10:00:00 --> 00:00:06So far in these lectures

200:00:02 --> 00:00:08we've talked about mass, aboutacceleration and about forces,

300:00:07 --> 00:00:13but we never used the word"weight," and weight is

400:00:11 --> 00:00:17a very nonintuitiveand a very tricky thing

500:00:14 --> 00:00:20which is the entire subjectof today's lecture.

600:00:18 --> 00:00:24What is weight?

700:00:21 --> 00:00:27Here you standon a bathroom scale.

800:00:28 --> 00:00:34Gravity is acting upon you,the force is mg, your mass is m.

900:00:38 --> 00:00:44The bathroom scale is pushingon you with a force F scale

1000:00:43 --> 00:00:49and that F scale--which in this case

1100:00:45 --> 00:00:51if the systemis not being accelerated

1200:00:49 --> 00:00:55is the same as mg--

1300:00:51 --> 00:00:57that force from

the bathroom scale on you

1400:00:56 --> 00:01:02we define as weight.

1500:00:59 --> 00:01:05When I standon the bathroom scale

1600:01:01 --> 00:01:07I could seemy weight is about 165 pounds.

1700:01:05 --> 00:01:11Now, it may becalibrated in newtons

1800:01:07 --> 00:01:13but that's, of course,very unusual.

1900:01:11 --> 00:01:17If I weigh myself on the moon

2000:01:12 --> 00:01:18where the gravitationalacceleration is six times less

2100:01:15 --> 00:01:21then I would weigh six timesless-- so far, so good.

2200:01:23 --> 00:01:29Now I'm going to put youin an elevator

2300:01:28 --> 00:01:34and I'm goingto accelerate you upwards

2400:01:34 --> 00:01:40and you're standingon your bathroom scale.

2500:01:37 --> 00:01:43Acceleration isin this direction

2600:01:40 --> 00:01:46and I will call this "plus"and I will call this "minus."

2700:01:44 --> 00:01:50Gravity is acting upon you, mg

2800:01:48 --> 00:01:54and the bathroom scale ispushing on you with a force F.

2900:01:54 --> 00:02:00That force,by definition, is weight.

3000:02:00 --> 00:02:06Before I write down someequations, I want you to realize

3100:02:03 --> 00:02:09that whenever, whenever you seein any of my equations "g"

3200:02:08 --> 00:02:14g is always plus 9.8.

3300:02:11 --> 00:02:17And my signs, my minus signstake care of the directions

3400:02:14 --> 00:02:20but g isalways plus 9.8or plus 10, if you prefer that.

3500:02:19 --> 00:02:25Okay, it's clear thatif this is accelerated upwards

3600:02:23 --> 00:02:29that F of s must belarger than mg;

3700:02:25 --> 00:02:31otherwise Icannot be accelerated.

3800:02:27 --> 00:02:33

And so we getNewton's Second Law:

3900:02:30 --> 00:02:36F of s is in plus direction...

4000:02:33 --> 00:02:39minus mg-- it's in thisdirection-- equals m times a

4100:02:40 --> 00:02:46and so the bathroom scaleindicates m times a plus g.

4200:02:47 --> 00:02:53And I have gained weight.

4300:02:50 --> 00:02:56If this acceleration is

4400:02:52 --> 00:02:58five meters per second squaredin this direction

4500:02:55 --> 00:03:01I am one and a half timesmy normal weight.

4600:03:00 --> 00:03:06If I look on the bathroom scale,that's what I see.

4700:03:03 --> 00:03:09Seeing is believing--that is my weight.

4800:03:07 --> 00:03:13If I accelerate upwards, with 30meters per second squared

4900:03:10 --> 00:03:1630 plus 10 is 40-- I amfour times my normal weight.

5000:03:18 --> 00:03:24Instead of my 165 pounds, Iwould weigh close to 700 pounds.

5100:03:24 --> 00:03:30I see that--seeing is believing.

5200:03:26 --> 00:03:32That is my weight.

5300:03:29 --> 00:03:35Now I am going to put youin the elevator-- here you are--

5400:03:36 --> 00:03:42and I'm going to accelerateyou down.

5500:03:40 --> 00:03:46This is now a.

5600:03:43 --> 00:03:49And just for my convenience

5700:03:44 --> 00:03:50I call this nowthe plus direction

5800:03:47 --> 00:03:53just for my convenience--it doesn't really matter.

5900:03:49 --> 00:03:55So now we have here mg--that is gravity acting upon you.

6000:03:54 --> 00:04:00And now you have the forcefrom the bathroom scale.

6100:03:59 --> 00:04:05Clearly, mg must belarger than F of s;

6200:04:02 --> 00:04:08otherwise you couldn't gobeing accelerated downwards.

6300:04:05 --> 00:04:11So if now we write down

Newton's Second Law

6400:04:08 --> 00:04:14then we get mg minus F of smust be m times a.

6500:04:15 --> 00:04:21This holds for acceleration down

6600:04:17 --> 00:04:23and so I get F of sequals m times g minus a.

6700:04:24 --> 00:04:30

6800:04:26 --> 00:04:32This is one way of doing it

6900:04:28 --> 00:04:34and you putin positive values for a.

7000:04:31 --> 00:04:37If a is five metersper second squared

7100:04:33 --> 00:04:39you get ten minus five is five--your weight is half.

7200:04:36 --> 00:04:42You've lost weight.

7300:04:38 --> 00:04:44Being accelerated down,you've lost weight.

7400:04:41 --> 00:04:47You could alsohave used this equation

7500:04:43 --> 00:04:49and not go through this trouble

7600:04:44 --> 00:04:50of setting upNewton's Law again.

7700:04:49 --> 00:04:55You could simply have said

7800:04:50 --> 00:04:56"Okay, this a is minusin this coordinate system"

7900:04:53 --> 00:04:59and so you put ina minus five and a plus ten--

8000:04:55 --> 00:05:01you get the same answer.

8100:04:57 --> 00:05:03So you have lost weightwhen you accelerate downwards.

8200:05:01 --> 00:05:07Suppose now I cut the cable...cut it.

8300:05:08 --> 00:05:14Then this a is ten metersper second squared

8400:05:11 --> 00:05:17if we round it off.

8500:05:13 --> 00:05:19You go down with ten metersper second squared

8600:05:15 --> 00:05:21so g minus a is zero.

8700:05:19 --> 00:05:25You are now weightless,you are free-falling.

8800:05:23 --> 00:05:29You have no longer any weight.

8900:05:25 --> 00:05:31You look at the bathroom scale

9000:05:27 --> 00:05:33and the bathroom scalewill indicate zero.

9100:05:30 --> 00:05:36You're floating, everythingin the elevator is floating.

9200:05:34 --> 00:05:40If you had a glass with water

9300:05:37 --> 00:05:43you could turn it over andthe water would not fall out.

9400:05:42 --> 00:05:48It's like havingthe shuttle in orbit

9500:05:45 --> 00:05:51with the astronautsbeing weightless.

9600:05:50 --> 00:05:56There is a great similarity

9700:05:52 --> 00:05:58between the astronautsin the shuttle

9800:05:55 --> 00:06:01and a free-falling elevator.

9900:05:57 --> 00:06:03The only difference is

10000:05:58 --> 00:06:04that the elevatorwill crash, will kill you.

10100:06:02 --> 00:06:08In the case of the shuttle

10200:06:03 --> 00:06:09it never hits the earthbecause of its high speed.

10300:06:07 --> 00:06:13We'll talk about this much later

10400:06:10 --> 00:06:16when we deal with orbitsand with Kepler's Law.

10500:06:14 --> 00:06:20What exactly is free fall?

10600:06:19 --> 00:06:25Free fall is

10700:06:20 --> 00:06:26when the forces acting upon youare exclusively gravitational.

10800:06:25 --> 00:06:31Nothing is pushing on you;

10900:06:29 --> 00:06:35no seat is pushing on you,no string is pushing on you.

11000:06:31 --> 00:06:37Nothing is pulling on you,only gravity.

11100:06:36 --> 00:06:42I will returnto this weightlessness

11200:06:38 --> 00:06:44very shortly in great detail

11300:06:40 --> 00:06:46but before I do that, I wouldlike to address the issue--

11400:06:44 --> 00:06:50how could I determineyour weight

11500:06:47 --> 00:06:53if I hang you from a string?

116

00:06:52 --> 00:06:58So now, instead of standingon a bathroom scale

11700:06:56 --> 00:07:02you are here.

11800:07:00 --> 00:07:06Here is a string.

11900:07:01 --> 00:07:07You might even havein the string a tension meter

12000:07:04 --> 00:07:10as we have seen earlierin lectures.

12100:07:06 --> 00:07:12And you are holding desperatelyonto that string.

12200:07:09 --> 00:07:15Just like that.

12300:07:12 --> 00:07:18The system is not beingaccelerated, gravity is mg

12400:07:16 --> 00:07:22and so there must be tensionin the string, T

12500:07:20 --> 00:07:26which is pulling you up

12600:07:22 --> 00:07:28which, if there is noacceleration, must be mg.

12700:07:28 --> 00:07:34I read the scaleand I read my weight.

12800:07:32 --> 00:07:38This scale indicates,in my case, 165 pounds.

12900:07:37 --> 00:07:43While I'm hanging,I can see my weight.

13000:07:41 --> 00:07:47So you see,it makes very little difference

13100:07:42 --> 00:07:48whether I am standingon a bathroom scale

13200:07:45 --> 00:07:51and read the force

13300:07:47 --> 00:07:53with which the bathroom scalepushes up on me

13400:07:50 --> 00:07:56or whether I hang from a scale

13500:07:54 --> 00:08:00extend a springand read that value.

13600:07:57 --> 00:08:03It makes no difference.

13700:07:59 --> 00:08:05The tension herewould indicate my weight.

13800:08:02 --> 00:08:08There is a complete similaritywith the bathroom scale

13900:08:05 --> 00:08:11except in one case,something is pulling on me;

14000:08:08 --> 00:08:14in the other case, something ispushing on me from below.

14100:08:13 --> 00:08:19Now let's accelerate this system

upwards with an acceleration a--

14200:08:20 --> 00:08:26and I call this plus.

14300:08:22 --> 00:08:28Then, of course,this T must grow;

14400:08:24 --> 00:08:30otherwise youcannot be accelerated.

14500:08:27 --> 00:08:33Newton's Second Law,T minus mg must be ma.

14600:08:33 --> 00:08:39The tension in the stringequals m times a plus g.

14700:08:38 --> 00:08:44Ah! We've seen that before.

14800:08:40 --> 00:08:46No difference with the elevator.

14900:08:42 --> 00:08:48You accelerate the system,the tension will increase

15000:08:46 --> 00:08:52and you will see that,you will read that on the scale.

15100:08:49 --> 00:08:55Your weight has increased,you weigh more.

15200:08:53 --> 00:08:59Needless to say, of course, ifyou accelerate the system down

15300:08:57 --> 00:09:03that you will weigh less-- wejust went through that argument.

154

00:09:00 --> 00:09:06And if I cutthe cable completely

15500:09:02 --> 00:09:08you go into free fall.

15600:09:04 --> 00:09:10T will go to zero, a becomeminus ten plus ten is zero.

15700:09:10 --> 00:09:16You're in free fall.

15800:09:11 --> 00:09:17The scale reads zero,you are completely weightless.

15900:09:16 --> 00:09:22

16000:09:18 --> 00:09:24If we accept the idea

16100:09:20 --> 00:09:26of weight being indicatedby the tension in a string

16200:09:27 --> 00:09:33then there is a veryinteresting consequence of that.

16300:09:32 --> 00:09:38I have here a pin whichis completely frictionless

16400:09:36 --> 00:09:42and I have on both sidesa string

16500:09:39 --> 00:09:45and this string hasnegligibly small mass.

16600:09:42 --> 00:09:48Now, just assumethat it is massless.

167

00:09:45 --> 00:09:51And there is here an object m1and there is here an object m2

16800:09:52 --> 00:09:58and I am telling youthat m2 is larger than m1.

16900:09:56 --> 00:10:02So we all knowwhat's going to happen.

17000:09:59 --> 00:10:05The system is goingto accelerate in this direction.

17100:10:02 --> 00:10:08M2 will be accelerated downand m1 will be accelerated up.

17200:10:08 --> 00:10:14What comes now is important,that you grasp that.

17300:10:12 --> 00:10:18I claim that the tension onthe left side must be the same

17400:10:17 --> 00:10:23as the tension in this stringon the right side.

17500:10:21 --> 00:10:27T Left must be T Right.

17600:10:23 --> 00:10:29Why is that?

17700:10:25 --> 00:10:31It is because the pinis frictionless

17800:10:28 --> 00:10:34and it is becausethe string is massless.

17900:10:32 --> 00:10:38Take a little section

of the string here

18000:10:36 --> 00:10:42a teeny-weeny little section.

18100:10:38 --> 00:10:44If there is a tension on it--

18200:10:40 --> 00:10:46that is, a forcein this direction

18300:10:42 --> 00:10:48and there is a forcein this direction--

18400:10:44 --> 00:10:50these two couldnever be different

18500:10:46 --> 00:10:52because thenthis massless string

18600:10:48 --> 00:10:54would getan infinite acceleration.

18700:10:50 --> 00:10:56So there can never bea change in tension

18800:10:52 --> 00:10:58from this side of the stringto the other.

18900:10:54 --> 00:11:00If you take a little sectionof the string here--

19000:10:57 --> 00:11:03there it is,teeny-weeny little section

19100:11:00 --> 00:11:06so there is tensionon the string

19200:11:02 --> 00:11:08and there is tensionon the string--

19300:11:04 --> 00:11:10this one couldnever be larger than that

19400:11:07 --> 00:11:13because this little pieceof string

19500:11:09 --> 00:11:15would getan infinite acceleration.

19600:11:10 --> 00:11:16So because there isno friction on the pin

19700:11:14 --> 00:11:20and because the stringsare massless--

19800:11:16 --> 00:11:22only because of that must thetension be everywhere the same.

19900:11:19 --> 00:11:25If there is friction in thepin-- which we will do later--

20000:11:22 --> 00:11:28then that's not the case.

20100:11:24 --> 00:11:30Given the factthat the tension left

20200:11:27 --> 00:11:33and the tension rightare the same

20300:11:30 --> 00:11:36I must now conclude that thesetwo objects have the same weight

204

00:11:35 --> 00:11:41because didn't we agree

20500:11:36 --> 00:11:42that tension is an indicationof weight?

20600:11:40 --> 00:11:46So these objects have nowthe same weight.

20700:11:42 --> 00:11:48And some people may say

20800:11:44 --> 00:11:50"Oh, that's a lot of nonsense,you must be kidding.

20900:11:46 --> 00:11:52"If m2 is larger than m1

21000:11:47 --> 00:11:53this must havea larger weight than that."

21100:11:49 --> 00:11:55Well, they are confusingweight with mass.

21200:11:51 --> 00:11:57It is true that m2 isa larger mass than m1

21300:11:55 --> 00:12:01but it is equally true

21400:11:56 --> 00:12:02that the weight of thesetwo objects is now the same

21500:12:00 --> 00:12:06according tomy definition of weight.

21600:12:04 --> 00:12:10Let us calculatethe acceleration of this system

21700:12:07 --> 00:12:13and let's calculate the tensionand let's see what comes out.

21800:12:12 --> 00:12:18I first isolate hereobject number one.

21900:12:16 --> 00:12:22This is my object number one.

22000:12:18 --> 00:12:24I have gravity, m1 g,and I have a tension T.

22100:12:26 --> 00:12:32Nonnegotiable.

22200:12:27 --> 00:12:33T better be larger than m1 g.

22300:12:29 --> 00:12:35Otherwise it wouldnever be accelerated up

22400:12:31 --> 00:12:37and we knowit will be accelerated up.

22500:12:34 --> 00:12:40So what do we get? We get T--

22600:12:36 --> 00:12:42I will call this plus direction,by the way--

22700:12:39 --> 00:12:45minus m1 g equals m times a.

22800:12:45 --> 00:12:51So the tension equalsm1 times a plus g.

22900:12:52 --> 00:12:58Hey! We've seen that one before.

230

00:12:55 --> 00:13:01This one is beingaccelerated upwards.

23100:12:58 --> 00:13:04Notice it gains weight.

23200:13:00 --> 00:13:06That's the tensionand this is the acceleration.

23300:13:03 --> 00:13:09I have one equationwith two unknowns

23400:13:06 --> 00:13:12so I can't solve it yet.

23500:13:09 --> 00:13:15But there is another one,there is number two here.

23600:13:14 --> 00:13:20For number two,we have a force, m2 g

23700:13:19 --> 00:13:25and we have the tension up.

23800:13:21 --> 00:13:27This one better be largerthan that one;

23900:13:23 --> 00:13:29otherwise itwouldn't be accelerated down.

24000:13:26 --> 00:13:32Let me call this direction plus.

24100:13:29 --> 00:13:35The reason why I now switchdirections and call this plus--

24200:13:33 --> 00:13:39as well as this--is a good reason for it.

24300:13:35 --> 00:13:41It's not so arbitrary anymore.

24400:13:38 --> 00:13:44I know that this acceleration

24500:13:40 --> 00:13:46is going to bea positive number.

24600:13:42 --> 00:13:48Because it's goingin this direction, it's a given.

24700:13:44 --> 00:13:50If I called this negative,

24800:13:46 --> 00:13:52I would get herea negative acceleration

24900:13:49 --> 00:13:55for the same thingfor which I get here a positive.

25000:13:51 --> 00:13:57That's a pain in the neck.

25100:13:52 --> 00:13:58I don't want to have a plusand a minus sign there,

25200:13:54 --> 00:14:00have to think about thatit means the same thing.

25300:13:56 --> 00:14:02So the moment that I decide todefine this the plus direction

25400:14:00 --> 00:14:06I know that this acceleration

25500:14:02 --> 00:14:08will also come out to bethe same sign as this one.

25600:14:06 --> 00:14:12So I flip the signs there.

25700:14:07 --> 00:14:13So now I apply Newton's Law.

25800:14:10 --> 00:14:16I get m2 g minus T equals m2 a.

25900:14:16 --> 00:14:22And so I get T--I'll write it here--

26000:14:20 --> 00:14:26equals m2 times g minus a.

26100:14:29 --> 00:14:35Two equations with two unknowns.

26200:14:35 --> 00:14:41Well, that shouldn't be so hardto solve these two equations.

26300:14:39 --> 00:14:45You can immediately eliminate T,by the way.

26400:14:42 --> 00:14:48If you add this onewith this one, you really--

26500:14:45 --> 00:14:51I call this equation one,you call this equation two--

26600:14:48 --> 00:14:54you immediately lose your T andyou get that the acceleration, a

26700:14:54 --> 00:15:00equals m2 minus m1divided by m1 plus m2 times g.

26800:15:05 --> 00:15:11And you substitute that "a"in that equation and you'll find

26900:15:09 --> 00:15:15that the tension equals 2mgdivided by m1 plus m2.

27000:15:15 --> 00:15:21This is very easy for youto verify.

27100:15:20 --> 00:15:26Let us look.

27200:15:22 --> 00:15:28This is m1, m2...

27300:15:26 --> 00:15:322m1, m2--I lost one m-- 2m1, m2.

27400:15:32 --> 00:15:38Let's look at these equations,let's scrutinize them a little.

27500:15:34 --> 00:15:40Let's get some feeling for it

27600:15:36 --> 00:15:42rather than accepting themas being dumb equations.

27700:15:40 --> 00:15:46Let's first take the case

27800:15:42 --> 00:15:48that m2 equals m1,and I'll call that "m."

27900:15:47 --> 00:15:53Notice that a becomes zero

28000:15:52 --> 00:15:58and notice, if you substitutefor m1 and m2 "m" here

28100:15:56 --> 00:16:02that you get 2m, you get mg.

282

00:15:59 --> 00:16:05So T becomes mg.

28300:16:02 --> 00:16:08That isutterly obvious.

28400:16:04 --> 00:16:10If m1 and m2 are the same,nothing is going to happen.

28500:16:08 --> 00:16:14They're going to sit there,acceleration will be zero

28600:16:11 --> 00:16:17and the tension on both sides--

28700:16:13 --> 00:16:19which is always the same,we argued that--

28800:16:15 --> 00:16:21is going to be mg.

28900:16:16 --> 00:16:22Clear.

29000:16:18 --> 00:16:24Now we're going to makeit more interesting.

29100:16:21 --> 00:16:27Suppose we make m2much, much larger than m1

29200:16:26 --> 00:16:32and in a limiting casewe even go with m1 to zero.

29300:16:30 --> 00:16:36Let's do that.

29400:16:33 --> 00:16:39What you see now,if m1 goes to zero

29500:16:37 --> 00:16:43

this goes away, this goes away,a goes to g and T goes to zero.

29600:16:47 --> 00:16:53If m1 is zero, T goes to zero.

29700:16:50 --> 00:16:56That is obvious!

29800:16:54 --> 00:17:00Because if I make m1 zero,m2 goes into free fall.

29900:17:00 --> 00:17:06And if m2 goes into free fall

30000:17:02 --> 00:17:08its weight is zeroand so the tension is zero--

30100:17:05 --> 00:17:11that's exactly what you see--

30200:17:07 --> 00:17:13and you see thatthe acceleration of that object

30300:17:09 --> 00:17:15is g, which it better be,because it's in free fall.

30400:17:12 --> 00:17:18So you see, this makes sense.

30500:17:15 --> 00:17:21This is exactly consistentwith your intuition.

30600:17:18 --> 00:17:24And if you wanted to make m1much, much larger than m2

30700:17:22 --> 00:17:28and you take the limiting casefor m2 goes to zero

30800:17:26 --> 00:17:32

you'll find again that a goesto g and that T goes to zero

30900:17:31 --> 00:17:37except that now the accelerationis not this way...

31000:17:35 --> 00:17:41(makes whooshing sound )

31100:17:37 --> 00:17:43but now the accelerationis this way

31200:17:39 --> 00:17:45and now this object will gointo free fall.

31300:17:43 --> 00:17:49And therefore there is notension in the string anymore.

31400:17:48 --> 00:17:54

31500:17:51 --> 00:17:57M1, if I return to the casewhich we have there--

31600:17:55 --> 00:18:01that m2 is larger than m1--

31700:17:58 --> 00:18:04m1 is beingaccelerated upwards.

31800:18:00 --> 00:18:06That's nonnegotiable,so it must have gained weight.

31900:18:03 --> 00:18:09M2 is being accelerated down,so it must have lost weight.

32000:18:08 --> 00:18:14Just like being in an elevator,there's no difference.

321

00:18:12 --> 00:18:18They each weigh the same--

32200:18:14 --> 00:18:20one loses weight,the other gains weight.

32300:18:17 --> 00:18:23They each weigh the same,and so I can make the prediction

32400:18:21 --> 00:18:27that if this is m2 g,which was its original weight

32500:18:27 --> 00:18:33and this nowis the new weight, T

32600:18:29 --> 00:18:35that m2 g must be larger than T.

32700:18:32 --> 00:18:38M1 gains weight,so T must be larger than m1 g.

32800:18:35 --> 00:18:41M2 loses weight,so T must be smaller than m2 g.

32900:18:40 --> 00:18:46That's my prediction--it has to be.

33000:18:43 --> 00:18:49And we can... I can show youthat with some easy numbers.

33100:18:46 --> 00:18:52Let m1 be 1.1 kilogramsand let m2 be 1.25 kilograms.

33200:18:56 --> 00:19:02Frictionless system, and thestring has a negligible mass.

33300:19:02 --> 00:19:08What is the acceleration "a"

of the system?

33400:19:05 --> 00:19:11I get m2 minus m1--

33500:19:07 --> 00:19:13that is 0.15 dividedby the sum, which is 2.35

33600:19:14 --> 00:19:20and that is approximately0.064 g, approximately 0.064 g.

33700:19:22 --> 00:19:28It's about 1/16th ofthe gravitational acceleration.

33800:19:25 --> 00:19:31It's a very modest acceleration.

33900:19:29 --> 00:19:35What is the tension?

34000:19:31 --> 00:19:37Well, I substitute my numbersfor m1 and m2 in there.

34100:19:35 --> 00:19:41You can take, for g,10, if you like that

34200:19:37 --> 00:19:43and you will findthat the tension equals 1.17 g.

34300:19:44 --> 00:19:50And now lookat what I predicted.

34400:19:48 --> 00:19:54They both weigh 1.17 g,that's nonnegotiable.

34500:19:53 --> 00:19:59That is my definitionof weight--

346

00:19:54 --> 00:20:00the tension in both sidesis the same.

34700:19:56 --> 00:20:02That's my definition of weight.

34800:19:58 --> 00:20:04This is their weight.

34900:20:00 --> 00:20:06This one had a weight 1.25 gwithout being accelerated.

35000:20:08 --> 00:20:14You see, it has lost weight,because it accelerated down.

35100:20:12 --> 00:20:18This one had a weight of 1.1 g.

35200:20:16 --> 00:20:22You see, it has gained weight,because it has accelerated up.

35300:20:20 --> 00:20:26So you see, the whole pictureties together very neatly

35400:20:23 --> 00:20:29and it's importantthat you look at it that way.

35500:20:27 --> 00:20:33I now want to return to the ideaof complete weightlessness

35600:20:34 --> 00:20:40and I want to remind you,a few lectures ago

35700:20:37 --> 00:20:43how I was swinging you at theend of a string in the vertical.

35800:20:41 --> 00:20:47I was swinging you like this.

35900:20:43 --> 00:20:49And I was swinginga bucket of water like this.

36000:20:47 --> 00:20:53And I want to return to that.

36100:20:50 --> 00:20:56I want to look at you when youare at the bottom of your circle

36200:20:57 --> 00:21:03and when you areat the very top of that circle.

36300:21:01 --> 00:21:07

36400:21:04 --> 00:21:10You go around a circlewhich has radius R.

36500:21:09 --> 00:21:15Here is that circle.

36600:21:10 --> 00:21:16

36700:21:15 --> 00:21:21There's a string here,you're here.

36800:21:18 --> 00:21:24And there's a string here

36900:21:20 --> 00:21:26and at some point in time,you're there.

37000:21:22 --> 00:21:28And you're going around...let's assume

37100:21:24 --> 00:21:30that you're going aroundwith an angular velocity omega

37200:21:28 --> 00:21:34

and for simplicity,we keep omega constant.

37300:21:30 --> 00:21:36But that's reallynot that important.

37400:21:34 --> 00:21:40Okay, this is point Pand this is point S.

37500:21:39 --> 00:21:45Let's first lookat the situation at point P.

37600:21:43 --> 00:21:49You have a mass and sogravity acts upon you, mg.

37700:21:49 --> 00:21:55There is tensionin the string, T.

37800:21:53 --> 00:21:59There must be--this is nonnegotiable--

37900:21:55 --> 00:22:01a centripetal accelerationupwards.

38000:21:58 --> 00:22:04Otherwise,you could never do this.

38100:22:01 --> 00:22:07Remember, from the uniformcircular motion.

38200:22:03 --> 00:22:09So there must be herecentripetal acceleration

38300:22:08 --> 00:22:14which is omega squared R

38400:22:10 --> 00:22:16or, if you prefer,

v squared divided by R

38500:22:14 --> 00:22:20if v is the speed,tangential speed at that point.

38600:22:18 --> 00:22:24It must be there.

38700:22:22 --> 00:22:28Let's look here.

38800:22:24 --> 00:22:30Right there,gravity is acting upon you, mg.

38900:22:31 --> 00:22:37Let's assume this stringis pulling on you.

39000:22:33 --> 00:22:39Let's assume that for now,so there is a tension.

39100:22:38 --> 00:22:44The string is pulling on you.

39200:22:41 --> 00:22:47Therefore, nonnegotiable, whenyou make this curvature here

39300:22:46 --> 00:22:52there must bea centripetal acceleration

39400:22:49 --> 00:22:55and that centripetalacceleration

39500:22:51 --> 00:22:57must be omega squared R.

39600:22:53 --> 00:22:59That is nonnegotiable,it has to be there.

39700:22:57 --> 00:23:03

Let's now evaluatefirst the situation at P

39800:23:01 --> 00:23:07and I will call this plus

39900:23:04 --> 00:23:10and I will call this minus.

40000:23:07 --> 00:23:13So what I get now is

40100:23:09 --> 00:23:15that T minus mg

40200:23:13 --> 00:23:19must be m timesthe centripetal acceleration

40300:23:18 --> 00:23:24so T must be m times thecentripetal acceleration plus g.

40400:23:24 --> 00:23:30Hey! That looks very familiar.

40500:23:27 --> 00:23:33It looks like someone is beingaccelerated in an elevator--

40600:23:31 --> 00:23:37almost the same equation.

40700:23:35 --> 00:23:41If the centripetal accelerationat this point

40800:23:40 --> 00:23:46for instance, were 10 metersper second squared

40900:23:44 --> 00:23:50then you would weigh twiceyour normal weight.

41000:23:47 --> 00:23:53The tension here

would be twice mg.

41100:23:53 --> 00:23:59If this were five metersper second squared

41200:23:56 --> 00:24:02then you would be1½ times your weight.

41300:24:01 --> 00:24:07Let's now lookat the situation at S.

41400:24:05 --> 00:24:11

41500:24:07 --> 00:24:13At point S, I'm going to callthis plus and that minus.

41600:24:16 --> 00:24:22I'm going to find that T plus mg

41700:24:22 --> 00:24:28must be m timesthe centripetal acceleration--

41800:24:25 --> 00:24:31Newton's Second Law.

41900:24:27 --> 00:24:33So I find that the tension thereequals m times a of c minus g.

42000:24:35 --> 00:24:41Hey! Very similarto what I've seen before.

42100:24:39 --> 00:24:45This object is losing weight.

42200:24:44 --> 00:24:50Let us take the situation

42300:24:47 --> 00:24:53that a of c is exactly10 meters per second squared

42400:24:50 --> 00:24:56and we discussed that last time

42500:24:52 --> 00:24:58when we had the bucket of waterin our hands.

42600:24:54 --> 00:25:00If a of c...

42700:24:56 --> 00:25:02if the centripetal accelerationwhen it goes through the top

42800:24:59 --> 00:25:05is 10, then this is zero.

42900:25:02 --> 00:25:08So the string has no tension,the string goes limp

43000:25:06 --> 00:25:12and the bucket of waterand you are weightless.

43100:25:11 --> 00:25:17If the centripetal accelerationis larger than 10

43200:25:16 --> 00:25:22then, of course,the string will be tight.

43300:25:19 --> 00:25:25There will be a force on you

43400:25:21 --> 00:25:27and whatever comes out of herewill indicate your weight.

43500:25:26 --> 00:25:32If a of c is smaller than 10,that's meaningless.

43600:25:33 --> 00:25:39

The tension cannever be negative.

43700:25:36 --> 00:25:42A string with negative tensionhas no physical meaning.

43800:25:39 --> 00:25:45What it means isthat the bucket of water

43900:25:41 --> 00:25:47would never have made itto this point.

44000:25:43 --> 00:25:49If you try to swing it up--

44100:25:45 --> 00:25:51as someone triedin the second lecture--

44200:25:47 --> 00:25:53but didn't make it to that point

44300:25:48 --> 00:25:54the bucket of waterwill just fall.

44400:25:51 --> 00:25:57You end up with a mess,but that's a detail.

44500:25:55 --> 00:26:01So the bucket of water,when it is here...

44600:26:00 --> 00:26:06If the acceleration there,the centripetal acceleration

44700:26:03 --> 00:26:09were exactly 10 metersper second squared

44800:26:05 --> 00:26:11then that bucket of waterwould be weightless.

44900:26:11 --> 00:26:17So I said earlierthat when you're in free fall

45000:26:14 --> 00:26:20all objects in free fallare weightless.

45100:26:17 --> 00:26:23It's like a spacecraft in orbitor an elevator with a cut cable.

45200:26:23 --> 00:26:29It also meansthat if I jump off the table

45300:26:28 --> 00:26:34that I'm weightless whileI am in mid-air, so to speak.

45400:26:33 --> 00:26:39It means this tennis ball...

45500:26:35 --> 00:26:41while it is in free fall,it has no weight.

45600:26:38 --> 00:26:44Now it has weight.

45700:26:41 --> 00:26:47Now the weight is even higherbecause I am accelerating it

45800:26:44 --> 00:26:50and now it has no weight.

45900:26:46 --> 00:26:52The tennis ball is weightless

46000:26:48 --> 00:26:54and I assume, for now,that the air drag plays no role.

46100:26:55 --> 00:27:01If I jump off the table

46200:26:58 --> 00:27:04I will be weightlessfor about half a second.

46300:27:01 --> 00:27:07This is about one meter.

46400:27:03 --> 00:27:09If I jump from a towerwhich is 100 meters high

46500:27:06 --> 00:27:12I will be weightlessfor 4½ seconds

46600:27:09 --> 00:27:15ignoring air drag.

46700:27:11 --> 00:27:17I prefer todaythe half a second.

46800:27:17 --> 00:27:23I am going to jumpoff this table

46900:27:20 --> 00:27:26with this water in my hand.

47000:27:25 --> 00:27:31And I'm going to tell youhow I can convince you

47100:27:28 --> 00:27:34that as I jump, that I will,indeed, be weightless.

47200:27:33 --> 00:27:39Here is the bottle.

47300:27:35 --> 00:27:41There is a gravitational forceon the bottle.

47400:27:39 --> 00:27:45My hands are pushing up

on this bottle.

47500:27:43 --> 00:27:49My hands are beinga bathroom scale.

47600:27:46 --> 00:27:52I feel, in my muscles,the need to push up.

47700:27:50 --> 00:27:56In fact, I might even be ableto estimate the weight

47800:27:53 --> 00:27:59playing the roleof a bathroom scale.

47900:27:56 --> 00:28:02It's a gallon of water,it's about nine pounds.

48000:28:00 --> 00:28:06

48100:28:04 --> 00:28:10Now my own body...gravity is acting upon me

48200:28:07 --> 00:28:13but I am being pushed up,right there.

48300:28:13 --> 00:28:19Suppose we jumped.

48400:28:17 --> 00:28:23There would be no pushingfrom me on the bottle anymore

48500:28:21 --> 00:28:27no pushing there on me,the table.

48600:28:25 --> 00:28:31Only gravitation would act uponus and we would be weightless.

487

00:28:30 --> 00:28:36How can I show youthat we are weightless?

48800:28:32 --> 00:28:38Well, if I don't have to use

48900:28:34 --> 00:28:40my muscles to pushon this bottle upwards

49000:28:37 --> 00:28:43I might as welllower my hands a little bit

49100:28:39 --> 00:28:45during this free fall.

49200:28:41 --> 00:28:47And you will see that the bottlewill just stay above my hands

49300:28:45 --> 00:28:51without my having to push up.

49400:28:47 --> 00:28:53Therefore,being the bathroom scale

49500:28:50 --> 00:28:56I no longer have to push on it.

49600:28:52 --> 00:28:58I no longer... my musclesdon't feel anything

49700:28:55 --> 00:29:01and the bottle istherefore weightless.

49800:28:58 --> 00:29:04The bottle is weightlesswhen we jump;

49900:29:00 --> 00:29:06I am weightless and eventhis bagel is weightless.

50000:29:03 --> 00:29:09We're all weightlessduring half a second.

50100:29:07 --> 00:29:13There is no such thingin physics as a free lunch.

50200:29:12 --> 00:29:18You have to pay a price for thishalf a second of weightlessness.

50300:29:17 --> 00:29:23What happenswhen I hit the floor?

50400:29:19 --> 00:29:25I hit the floor with a velocityin this direction

50500:29:22 --> 00:29:28which is aboutfive meters per second.

50600:29:24 --> 00:29:30You can calculate that.

50700:29:26 --> 00:29:32But a little later,I've come to a stop.

50800:29:29 --> 00:29:35That means during the impact

50900:29:30 --> 00:29:36there must bean acceleration upwards.

51000:29:33 --> 00:29:39Otherwise my velocityin this direction

51100:29:35 --> 00:29:41could never become zero.

51200:29:38 --> 00:29:44Therefore, I will weighmore

during this impact--

51300:29:42 --> 00:29:48there is an accelerationin this direction.

51400:29:44 --> 00:29:50The five metersper second goes to zero.

51500:29:49 --> 00:29:55If I make the assumption

51600:29:50 --> 00:29:56that it takestwo-tenths of a second--

51700:29:52 --> 00:29:58that's a very rough guess,this impact time--

51800:29:53 --> 00:29:59then the average acceleration

51900:29:55 --> 00:30:01will be five meters per seconddivided by 0.2;

52000:29:58 --> 00:30:04that is 25 metersper second squared.

52100:30:01 --> 00:30:07That means the accelerationupwards is 2½ g.

52200:30:06 --> 00:30:12That means I will weigh3½ times more.

52300:30:09 --> 00:30:15Remember it is a plus g,

52400:30:11 --> 00:30:17so a is 2½ g upplus the g that we already have;

525

00:30:14 --> 00:30:20that makes it 3½ g.

52600:30:17 --> 00:30:23So insteadof weighing 165 pounds

52700:30:19 --> 00:30:25I weigh close to 600 poundsfor two-tenths of a second.

52800:30:23 --> 00:30:29So we get four phases.

52900:30:25 --> 00:30:31Right now, I'm my normal weight

53000:30:27 --> 00:30:33if I standon a bathroom scale.

53100:30:29 --> 00:30:35I jump for half a second,weightless

53200:30:31 --> 00:30:37hit the floor for abouttwo-tenths of a second

53300:30:34 --> 00:30:40maybe close to 600 pounds.

53400:30:37 --> 00:30:43And then after that I will havemy normal weight again.

53500:30:40 --> 00:30:46Now, you're going to haveonly half a second to see

53600:30:44 --> 00:30:50that this bottle, as I jump,is floating above my hands.

53700:30:48 --> 00:30:54I will pull my hands off

538

00:30:50 --> 00:30:56so you will see thatI no longer have to push it.

53900:30:54 --> 00:31:00That means it's weightless.

54000:30:57 --> 00:31:03Are you ready? I'm ready.

54100:31:01 --> 00:31:07Three, two, one, zero.

54200:31:03 --> 00:31:09Did you see it floatingabove my hands?

54300:31:07 --> 00:31:13We were both weightless.

54400:31:09 --> 00:31:15Now, I have been thinkingabout this

54500:31:14 --> 00:31:20for a long, long time.

54600:31:16 --> 00:31:22I have been thinking whether

54700:31:18 --> 00:31:24perhaps this could not be shownin a more dramatic way

54800:31:23 --> 00:31:29perhaps evena more convincing way.

54900:31:27 --> 00:31:33And so I thought of the idea

55000:31:28 --> 00:31:34of putting a bathroom scaleunder my feet

55100:31:31 --> 00:31:37tying it very loosely so that it

wouldn't fall off when I jump

55200:31:35 --> 00:31:41and then show you that while Iam half a second in free fall

55300:31:39 --> 00:31:45that the bathroom scaleindeed indicates zero.

55400:31:43 --> 00:31:49And don't thinkthat I haven't tried it.

55500:31:45 --> 00:31:51I've tried it many timeswith many bathroom scales.

55600:31:47 --> 00:31:53I made many jumps.

55700:31:49 --> 00:31:55There is a problem,and the problem is

55800:31:51 --> 00:31:57the bathroom scalesthat you buy--

55900:31:54 --> 00:32:00that you normallyget commercially--

56000:31:56 --> 00:32:02they indeed want to go to zero.

56100:31:58 --> 00:32:04It takes them a long time.

56200:32:00 --> 00:32:06They have a lot of inertia,their response time is slow.

56300:32:04 --> 00:32:10But even if they make it to zeroby the time you hit the floor

564

00:32:08 --> 00:32:14then immediatelythe weight increases

56500:32:12 --> 00:32:18because you hit the floor

56600:32:13 --> 00:32:19and your weight comes upby 3½ times.

56700:32:14 --> 00:32:20So it begins to swingback and forth

56800:32:17 --> 00:32:23and it becomescompletely chaotic

56900:32:18 --> 00:32:24and you can no longer seewhat's happening.

57000:32:21 --> 00:32:27And it just so happened thatabout six months ago, Dave...

57100:32:24 --> 00:32:30I had dinnerwith Professor Dave Trumper

57200:32:27 --> 00:32:33and I explained it to himthat it is just unfortunate

57300:32:30 --> 00:32:36that you cannever really show it

57400:32:32 --> 00:32:38that you jump off the table,have a bathroom scale under you

57500:32:35 --> 00:32:41and see that weight go down tozero when you are in free fall.

57600:32:38 --> 00:32:44

And he said, "Duck soup--I can do that."

57700:32:41 --> 00:32:47He says, "I can make you a scale

57800:32:44 --> 00:32:50"which has a response timeof maybe 10 milliseconds

57900:32:48 --> 00:32:54"so when you jump off the table

58000:32:50 --> 00:32:56in 10 milliseconds you will seethat thing go down to zero."

58100:32:54 --> 00:33:00And he delivered,he came through.

58200:32:59 --> 00:33:05He built this wonderful device

58300:33:01 --> 00:33:07which he and I are goingto demonstrate to you.

58400:33:05 --> 00:33:11Let me first give yousome reasonable light for this.

58500:33:13 --> 00:33:19And I would like to show youon the scale there

58600:33:18 --> 00:33:24what this scale that he builtis indicating.

58700:33:21 --> 00:33:27Here is the scale,I have it in my hands.

58800:33:26 --> 00:33:32And on top of this scaleis a little platform

58900:33:28 --> 00:33:34just like on your scale.

59000:33:30 --> 00:33:36This platform weighs4½ pounds.

59100:33:33 --> 00:33:39And you can see that,it says about 4½.

59200:33:38 --> 00:33:44Now, you will say

59300:33:39 --> 00:33:45"Hmm! I wouldn't wantthat kind of a bathroom scale.

59400:33:42 --> 00:33:48"I mean, if I want to seemy bathroom scale

59500:33:44 --> 00:33:50"I want to see a zerobefore I want to go up.

59600:33:46 --> 00:33:52"I'm heavy enough all by myself.

59700:33:48 --> 00:33:54I don't want to getanother 4½ pounds."

59800:33:50 --> 00:33:56The manufacturer has simplyzeroed that scale for you

59900:33:54 --> 00:34:00but obviously also your bathroomscale has a cover on it.

60000:33:58 --> 00:34:04Once you have seenthese demonstrations

60100:34:01 --> 00:34:07you will be able to answer for

yourself why we don't zero this

60200:34:05 --> 00:34:11why we really leave thisto be 4½.

60300:34:08 --> 00:34:14That's the actual mass which ison top of the spring.

60400:34:12 --> 00:34:18But it's not really a spring--

60500:34:14 --> 00:34:20it is a pressure gauge,but think of it as a spring.

60600:34:17 --> 00:34:234½ pounds.

60700:34:19 --> 00:34:25Here we have a weight

60800:34:23 --> 00:34:29which is a barbell weight,which is 10 pounds.

60900:34:29 --> 00:34:35Is this from oneof your children, Dave

61000:34:33 --> 00:34:39or were you doing it yourself?

61100:34:35 --> 00:34:4110 pounds...we put it on top here.

61200:34:40 --> 00:34:46What do you see?Roughly 14½ pounds.

61300:34:44 --> 00:34:50All right, we are goingto tape it down.

61400:34:47 --> 00:34:53

61500:34:52 --> 00:34:58There we go.

61600:34:53 --> 00:34:59And we're going to drop it

61700:34:56 --> 00:35:02from about 1½, two meters

61800:34:59 --> 00:35:05and we drop it in here,well-cushioned

61900:35:02 --> 00:35:08because we don't want to breakthis beautiful device.

62000:35:04 --> 00:35:10

62100:35:07 --> 00:35:13When we drop it,the response is so fast

62200:35:11 --> 00:35:17that you will see, indeed,that pointer go to zero.

62300:35:14 --> 00:35:20Now, keep in mind,when it hits the cushion

62400:35:18 --> 00:35:24that the weight will go up.

62500:35:20 --> 00:35:26For now, I want youto concentrate

62600:35:22 --> 00:35:28only on the thing going to zeroand not what comes later.

62700:35:26 --> 00:35:32We will deal with thatwithin a minute.

62800:35:28 --> 00:35:34

62900:35:32 --> 00:35:38Okay... 14½ pounds.

63000:35:39 --> 00:35:45You know why the thingis actually jiggling

63100:35:41 --> 00:35:47back and forth?

63200:35:43 --> 00:35:49I can't hold it exactly still

63300:35:45 --> 00:35:51and so I slightly accelerate itupwards and downwards

63400:35:48 --> 00:35:54and when I accelerate itslightly upwards

63500:35:50 --> 00:35:56it weighs a little more

63600:35:51 --> 00:35:57and when I accelerate itdownwards, it weighs less.

63700:35:54 --> 00:36:00It's interesting.

63800:35:55 --> 00:36:01You can see I'm nervous.

63900:35:56 --> 00:36:02That's my nervoustension meter there.

64000:36:00 --> 00:36:06Okay, we're ready?

64100:36:02 --> 00:36:08Look and... don't look at me,now, look at that pointer.

64200:36:06 --> 00:36:12Three, two, one, zero.

64300:36:09 --> 00:36:15Did you see it go to zero?All the way to zero.

64400:36:14 --> 00:36:20Now comes somethingeven more remarkable.

64500:36:18 --> 00:36:24He said to me, "I can also makethe students see the response

64600:36:26 --> 00:36:32on a time scale of abouta fraction of a second."

64700:36:30 --> 00:36:36By the way, this is the herowho made all this stuff.

64800:36:33 --> 00:36:39He's fantastic.

64900:36:34 --> 00:36:40(class applauds )

65000:36:41 --> 00:36:47LEWIN:He can show you the weighton an electronic scale

65100:36:48 --> 00:36:54and this weight you will seeas a function of time.

65200:36:54 --> 00:37:00I will put the ten poundsback on again...

65300:36:58 --> 00:37:04tape it a little tighter

654

00:37:04 --> 00:37:10and so the level that you seenow is 14½ pounds.

65500:37:10 --> 00:37:16This is 14½ pounds and this iszero, this mark is zero.

65600:37:15 --> 00:37:21I'm going to hold it in my hand.

65700:37:24 --> 00:37:30And notice,if I can hold it still

65800:37:25 --> 00:37:31you're backto your 14½ pounds.

65900:37:27 --> 00:37:33

66000:37:28 --> 00:37:34Now I'm going to drop it.

66100:37:31 --> 00:37:37You will see it go down to zero.

66200:37:34 --> 00:37:40It will hit the floor,the cushion.

66300:37:37 --> 00:37:43It will getan acceleration upwards.

66400:37:39 --> 00:37:45It will become way heavierthan it was before

66500:37:41 --> 00:37:47and then it will even bebounced back up in the air

66600:37:45 --> 00:37:51and it goes againinto free fall.

667

00:37:47 --> 00:37:53We will freeze that for you,and you will be able...

66800:37:50 --> 00:37:56we will be able to analyze it,then, after it all happens.

66900:37:56 --> 00:38:02So, 14½ pounds...three, two, one, zero.

67000:38:02 --> 00:38:08

67100:38:05 --> 00:38:11And now Professor Trumperis freezing it for you.

67200:38:07 --> 00:38:13Now look at this, lookat this incredible picture.

67300:38:11 --> 00:38:17This is truly an eye-openerfor me, when I saw it.

67400:38:14 --> 00:38:20The physics in hereis unbelievable.

67500:38:17 --> 00:38:23Here is your 14½ pounds.

67600:38:20 --> 00:38:26Tick marks from here to hereare half a second.

67700:38:23 --> 00:38:29It was half a secondin free fall

67800:38:25 --> 00:38:31and it goes to zero,that's no weight.

67900:38:28 --> 00:38:34Now it hits the floor,the cushion

68000:38:30 --> 00:38:36and its weight goes up

68100:38:32 --> 00:38:38in somethinglike a tenth of a second.

68200:38:34 --> 00:38:40Look, this isabout one, two, three...

68300:38:36 --> 00:38:42It's about 3½ timesits weight now.

68400:38:39 --> 00:38:45So the 14½has to be multiplied

68500:38:42 --> 00:38:48by 3½ or four

68600:38:43 --> 00:38:49which is exactlywhat we predicted--

68700:38:45 --> 00:38:51that it would be much higher.

68800:38:46 --> 00:38:52But now it's being...

68900:38:48 --> 00:38:54it bounces off, becauseit's a very nice cushion.

69000:38:50 --> 00:38:56It throws it back up.

69100:38:51 --> 00:38:57So it goes back into the air

69200:38:53 --> 00:38:59so it goes immediatelyto weightlessness again

69300:38:55 --> 00:39:01and then it oscillatesback and forth.

69400:38:57 --> 00:39:03And then here you would expect

69500:38:59 --> 00:39:05that this level, 14½ pounds,would be the same as this.

69600:39:03 --> 00:39:09And the only reasonwhy that's not the case is

69700:39:05 --> 00:39:11there's a little cablethat fell with it

69800:39:07 --> 00:39:13which is pushing a little bit up

69900:39:09 --> 00:39:15on the upper... on the upperdisc that is there

70000:39:13 --> 00:39:19so it's making ita little lighter.

70100:39:14 --> 00:39:20Isn't it incredible?

70200:39:16 --> 00:39:22You see here in front of youthe weightlessness

70300:39:19 --> 00:39:25and you see the extra weightwhen it hits

70400:39:21 --> 00:39:27and again followedby weightlessness.

70500:39:25 --> 00:39:31Dave, A-plus,

you passed the course.

70600:39:27 --> 00:39:33

70700:39:31 --> 00:39:37There is a great interest

70800:39:33 --> 00:39:39in doing experimentsunder weightless conditions.

70900:39:37 --> 00:39:43NASA was very interested in it.

71000:39:41 --> 00:39:47And if you would jump100 meters up in the sky

71100:39:46 --> 00:39:52you would only benine seconds up.

71200:39:48 --> 00:39:54You wouldn't even be weightlessbecause of air drag.

71300:39:51 --> 00:39:57However, if you could jump up

71400:39:53 --> 00:39:59way near the topof the atmosphere--

71500:39:55 --> 00:40:01where the air dragis negligible--

71600:39:58 --> 00:40:04then you would be weightlessfor quite some time.

71700:40:01 --> 00:40:07And that iswhat people have been doing

71800:40:04 --> 00:40:10for the past few decades.

71900:40:06 --> 00:40:12Professor Youngand Professor Oman here

72000:40:08 --> 00:40:14at the Aeronautics Department

72100:40:10 --> 00:40:16have done what they call"zero gravity experiments"

72200:40:14 --> 00:40:20from airplanes-- and I willexplain that in detail--

72300:40:17 --> 00:40:23but first I want youto appreciate

72400:40:19 --> 00:40:25that "zero gravity"is a complete misnomer.

72500:40:23 --> 00:40:29"Zero weight," yes--"zero gravity," no.

72600:40:28 --> 00:40:34If you have an airplaneanywhere near Earth, flying

72700:40:30 --> 00:40:36whether the engines are onor whether the engines are off

72800:40:33 --> 00:40:39or whether it is free-fallingdoesn't matter.

72900:40:35 --> 00:40:41There is never zero gravity.

73000:40:36 --> 00:40:42There is always gravity--thank goodness.

731

00:40:39 --> 00:40:45But if you are in free fall,indeed, there is no weight.

73200:40:44 --> 00:40:50Apart from that, they call them"zero gravity experiments"

73300:40:48 --> 00:40:54and why not?

73400:40:49 --> 00:40:55Maybe it sells better.

73500:40:51 --> 00:40:57

73600:40:53 --> 00:40:59They fly an airplane,which is the KC-135

73700:40:59 --> 00:41:05and they do these experiments

73800:41:01 --> 00:41:07at an altitudeof about 30,000 feet.

73900:41:07 --> 00:41:13If I could clean thisas best as I can...

74000:41:10 --> 00:41:16

74100:41:12 --> 00:41:18The plane comes inat one point in time

74200:41:19 --> 00:41:25at an angle of about 45 degrees.

74300:41:21 --> 00:41:27There's nothing specialabout that 45 degrees.

74400:41:24 --> 00:41:30It's just...that's the way it's done.

74500:41:26 --> 00:41:32You have to also thinkof the convenience--

74600:41:29 --> 00:41:35convenience for the passengers.

74700:41:31 --> 00:41:37The speed is thenabout 425 miles per hour

74800:41:40 --> 00:41:46so the horizontal componentis about 300 miles per hour

74900:41:43 --> 00:41:49and the vertical component isalso 300.

75000:41:48 --> 00:41:54The air drag is very little.

75100:41:50 --> 00:41:56Let's assume, for the sakeof the argument

75200:41:52 --> 00:41:58that the engines are cut

75300:41:55 --> 00:42:01and the plane goesinto free fall.

75400:41:57 --> 00:42:03It's no differentfrom this tennis ball--

75500:41:59 --> 00:42:05(makes whooshing sound )

75600:42:01 --> 00:42:07the same thing.

75700:42:02 --> 00:42:08You're going to see a parabola.

75800:42:04 --> 00:42:10And so this planeis going to free-fall

75900:42:07 --> 00:42:13and comes back to this level.

76000:42:12 --> 00:42:18And let's analyze this arc,this parabola.

76100:42:15 --> 00:42:21Right here at the top, clearly

76200:42:18 --> 00:42:24there will still be300 meters per second

76300:42:21 --> 00:42:27in the absence of any air drag.

76400:42:23 --> 00:42:29You should be able to calculate

76500:42:24 --> 00:42:30with all the toolsthat you have available

76600:42:26 --> 00:42:32how high this goesfrom this level.

76700:42:30 --> 00:42:36In other words, what is the time

76800:42:32 --> 00:42:38that the velocity in the ydirection comes to zero?

76900:42:36 --> 00:42:42You can calculate that

77000:42:37 --> 00:42:43and then you knowhow much it has traveled.

771

00:42:39 --> 00:42:45Very crude number,this is about 900 meters.

77200:42:43 --> 00:42:49And it will take about 15seconds to reach this point

77300:42:47 --> 00:42:53so it will take about 30 secondsto go from here to here

77400:42:50 --> 00:42:56and in those 30 seconds

77500:42:54 --> 00:43:00the horizontal displacementis about 3½ kilometers.

77600:42:58 --> 00:43:04And all these numbersyou should be able to confirm.

77700:43:03 --> 00:43:09Right here,the engines are restarted.

77800:43:09 --> 00:43:15During this free fall, everyonein the airplane is weightless

77900:43:13 --> 00:43:19including the airplane itself.

78000:43:15 --> 00:43:21Now the engines start,and the engine is sort of...

78100:43:17 --> 00:43:23The plane is going to pull up,it goes into this phase

78200:43:21 --> 00:43:27and then the plane flieshorizontally for a while.

78300:43:24 --> 00:43:30During this phase,

as we just discussed

78400:43:26 --> 00:43:32it's like hitting the floor.

78500:43:28 --> 00:43:34You need an accelerationin this direction.

78600:43:31 --> 00:43:37There will be weight increase

78700:43:34 --> 00:43:40so there is herean acceleration upwards.

78800:43:37 --> 00:43:43And during this time,very roughly

78900:43:40 --> 00:43:46people haveabout twice their weight.

79000:43:43 --> 00:43:49And then here,they have again normal weight.

79100:43:46 --> 00:43:52And then the planepulls up again

79200:43:49 --> 00:43:55and here it goesand repeats the whole thing

79300:43:52 --> 00:43:58again going into free fall.

79400:43:56 --> 00:44:02So again here, people havemore than their normal weight.

79500:44:02 --> 00:44:08Zero weight,more than normal weight

796

00:44:05 --> 00:44:11normal weight, morethan normal weight, free fall.

79700:44:08 --> 00:44:14And the whole cycle takesabout 90 seconds.

79800:44:14 --> 00:44:20You can imaginethat it is very important

79900:44:16 --> 00:44:22when you are here in free fall,when you have no weight

80000:44:19 --> 00:44:25that when your weight comes backand your weight doubles--

80100:44:23 --> 00:44:29and Professor Oman told methat this change from zero

80200:44:26 --> 00:44:32to twice your weight takesless than a second--

80300:44:28 --> 00:44:34that you better know where yourfeet are and where your head is

80400:44:32 --> 00:44:38because if your head is down

80500:44:34 --> 00:44:40and you all of a suddendouble your weight

80600:44:36 --> 00:44:42you crush your skull,so you have to be sure

80700:44:39 --> 00:44:45that you are standingstraight up in the plane

80800:44:42 --> 00:44:48

when your weight beginsto double

80900:44:44 --> 00:44:50and we will see thatvery shortly, how that works.

81000:44:48 --> 00:44:54I want to show you first someslides from these experiments.

81100:44:53 --> 00:44:59So here you see the situationthat we just described.

81200:44:59 --> 00:45:05Let us start here, that iswhere I started with you.

81300:45:04 --> 00:45:10The plane turns the engines off.

81400:45:06 --> 00:45:12This is the parabola.

81500:45:07 --> 00:45:13Here the engines are restarted.

81600:45:10 --> 00:45:16This is the free-fall period.

81700:45:12 --> 00:45:18This is about 30 seconds.

81800:45:15 --> 00:45:21The engine is restarted,and during this time

81900:45:18 --> 00:45:24there is an acceleration upwardsand they call it "2g peak."

82000:45:22 --> 00:45:28Well, they really mean 1g.

82100:45:24 --> 00:45:30What they really mean,

that my weight doubles.

82200:45:27 --> 00:45:33They call that "2g"

82300:45:28 --> 00:45:34but, of course,they call this "0g"

82400:45:31 --> 00:45:37which is equally incorrect.

82500:45:32 --> 00:45:38It's not 0g--you have noweight.

82600:45:35 --> 00:45:41This is weightless,here your weight is double

82700:45:37 --> 00:45:43here your weight is normal,here your weight roughly doubles

82800:45:40 --> 00:45:46and you go intoanother free-fall period

82900:45:43 --> 00:45:49and the cycle from here to hereis about 90 seconds.

83000:45:48 --> 00:45:54Now, the irony has it

83100:45:50 --> 00:45:56that the reasonwhy these flights are done

83200:45:53 --> 00:45:59is to study motion sicknessunder weightless conditions.

83300:45:57 --> 00:46:03Astronauts were complainingabout motion sickness.

834

00:46:00 --> 00:46:06And so Professor Youngand Oman have done

83500:46:03 --> 00:46:09lots and lots of experimentswith airplanes

83600:46:05 --> 00:46:11and later, also, in the shuttleto study this motion sickness.

83700:46:09 --> 00:46:15I find it rather ironic

83800:46:10 --> 00:46:16because if you and I werepart of these experiments

83900:46:15 --> 00:46:21we would get terribly sickbecause of the experiments.

84000:46:18 --> 00:46:24Just imagine that you gofrom weightlessness

84100:46:20 --> 00:46:26into twice your weight,back to weightlessness.

84200:46:23 --> 00:46:29We would be puking all day!

84300:46:25 --> 00:46:31How can you study peoplewho are sick?

84400:46:29 --> 00:46:35How can you study the sicknessdue to weightlessness?

84500:46:32 --> 00:46:38Well, they musthave found a way.

84600:46:35 --> 00:46:41They do this

about 50 times per day.

84700:46:38 --> 00:46:44And now I want to show yousome real data

84800:46:41 --> 00:46:47which were kindly given to meby Professor Young

84900:46:47 --> 00:46:53where you see them actuallyin the plane.

85000:46:51 --> 00:46:57I believe I have to put thison one and start the...

85100:47:00 --> 00:47:06Can you turn offthe slide projector?

85200:47:02 --> 00:47:08

85300:47:06 --> 00:47:12So here you see themin the plane.

85400:47:08 --> 00:47:14They are not weightless,they are climbing up.

85500:47:11 --> 00:47:17

85600:47:20 --> 00:47:26I think this is Professor Young.

85700:47:22 --> 00:47:28The guys lying on the floormust be a bit tired.

85800:47:25 --> 00:47:31The light will shortly go on,and when the light goes on

85900:47:28 --> 00:47:34that's an indication that

the weightlessness is coming up.

86000:47:33 --> 00:47:39It already went on, I must havemissed it, I wasn't looking.

86100:47:37 --> 00:47:43And there they gointo weightlessness.

86200:47:42 --> 00:47:48See, this person isupside down here.

86300:47:44 --> 00:47:50You better get straight upbefore your weight doubles

86400:47:47 --> 00:47:53because you'll crashinto the floor.

86500:47:50 --> 00:47:56(class laughs )

86600:47:53 --> 00:47:59

86700:48:03 --> 00:48:09LEWIN:And now it takes 60 seconds

86800:48:06 --> 00:48:12because the whole cycleis 90 seconds

86900:48:09 --> 00:48:15and in these 60 seconds

87000:48:13 --> 00:48:19they get readyfor the next free fall--

87100:48:17 --> 00:48:23for the next weightlessness.

87200:48:18 --> 00:48:24And you will see very shortly

87300:48:20 --> 00:48:26the light will go on again,and that will tell them

87400:48:23 --> 00:48:29that the weightlessnessis coming up

87500:48:25 --> 00:48:31and then they will be weightlessfor another 30 seconds.

87600:48:29 --> 00:48:35

87700:48:33 --> 00:48:39The sound that you hear isobviously

87800:48:35 --> 00:48:41the engines of the plane.

87900:48:37 --> 00:48:43

88000:48:42 --> 00:48:48There you go-- light goes on,

88100:48:44 --> 00:48:50they get a warning, theytake their headphones off

88200:48:46 --> 00:48:52and everythingbecomes weightless.

88300:48:48 --> 00:48:54They may not like that

88400:48:50 --> 00:48:56and so they put their headphonesin a secure place.

88500:48:53 --> 00:48:59You see that hereProfessor Young takes his off.

886

00:48:57 --> 00:49:03And there they go again...swimming in mid-air.

88700:49:04 --> 00:49:10(class laughs )

88800:49:08 --> 00:49:1430 seconds weightless.

88900:49:10 --> 00:49:16

89000:49:16 --> 00:49:22(class laughs )

89100:49:17 --> 00:49:23LEWIN:And the planein which this happens...

89200:49:19 --> 00:49:25(class laughs )

89300:49:24 --> 00:49:30LEWIN:Yeah, these things happen.

89400:49:26 --> 00:49:32I'd like to show youa last slide of the plane

89500:49:30 --> 00:49:36that they dothese experiments from.

89600:49:33 --> 00:49:39This is the planewhile it is in free fall.

89700:49:37 --> 00:49:43About 45-degree angle

89800:49:41 --> 00:49:47and these people have donea tremendous job

89900:49:44 --> 00:49:50

in indeed makinga major contribution

90000:49:47 --> 00:49:53to the airsickness dueto weightlessness.

90100:49:52 --> 00:49:58All right, see you Friday.

90200:49:55 --> 00:50:01

90300:50:00 --> 00:50:06.000