tension here?

757
00:44:27 --> 00:44:33
Well, the tension here
is very close to zero.

758
00:44:30 --> 00:44:36
There's nothing hanging on it
and the string has no weight

759
00:44:33 --> 00:44:39
so there's no tension there--
you can see that.

760
00:44:36 --> 00:44:42

761
00:44:39 --> 00:44:45
Now I am going to pull on here

762
00:44:44 --> 00:44:50
and I'm going to increase
the tension on the bottom one

763
00:44:51 --> 00:44:57
until one of the two breaks.

764
00:44:55 --> 00:45:01
So this tension goes up and up

765
00:44:59 --> 00:45:05
and therefore, since this object
is not being accelerated--

766
00:45:04 --> 00:45:10
we're going to get a force
down now on this object--

767
00:45:09 --> 00:45:15
this tension must increase,
right?

768
00:45:12 --> 00:45:18
You see that?

769
00:45:13 --> 00:45:19
If I have a force on this one...

770
00:45:17 --> 00:45:23
so there's a force here,
and there is mg

771
00:45:22 --> 00:45:28
then, of course, this string
must now be mg plus this force.
 

772
00:45:26 --> 00:45:32
So the tension will go up here
and the tension will go up here.

773
00:45:31 --> 00:45:37
The strings are as identical
as they can be.

774
00:45:35 --> 00:45:41
Which of the strings
will break first?

775
00:45:38 --> 00:45:44
What do you think?

776
00:45:40 --> 00:45:46

777
00:45:42 --> 00:45:48
LEWIN:
Excuse me?

778
00:45:43 --> 00:45:49
(student answers
unintelligibly )

779
00:45:45 --> 00:45:51
I can't hear you.

780
00:45:46 --> 00:45:52
STUDENT:
The one on top.

781
00:45:47 --> 00:45:53
LEWIN:
The one on top.

782
00:45:48 --> 00:45:54
Who is in favor
of the one on top?

783
00:45:52 --> 00:45:58
Who says no, the bottom one?

784
00:45:54 --> 00:46:00
(Student answers
unintelligibly )

785
00:45:58 --> 00:46:04
LEWIN:
Who says they won't break
at all?

786
00:46:02 --> 00:46:08
Okay, let's take a look at it.

787
00:46:05 --> 00:46:11
The one on top--
that's the most likely, right?

788
00:46:10 --> 00:46:16
Three, two, one, zero.

789
00:46:12 --> 00:46:18

790
00:46:16 --> 00:46:22
The bottom one broke.

791
00:46:20 --> 00:46:26
My goodness.

792
00:46:21 --> 00:46:27
Newton's Second Law is at stake.

793
00:46:22 --> 00:46:28
Newton's Third Law is at stake.

794
00:46:24 --> 00:46:30
The whole world is at stake!

795
00:46:26 --> 00:46:32
Something is not working.

796
00:46:31 --> 00:46:37
I increased tension here,
this one didn't break.

797
00:46:34 --> 00:46:40
This one's stronger, perhaps.

798
00:46:36 --> 00:46:42
No, I don't cheat on you;
I'm not a magician.

799
00:46:39 --> 00:46:45
I want to teach you physics.

800
00:46:40 --> 00:46:46

801
00:46:43 --> 00:46:49
Did we overlook something?

802
00:46:45 --> 00:46:51
You know,
I'll give you a second chance.

803
00:46:48 --> 00:46:54
We'll do it again.

804
00:46:49 --> 00:46:55
Let's have another vote.

805
00:46:51 --> 00:46:57
So I'll give you a chance
to change your minds.

806
00:46:53 --> 00:46:59
It's nothing wrong in life,
changing your mind.

807
00:46:55 --> 00:47:01
It's one of the greatest things
that you can do.

808
00:46:58 --> 00:47:04

809
00:47:02 --> 00:47:08
What do you think
will happen now?

810
00:47:04 --> 00:47:10
Who is in favor still
of the top one?

811
00:47:07 --> 00:47:13
Seeing is believing.

812
00:47:08 --> 00:47:14
You still insist on the top one?

813
00:47:10 --> 00:47:16
Who is now in favor
of the bottom one?

814
00:47:12 --> 00:47:18
Ah, many of you
got converted, right?

815
00:47:15 --> 00:47:21
Okay, there we go.

816
00:47:17 --> 00:47:23
Three, two, one, zero.

817
00:47:19 --> 00:47:25

818
00:47:22 --> 00:47:28
The top one broke.

819
00:47:23 --> 00:47:29
So some of you were right.

820
00:47:25 --> 00:47:31
Now I'm getting so confused.

821
00:47:28 --> 00:47:34
I can't believe it anymore.

822
00:47:30 --> 00:47:36
First we argued
that the top one should break

823
00:47:33 --> 00:47:39
but it didn't--
the bottom one broke.

824
00:47:35 --> 00:47:41
Then we had another vote
and then the top one broke.

825
00:47:39 --> 00:47:45
Is someone pulling our leg?

826
00:47:41 --> 00:47:47
I suggest we do it
one more time.

827
00:47:43 --> 00:47:49
I suggest we do it one more time

828
00:47:46 --> 00:47:52
and whatever's going to happen,
that's the winner.

829
00:47:50 --> 00:47:56
If the top one breaks,
that's the winner.

830
00:47:53 --> 00:47:59
If the bottom one breaks, well,
then, we have to accept that.

831
00:47:58 --> 00:48:04
But I want you to vote again.

832
00:48:00 --> 00:48:06
I want you to vote again
on this decisive measurement

833
00:48:06 --> 00:48:12
whether the top one will break
first or the bottom one?

834
00:48:10 --> 00:48:16
Who is in favor of the top one?

835
00:48:13 --> 00:48:19

836
00:48:16 --> 00:48:22
Many of you are scared, right?

837
00:48:17 --> 00:48:23
You're notvoting anymore!

838
00:48:18 --> 00:48:24
(class laughs )

839
00:48:19 --> 00:48:25
LEWIN:
I can tell, you're not voting.

840
00:48:21 --> 00:48:27
Who is in favor
of the bottom one?

841
00:48:25 --> 00:48:31
Only ten people are voting.

842
00:48:28 --> 00:48:34
(class laughs )

843
00:48:30 --> 00:48:36
LEWIN:
Let's do this
in an undemocratic way.

844
00:48:33 --> 00:48:39
You may decide--
what's your name?

845
00:48:36 --> 00:48:42
Alicia?

846
00:48:37 --> 00:48:43
Georgia, close enough.

847
00:48:39 --> 00:48:45
(laughter )

848
00:48:40 --> 00:48:46
You may decide
whether the top one

849
00:48:43 --> 00:48:49
or the bottom one will break.

850
00:48:45 --> 00:48:51
Isn't that great?
 

851
00:48:46 --> 00:48:52
Doesn't it give you
a fantastic amount of power?

852
00:48:52 --> 00:48:58
The bottom one.

853
00:48:53 --> 00:48:59

854
00:48:54 --> 00:49:00
The bottom one.

855
00:48:56 --> 00:49:02
You ready?

856
00:48:57 --> 00:49:03
Three, two, one, zero.

857
00:49:00 --> 00:49:06
The bottom one broke.

858
00:49:01 --> 00:49:07
You were right.

859
00:49:02 --> 00:49:08
You will pass this course.

860
00:49:04 --> 00:49:10
Thank you,
and see you Wednesday.

861
00:49:07 --> 00:49:13
By the way, think about this,
think about this.

862
00:49:11 --> 00:49:17.000