English subtitles for clip: File:Secondlaw.ogv
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1 00:00:01,300 --> 00:00:04,900 Now we come to the second law. 2 00:00:04,900 --> 00:00:07,100 Newton's second law. 3 00:00:08,500 --> 00:00:10,800 I have a spring – 4 00:00:14,600 --> 00:00:16,000 forget gravity for now, 5 00:00:16,000 --> 00:00:17,900 you can do this somewhere in outer space – 6 00:00:17,900 --> 00:00:20,000 this is the relaxed length of the spring, 7 00:00:20,000 --> 00:00:23,100 and I extend the spring … 8 00:00:23,740 --> 00:00:26,300 I extend it over a certain amount – 9 00:00:26,300 --> 00:00:29,000 certain distance – in unimportant how much. 10 00:00:29,000 --> 00:00:31,650 And I know, that when I do that 11 00:00:31,650 --> 00:00:33,600 that there will be a pull. 12 00:00:33,800 --> 00:00:35,700 Non-negotiable. 13 00:00:36,750 --> 00:00:39,540 I put a mass m₁ here 14 00:00:40,250 --> 00:00:43,200 and I measure the acceleration 15 00:00:43,200 --> 00:00:45,150 that this pull causes on this mass 16 00:00:45,150 --> 00:00:46,660 immediately after I release – 17 00:00:46,660 --> 00:00:47,650 I can measure that. 18 00:00:47,650 --> 00:00:50,300 So I measure an acceleration a₁. 19 00:00:50,900 --> 00:00:53,500 Now I replace this object 20 00:00:53,500 --> 00:00:55,400 by mass m₂, 21 00:00:55,950 --> 00:00:58,050 but the extension is the same. 22 00:00:58,050 --> 00:00:59,700 So the pull must be the same, 23 00:00:59,700 --> 00:01:01,000 the spring doesn't know 24 00:01:01,000 --> 00:01:02,800 what the mass is at either end, right? 25 00:01:02,800 --> 00:01:04,500 So the pull is the same, 26 00:01:04,500 --> 00:01:06,600 I put m₂ there – different mass – 27 00:01:06,600 --> 00:01:08,300 and I measure 28 00:01:08,300 --> 00:01:10,300 new acceleration a₂. 29 00:01:10,400 --> 00:01:13,700 It is now an experimental fact, that 30 00:01:13,700 --> 00:01:19,500 m₁ a₁ = m₂ a₂. 31 00:01:20,900 --> 00:01:22,700 And this product, 32 00:01:22,700 --> 00:01:26,100 m a, we call the force. 33 00:01:26,100 --> 00:01:29,300 That is our definition of force. 34 00:01:29,600 --> 00:01:31,500 So the same pull 35 00:01:31,500 --> 00:01:33,800 on a ten times larger mass 36 00:01:33,800 --> 00:01:34,900 would give a 37 00:01:34,900 --> 00:01:37,800 ten times lower acceleration. 38 00:01:39,500 --> 00:01:43,000 The second law, I will read to you: 39 00:01:43,500 --> 00:01:46,200 “A force action on a body 40 00:01:46,200 --> 00:01:48,200 gives it an acceleration 41 00:01:48,200 --> 00:01:50,500 which is in the direction of the force […]” – 42 00:01:50,500 --> 00:01:51,900 that's also important, 43 00:01:51,900 --> 00:01:54,900 acceleration is in the direction of the force – 44 00:01:54,900 --> 00:01:58,100 “[…] and has a magnitude given by m a.” 45 00:01:58,200 --> 00:01:59,800 m a is the magnitude. 46 00:01:59,800 --> 00:02:01,500 And the direction is 47 00:02:01,500 --> 00:02:03,500 the direction of the force. 48 00:02:03,500 --> 00:02:05,400 So now we will write this, 49 00:02:05,400 --> 00:02:07,500 in all glorious, 50 00:02:07,500 --> 00:02:10,000 detailed is this the second law 51 00:02:10,600 --> 00:02:12,100 by Newton; 52 00:02:14,100 --> 00:02:17,000 Perhaps the most important law 53 00:02:17,800 --> 00:02:19,700 in <i>all</i> of physics, 54 00:02:19,700 --> 00:02:22,600 and certainly in all of 8.01. 55 00:02:22,600 --> 00:02:25,600 F ⃗ = m a ⃗. 56 00:02:25,800 --> 00:02:28,000 The units of this force 57 00:02:29,000 --> 00:02:34,600 are kilograms times meters per second squared – 58 00:02:34,600 --> 00:02:36,600 in honor of the great man 59 00:02:37,100 --> 00:02:39,100 we call that one Newton. 60 00:02:41,100 --> 00:02:43,800 Like the first law the second law 61 00:02:43,800 --> 00:02:47,000 <i>only</i> holds in inertial reference frames. 62 00:02:48,500 --> 00:02:51,500 Can the first law, the second law be proven? 63 00:02:51,600 --> 00:02:52,800 No. 64 00:02:53,300 --> 00:02:54,900 Do we believe in it? 65 00:02:55,100 --> 00:02:56,100 Yes. 66 00:02:56,100 --> 00:02:57,600 Why do we believe in it? 67 00:02:57,600 --> 00:02:59,500 Because <i>all</i> experiments 68 00:02:59,500 --> 00:03:00,700 and <i>all</i> measurements 69 00:03:00,700 --> 00:03:03,100 within the uncertainty of the measurements 70 00:03:03,100 --> 00:03:07,200 are in agreement with the second law. 71 00:03:09,500 --> 00:03:11,400 Now you may object. 72 00:03:11,600 --> 00:03:13,200 And you may say: 73 00:03:13,200 --> 00:03:15,700 “This is strange what you've been doing.” 74 00:03:15,700 --> 00:03:17,500 “How can you ever determine 75 00:03:17,500 --> 00:03:18,900 a mass 76 00:03:18,900 --> 00:03:20,800 if there is no force somewhere?” 77 00:03:20,800 --> 00:03:22,800 Because if you wanna determine the mass 78 00:03:22,800 --> 00:03:24,300 maybe you put it on a scale 79 00:03:24,300 --> 00:03:25,700 and when you put it on the scale 80 00:03:25,700 --> 00:03:26,700 to determine the mass 81 00:03:26,700 --> 00:03:28,400 you make use of the gravitational force; 82 00:03:28,400 --> 00:03:29,740 So, isn't that some kind of a 83 00:03:29,740 --> 00:03:31,700 circular argument that you're using? 84 00:03:31,700 --> 00:03:33,400 And your answer is: No. 85 00:03:35,000 --> 00:03:36,750 I can be somewhere in outer space 86 00:03:36,750 --> 00:03:38,400 where there's no gravity. 87 00:03:38,400 --> 00:03:40,500 I have two pieces of cheese 88 00:03:40,500 --> 00:03:42,400 that are <i>identical</i> in size – 89 00:03:42,400 --> 00:03:44,200 this is cheese without holes, by the way. 90 00:03:44,200 --> 00:03:46,300 They are identical in size. 91 00:03:46,900 --> 00:03:48,300 The sum of the two 92 00:03:48,300 --> 00:03:50,300 has double the mass of one. 93 00:03:50,300 --> 00:03:51,800 Mass is determined by 94 00:03:51,800 --> 00:03:52,800 how many molecules 95 00:03:52,800 --> 00:03:54,000 how many atoms that I have. 96 00:03:54,000 --> 00:03:55,300 I don't need gravity 97 00:03:55,300 --> 00:03:57,150 to have a relative scale of masses 98 00:03:57,150 --> 00:03:58,280 so I can determine 99 00:03:58,280 --> 00:04:00,100 the relative scale of these masses 100 00:04:00,100 --> 00:04:02,100 without ever using a force. 101 00:04:02,500 --> 00:04:06,300 So, this is a very legitimate way of … 102 00:04:08,300 --> 00:04:11,600 … checking up on the second law. 103 00:04:13,040 --> 00:04:39,150 [video glitch] 104 00:04:42,200 --> 00:04:43,800 Since all objects 105 00:04:44,400 --> 00:04:45,800 in this lecture hall 106 00:04:45,800 --> 00:04:47,100 and the earth 107 00:04:47,400 --> 00:04:48,600 fall is the 108 00:04:48,600 --> 00:04:50,800 constant acceleration, which is g, 109 00:04:51,500 --> 00:04:52,900 we can write down 110 00:04:53,800 --> 00:04:54,600 that 111 00:04:54,600 --> 00:04:56,500 the gravitational force 112 00:04:56,500 --> 00:04:57,300 would be 113 00:04:57,300 --> 00:05:00,500 m times this acceleration g ⃗. 114 00:05:00,500 --> 00:05:01,900 Normally I write an a ⃗ for it, 115 00:05:01,900 --> 00:05:03,400 but I make an exception now, 116 00:05:03,400 --> 00:05:05,300 because gravity I call it 117 00:05:05,600 --> 00:05:07,150 gravitational force. 118 00:05:07,150 --> 00:05:08,300 And so you see 119 00:05:08,300 --> 00:05:10,400 that the gravitational force 120 00:05:10,400 --> 00:05:11,600 due to the earth 121 00:05:11,600 --> 00:05:12,900 on a particular mass 122 00:05:13,400 --> 00:05:15,300 is [unintelligible] proportional 123 00:05:15,300 --> 00:05:16,300 with the mass 124 00:05:16,300 --> 00:05:18,700 if the mass becomes ten times larger 125 00:05:18,700 --> 00:05:20,600 then the force 126 00:05:20,600 --> 00:05:22,000 due to gravity 127 00:05:22,000 --> 00:05:24,000 goes up by a factor of ten. 128 00:05:26,250 --> 00:05:27,800 Suppose I have here 129 00:05:28,000 --> 00:05:29,900 this softball in my hand. 130 00:05:31,000 --> 00:05:33,300 In the reference frame 131 00:05:33,860 --> 00:05:35,900 26.100, [unintelligible] we will accept 132 00:05:35,900 --> 00:05:37,600 to be an inertial reference frame. 133 00:05:37,850 --> 00:05:39,250 Is not being accelerated 134 00:05:39,250 --> 00:05:40,450 in our reference frame. 135 00:05:41,000 --> 00:05:42,400 That means, 136 00:05:43,000 --> 00:05:45,010 the force on it must be zero. 137 00:05:45,500 --> 00:05:46,700 So here 138 00:05:47,150 --> 00:05:48,400 is that ball. 139 00:05:49,500 --> 00:05:51,500 And we know, if it has mass m, 140 00:05:51,500 --> 00:05:53,900 which is in this case is about half a kilogram, 141 00:05:54,400 --> 00:05:56,300 that there must be a force here, 142 00:05:56,300 --> 00:05:57,500 m g, 143 00:05:57,500 --> 00:05:58,800 which is about 144 00:05:59,000 --> 00:06:00,200 five Newton, 145 00:06:00,400 --> 00:06:02,000 or half a kilogram. 146 00:06:02,200 --> 00:06:04,000 But the net force 147 00:06:04,000 --> 00:06:05,000 is zero. 148 00:06:05,500 --> 00:06:06,600 Therefore, 149 00:06:06,600 --> 00:06:08,200 it is very clear 150 00:06:08,200 --> 00:06:10,200 that I, Walter Lewin, 151 00:06:10,200 --> 00:06:12,400 must push up 152 00:06:12,400 --> 00:06:14,400 with a force 153 00:06:14,400 --> 00:06:16,400 from my hand onto the ball, 154 00:06:16,400 --> 00:06:17,600 which is about 155 00:06:17,600 --> 00:06:19,400 or as the same, which is exactly the same 156 00:06:19,400 --> 00:06:20,500 five Newtons. 157 00:06:20,500 --> 00:06:22,300 Only now is there 158 00:06:22,300 --> 00:06:24,200 no acceleration. 159 00:06:24,400 --> 00:06:26,690 So I can write down, that 160 00:06:28,600 --> 00:06:30,800 force of Walter Lewin 161 00:06:30,800 --> 00:06:33,800 plus the force of gravity 162 00:06:33,800 --> 00:06:35,200 equal zero, 163 00:06:35,200 --> 00:06:37,200 because it's a one-dimensional problem 164 00:06:37,200 --> 00:06:38,600 you could say, that 165 00:06:38,600 --> 00:06:40,300 the force of Walter Lewin 166 00:06:40,300 --> 00:06:43,000 equals minus m g. 167 00:06:46,700 --> 00:06:48,500 F ⃗ = m a ⃗. 168 00:06:48,900 --> 00:06:50,100 Notice, 169 00:06:50,800 --> 00:06:53,200 that there's no statement made 170 00:06:53,800 --> 00:06:55,800 on velocity nor speed. 171 00:06:56,150 --> 00:06:57,600 As long as you know F ⃗, 172 00:06:58,000 --> 00:06:59,500 and as long as you know m, 173 00:06:59,500 --> 00:07:01,500 a ⃗ is uniquely specified. 174 00:07:01,500 --> 00:07:04,000 <i>No</i> information is needed on the speed. 175 00:07:04,700 --> 00:07:06,100 But that would mean, 176 00:07:06,100 --> 00:07:07,400 if we take gravity 177 00:07:07,400 --> 00:07:09,200 and an object was falling down 178 00:07:09,200 --> 00:07:11,300 with five meters per second, 179 00:07:11,500 --> 00:07:13,000 that the law would hold. 180 00:07:14,000 --> 00:07:15,500 If it would fall down 181 00:07:16,000 --> 00:07:18,400 with 5,000 meters per second, 182 00:07:19,250 --> 00:07:20,500 it would <i>also</i> hold. 183 00:07:21,300 --> 00:07:23,100 Will it <i>always</i> hold? 184 00:07:23,400 --> 00:07:24,150 No. 185 00:07:25,700 --> 00:07:26,500 Once 186 00:07:26,500 --> 00:07:27,900 your speed 187 00:07:27,900 --> 00:07:29,800 approaches the speed of light, 188 00:07:29,800 --> 00:07:32,100 then it would only mechanics no longer works, 189 00:07:32,100 --> 00:07:33,100 then you have to use 190 00:07:33,100 --> 00:07:35,200 Einstein's theory of special relativity. 191 00:07:35,750 --> 00:07:37,100 So this is only valid 192 00:07:37,100 --> 00:07:38,700 as long as we have 193 00:07:38,700 --> 00:07:40,050 speeds that are 194 00:07:40,050 --> 00:07:41,600 substantially smaller, 195 00:07:41,600 --> 00:07:43,800 say, than the speed of light.