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8.01x - Lect 7 - Weight, Weightlessness in Free Fall, Weight in Orbit — Transcript

by Lectures by Walter Lewin. They will make you ♥ Physics. · 6,784 words · 880 segments · language en · Watch on YouTube

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0:02So far in these lectures
0:03we've talked about mass, about acceleration and about forces,
0:08but we never used the word "weight," and weight is
0:12a very nonintuitive and a very tricky thing
0:15which is the entire subject of today's lecture.
0:19What is weight?
0:22Here you stand on a bathroom scale.
0:30Gravity is acting upon you, the force is mg, your mass is m.
0:39The bathroom scale is pushing on you with a force F scale
0:44and that F scale-- which in this case
0:48if the system is not being accelerated
0:50is the same as mg--
0:52that force from the bathroom scale on you
0:57we define as weight.
1:00When I stand on the bathroom scale
1:03I could see my weight is about 165 pounds.
1:06Now, it may be calibrated in newtons
1:08but that's, of course, very unusual.
1:12If I weigh myself on the moon
1:13where the gravitational acceleration is six times less
1:17then I would weigh six times less-- so far, so good.
1:24Now I'm going to put you in an elevator
1:29and I'm going to accelerate you upwards
1:35and you're standing on your bathroom scale.
1:39Acceleration is in this direction
1:41and I will call this "plus" and I will call this "minus."
1:46Gravity is acting upon you, mg
1:49and the bathroom scale is pushing on you with a force F.
1:55That force, by definition, is weight.
2:01Before I write down some equations, I want you to realize
2:05that whenever, whenever you see in any of my equations "g"
2:09g is always plus 9.8.
2:12And my signs, my minus signs take care of the directions
2:16but g isalways plus 9.8 or plus 10, if you prefer that.
2:21Okay, it's clear that if this is accelerated upwards
2:24that F of s must be larger than mg;
2:27otherwise I cannot be accelerated.
2:29And so we get Newton's Second Law:
2:31F of s is in plus direction...
2:34minus mg-- it's in this direction-- equals m times a
2:41and so the bathroom scale indicates m times a plus g.
2:48And I have gained weight.
2:51If this acceleration is
2:54five meters per second squared in this direction
2:56I am one and a half times my normal weight.
3:01If I look on the bathroom scale, that's what I see.
3:05Seeing is believing-- that is my weight.
3:08If I accelerate upwards, with 30 meters per second squared
3:1330 plus 10 is 40-- I am four times my normal weight.
3:19Instead of my 165 pounds, I would weigh close to 700 pounds.
3:25I see that-- seeing is believing.
3:28That is my weight.
3:31Now I am going to put you in the elevator-- here you are--
3:37and I'm going to accelerate you down.
3:42This is now a.
3:44And just for my convenience
3:46I call this now the plus direction
3:48just for my convenience-- it doesn't really matter.
3:51So now we have here mg-- that is gravity acting upon you.
3:55And now you have the force from the bathroom scale.
4:00Clearly, mg must be larger than F of s;
4:03otherwise you couldn't go being accelerated downwards.
4:06So if now we write down Newton's Second Law
4:09then we get mg minus F of s must be m times a.
4:16This holds for acceleration down
4:18and so I get F of s equals m times g minus a.
4:27This is one way of doing it
4:29and you put in positive values for a.
4:32If a is five meters per second squared
4:34you get ten minus five is five-- your weight is half.
4:37You've lost weight.
4:39Being accelerated down, you've lost weight.
4:43You could also have used this equation
4:44and not go through this trouble
4:46of setting up Newton's Law again.
4:50You could simply have said
4:51"Okay, this a is minus in this coordinate system"
4:53and so you put in a minus five and a plus ten--
4:55you get the same answer.
4:57So you have lost weight when you accelerate downwards.
5:02Suppose now I cut the cable... cut it.
5:09Then this a is ten meters per second squared
5:12if we round it off.
5:14You go down with ten meters per second squared
5:16so g minus a is zero.
5:20You are now weightless, you are free-falling.
5:25You have no longer any weight.
5:26You look at the bathroom scale
5:28and the bathroom scale will indicate zero.
5:32You're floating, everything in the elevator is floating.
5:36If you had a glass with water
5:38you could turn it over and the water would not fall out.
5:43It's like having the shuttle in orbit
5:47with the astronauts being weightless.
5:50There is a great similarity
5:52between the astronauts in the shuttle
5:55and a free-falling elevator.
5:57The only difference is
5:59that the elevator will crash, will kill you.
6:03In the case of the shuttle
6:04it never hits the earth because of its high speed.
6:08We'll talk about this much later
6:10when we deal with orbits and with Kepler's Law.
6:16What exactly is free fall?
6:19Free fall is
6:20when the forces acting upon you are exclusively gravitational.
6:26Nothing is pushing on you;
6:29no seat is pushing on you, no string is pushing on you.
6:32Nothing is pulling on you, only gravity.
6:37I will return to this weightlessness
6:39very shortly in great detail
6:41but before I do that, I would like to address the issue--
6:46how could I determine your weight
6:48if I hang you from a string?
6:53So now, instead of standing on a bathroom scale
6:57you are here.
7:01Here is a string.
7:02You might even have in the string a tension meter
7:05as we have seen earlier in lectures.
7:07And you are holding desperately onto that string.
7:10Just like that.
7:13The system is not being accelerated, gravity is mg
7:18and so there must be tension in the string, T
7:21which is pulling you up
7:22which, if there is no acceleration, must be mg.
7:28I read the scale and I read my weight.
7:33This scale indicates, in my case, 165 pounds.
7:38While I'm hanging, I can see my weight.
7:41So you see, it makes very little difference
7:43whether I am standing on a bathroom scale
7:46and read the force
7:48with which the bathroom scale pushes up on me
7:51or whether I hang from a scale
7:54extend a spring and read that value.
7:58It makes no difference.
7:59The tension here would indicate my weight.
8:03There is a complete similarity with the bathroom scale
8:06except in one case, something is pulling on me;
8:09in the other case, something is pushing on me from below.
8:14Now let's accelerate this system upwards with an acceleration a--
8:21and I call this plus.
8:23Then, of course, this T must grow;
8:26otherwise you cannot be accelerated.
8:28Newton's Second Law, T minus mg must be ma.
8:34The tension in the string equals m times a plus g.
8:39Ah! We've seen that before.
8:41No difference with the elevator.
8:44You accelerate the system, the tension will increase
8:47and you will see that, you will read that on the scale.
8:50Your weight has increased, you weigh more.
8:54Needless to say, of course, if you accelerate the system down
8:58that you will weigh less-- we just went through that argument.
9:01And if I cut the cable completely
9:04you go into free fall.
9:05T will go to zero, a become minus ten plus ten is zero.
9:11You're in free fall.
9:12The scale reads zero, you are completely weightless.
9:19If we accept the idea
9:21of weight being indicated by the tension in a string
9:29then there is a very interesting consequence of that.
9:33I have here a pin which is completely frictionless
9:37and I have on both sides a string
9:40and this string has negligibly small mass.
9:44Now, just assume that it is massless.
9:46And there is here an object m1 and there is here an object m2
9:53and I am telling you that m2 is larger than m1.
9:58So we all know what's going to happen.
10:00The system is going to accelerate in this direction.
10:03M2 will be accelerated down and m1 will be accelerated up.
10:10What comes now is important, that you grasp that.
10:14I claim that the tension on the left side must be the same
10:18as the tension in this string on the right side.
10:22T Left must be T Right.
10:25Why is that?
10:27It is because the pin is frictionless
10:29and it is because the string is massless.
10:34Take a little section of the string here
10:37a teeny-weeny little section.
10:40If there is a tension on it--
10:41that is, a force in this direction
10:43and there is a force in this direction--
10:46these two could never be different
10:47because then this massless string
10:49would get an infinite acceleration.
10:51So there can never be a change in tension
10:53from this side of the string to the other.
10:56If you take a little section of the string here--
10:59there it is, teeny-weeny little section
11:02so there is tension on the string
11:04and there is tension on the string--
11:07this one could never be larger than that
11:09because this little piece of string
11:10would get an infinite acceleration.
11:12So because there is no friction on the pin
11:15and because the strings are massless--
11:18only because of that must the tension be everywhere the same.
11:21If there is friction in the pin-- which we will do later--
11:24then that's not the case.
11:26Given the fact that the tension left
11:29and the tension right are the same
11:31I must now conclude that these two objects have the same weight
11:36because didn't we agree
11:38that tension is an indication of weight?
11:41So these objects have now the same weight.
11:44And some people may say
11:45"Oh, that's a lot of nonsense, you must be kidding.
11:47"If m2 is larger than m1
11:48this must have a larger weight than that."
11:50Well, they are confusing weight with mass.
11:53It is true that m2 is a larger mass than m1
11:56but it is equally true
11:58that the weight of these two objects is now the same
12:01according to my definition of weight.
12:05Let us calculate the acceleration of this system
12:09and let's calculate the tension and let's see what comes out.
12:13I first isolate here object number one.
12:18This is my object number one.
12:19I have gravity, m1 g, and I have a tension T.
12:27Nonnegotiable.
12:28T better be larger than m1 g.
12:30Otherwise it would never be accelerated up
12:32and we know it will be accelerated up.
12:35So what do we get? We get T--
12:38I will call this plus direction, by the way--
12:40minus m1 g equals m times a.
12:46So the tension equals m1 times a plus g.
12:53Hey! We've seen that one before.
12:56This one is being accelerated upwards.
12:59Notice it gains weight.
13:01That's the tension and this is the acceleration.
13:04I have one equation with two unknowns
13:08so I can't solve it yet.
13:10But there is another one, there is number two here.
13:15For number two, we have a force, m2 g
13:20and we have the tension up.
13:22This one better be larger than that one;
13:24otherwise it wouldn't be accelerated down.
13:28Let me call this direction plus.
13:31The reason why I now switch directions and call this plus--
13:34as well as this-- is a good reason for it.
13:36It's not so arbitrary anymore.
13:39I know that this acceleration
13:41is going to be a positive number.
13:43Because it's going in this direction, it's a given.
13:45If I called this negative,
13:47I would get here a negative acceleration
13:50for the same thing for which I get here a positive.
13:52That's a pain in the neck.
13:53I don't want to have a plus and a minus sign there,
13:55have to think about that it means the same thing.
13:58So the moment that I decide to define this the plus direction
14:01I know that this acceleration
14:03will also come out to be the same sign as this one.
14:06So I flip the signs there.
14:08So now I apply Newton's Law.
14:11I get m2 g minus T equals m2 a.
14:18And so I get T-- I'll write it here--
14:21equals m2 times g minus a.
14:31Two equations with two unknowns.
14:37Well, that shouldn't be so hard to solve these two equations.
14:41You can immediately eliminate T, by the way.
14:43If you add this one with this one, you really--
14:46I call this equation one, you call this equation two--
14:50you immediately lose your T and you get that the acceleration, a
14:56equals m2 minus m1 divided by m1 plus m2 times g.
15:06And you substitute that "a" in that equation and you'll find
15:10that the tension equals 2mg divided by m1 plus m2.
15:17This is very easy for you to verify.
15:22Let us look.
15:23This is m1, m2...
15:282m1, m2-- I lost one m-- 2m1, m2.
15:33Let's look at these equations, let's scrutinize them a little.
15:35Let's get some feeling for it
15:37rather than accepting them as being dumb equations.
15:41Let's first take the case
15:43that m2 equals m1, and I'll call that "m."
15:49Notice that a becomes zero
15:53and notice, if you substitute for m1 and m2 "m" here
15:58that you get 2m, you get mg.
16:00So T becomes mg.
16:03That isutterly obvious.
16:06If m1 and m2 are the same, nothing is going to happen.
16:09They're going to sit there, acceleration will be zero
16:13and the tension on both sides--
16:14which is always the same, we argued that--
16:16is going to be mg.
16:18Clear.
16:20Now we're going to make it more interesting.
16:22Suppose we make m2 much, much larger than m1
16:27and in a limiting case we even go with m1 to zero.
16:33Let's do that.
16:35What you see now, if m1 goes to zero
16:38this goes away, this goes away, a goes to g and T goes to zero.
16:48If m1 is zero, T goes to zero.
16:52That is obvious!
16:55Because if I make m1 zero, m2 goes into free fall.
17:02And if m2 goes into free fall
17:04its weight is zero and so the tension is zero--
17:07that's exactly what you see--
17:08and you see that the acceleration of that object
17:11is g, which it better be, because it's in free fall.
17:14So you see, this makes sense.
17:17This is exactly consistent with your intuition.
17:19And if you wanted to make m1 much, much larger than m2
17:24and you take the limiting case for m2 goes to zero
17:28you'll find again that a goes to g and that T goes to zero
17:33except that now the acceleration is not this way...
17:37(makes whooshing sound)
17:38but now the acceleration is this way
17:40and now this object will go into free fall.
17:45And therefore there is no tension in the string anymore.
17:52M1, if I return to the case which we have there--
17:56that m2 is larger than m1--
17:59m1 is being accelerated upwards.
18:01That's nonnegotiable, so it must have gained weight.
18:04M2 is being accelerated down, so it must have lost weight.
18:09Just like being in an elevator, there's no difference.
18:14They each weigh the same--
18:16one loses weight, the other gains weight.
18:19They each weigh the same, and so I can make the prediction
18:23that if this is m2 g, which was its original weight
18:28and this now is the new weight, T
18:31that m2 g must be larger than T.
18:33M1 gains weight, so T must be larger than m1 g.
18:37M2 loses weight, so T must be smaller than m2 g.
18:42That's my prediction-- it has to be.
18:44And we can... I can show you that with some easy numbers.
18:47Let m1 be 1.1 kilograms and let m2 be 1.25 kilograms.
18:58Frictionless system, and the string has a negligible mass.
19:04What is the acceleration "a" of the system?
19:06I get m2 minus m1--
19:08that is 0.15 divided by the sum, which is 2.35
19:15and that is approximately 0.064 g, approximately 0.064 g.
19:23It's about 1/16th of the gravitational acceleration.
19:27It's a very modest acceleration.
19:31What is the tension?
19:32Well, I substitute my numbers for m1 and m2 in there.
19:36You can take, for g, 10, if you like that
19:39and you will find that the tension equals 1.17 g.
19:46And now look at what I predicted.
19:50They both weigh 1.17 g, that's nonnegotiable.
19:54That is my definition of weight--
19:56the tension in both sides is the same.
19:58That's my definition of weight.
19:59This is their weight.
20:02This one had a weight 1.25 g without being accelerated.
20:09You see, it has lost weight, because it accelerated down.
20:13This one had a weight of 1.1 g.
20:17You see, it has gained weight, because it has accelerated up.
20:21So you see, the whole picture ties together very neatly
20:25and it's important that you look at it that way.
20:29I now want to return to the idea of complete weightlessness
20:36and I want to remind you, a few lectures ago
20:38how I was swinging you at the end of a string in the vertical.
20:42I was swinging you like this.
20:44And I was swinging a bucket of water like this.
20:48And I want to return to that.
20:51I want to look at you when you are at the bottom of your circle
20:58and when you are at the very top of that circle.
21:05You go around a circle which has radius R.
21:10Here is that circle.
21:16There's a string here, you're here.
21:20And there's a string here
21:22and at some point in time, you're there.
21:23And you're going around... let's assume
21:25that you're going around with an angular velocity omega
21:29and for simplicity, we keep omega constant.
21:32But that's really not that important.
21:35Okay, this is point P and this is point S.
21:40Let's first look at the situation at point P.
21:44You have a mass and so gravity acts upon you, mg.
21:50There is tension in the string, T.
21:54There must be-- this is nonnegotiable--
21:57a centripetal acceleration upwards.
22:00Otherwise, you could never do this.
22:02Remember, from the uniform circular motion.
22:05So there must be here centripetal acceleration
22:10which is omega squared R
22:12or, if you prefer, v squared divided by R
22:15if v is the speed, tangential speed at that point.
22:20It must be there.
22:23Let's look here.
22:25Right there, gravity is acting upon you, mg.
22:33Let's assume this string is pulling on you.
22:34Let's assume that for now, so there is a tension.
22:39The string is pulling on you.
22:42Therefore, nonnegotiable, when you make this curvature here
22:48there must be a centripetal acceleration
22:50and that centripetal acceleration
22:52must be omega squared R.
22:54That is nonnegotiable, it has to be there.
22:58Let's now evaluate first the situation at P
23:03and I will call this plus
23:06and I will call this minus.
23:09So what I get now is
23:10that T minus mg
23:14must be m times the centripetal acceleration
23:20so T must be m times the centripetal acceleration plus g.
23:25Hey! That looks very familiar.
23:28It looks like someone is being accelerated in an elevator--
23:32almost the same equation.
23:36If the centripetal acceleration at this point
23:41for instance, were 10 meters per second squared
23:45then you would weigh twice your normal weight.
23:48The tension here would be twice mg.
23:54If this were five meters per second squared
23:58then you would be 1½ times your weight.
24:03Let's now look at the situation at S.
24:08At point S, I'm going to call this plus and that minus.
24:18I'm going to find that T plus mg
24:23must be m times the centripetal acceleration--
24:27Newton's Second Law.
24:29So I find that the tension there equals m times a of c minus g.
24:36Hey! Very similar to what I've seen before.
24:40This object is losing weight.
24:46Let us take the situation
24:48that a of c is exactly 10 meters per second squared
24:52and we discussed that last time
24:53when we had the bucket of water in our hands.
24:56If a of c...
24:57if the centripetal acceleration when it goes through the top
25:01is 10, then this is zero.
25:04So the string has no tension, the string goes limp
25:08and the bucket of water and you are weightless.
25:13If the centripetal acceleration is larger than 10
25:17then, of course, the string will be tight.
25:20There will be a force on you
25:22and whatever comes out of here will indicate your weight.
25:28If a of c is smaller than 10, that's meaningless.
25:34The tension can never be negative.
25:37A string with negative tension has no physical meaning.
25:40What it means is that the bucket of water
25:42would never have made it to this point.
25:44If you try to swing it up--
25:46as someone tried in the second lecture--
25:48but didn't make it to that point
25:50the bucket of water will just fall.
25:53You end up with a mess, but that's a detail.
25:56So the bucket of water, when it is here...
26:01If the acceleration there, the centripetal acceleration
26:04were exactly 10 meters per second squared
26:07then that bucket of water would be weightless.
26:13So I said earlier that when you're in free fall
26:16all objects in free fall are weightless.
26:19It's like a spacecraft in orbit or an elevator with a cut cable.
26:25It also means that if I jump off the table
26:30that I'm weightless while I am in mid-air, so to speak.
26:35It means this tennis ball...
26:37while it is in free fall, it has no weight.
26:40Now it has weight.
26:42Now the weight is even higher because I am accelerating it
26:45and now it has no weight.
26:47The tennis ball is weightless
26:50and I assume, for now, that the air drag plays no role.
26:56If I jump off the table
27:00I will be weightless for about half a second.
27:02This is about one meter.
27:04If I jump from a tower which is 100 meters high
27:07I will be weightless for 4½ seconds
27:10ignoring air drag.
27:12I prefer today the half a second.
27:18I am going to jump off this table
27:21with this water in my hand.
27:26And I'm going to tell you how I can convince you
27:30that as I jump, that I will, indeed, be weightless.
27:34Here is the bottle.
27:37There is a gravitational force on the bottle.
27:40My hands are pushing up on this bottle.
27:44My hands are being a bathroom scale.
27:47I feel, in my muscles, the need to push up.
27:51In fact, I might even be able to estimate the weight
27:54playing the role of a bathroom scale.
27:57It's a gallon of water, it's about nine pounds.
28:05Now my own body... gravity is acting upon me
28:09but I am being pushed up, right there.
28:14Suppose we jumped.
28:19There would be no pushing from me on the bottle anymore
28:22no pushing there on me, the table.
28:26Only gravitation would act upon us and we would be weightless.
28:31How can I show you that we are weightless?
28:34Well, if I don't have to use
28:36my muscles to push on this bottle upwards
28:38I might as well lower my hands a little bit
28:41during this free fall.
28:43And you will see that the bottle will just stay above my hands
28:46without my having to push up.
28:48Therefore, being the bathroom scale
28:51I no longer have to push on it.
28:53I no longer... my muscles don't feel anything
28:56and the bottle is therefore weightless.
28:59The bottle is weightless when we jump;
29:02I am weightless and even this bagel is weightless.
29:05We're all weightless during half a second.
29:09There is no such thing in physics as a free lunch.
29:13You have to pay a price for this half a second of weightlessness.
29:18What happens when I hit the floor?
29:21I hit the floor with a velocity in this direction
29:23which is about five meters per second.
29:26You can calculate that.
29:27But a little later, I've come to a stop.
29:30That means during the impact
29:32there must be an acceleration upwards.
29:35Otherwise my velocity in this direction
29:36could never become zero.
29:39Therefore, I will weigh more during this impact--
29:43there is an acceleration in this direction.
29:46The five meters per second goes to zero.
29:50If I make the assumption
29:51that it takes two-tenths of a second--
29:53that's a very rough guess, this impact time--
29:55then the average acceleration
29:57will be five meters per second divided by 0.2;
30:00that is 25 meters per second squared.
30:03That means the acceleration upwards is 2½ g.
30:07That means I will weigh 3½ times more.
30:11Remember it is a plus g,
30:12so a is 2½ g up plus the g that we already have;
30:16that makes it 3½ g.
30:18So instead of weighing 165 pounds
30:21I weigh close to 600 pounds for two-tenths of a second.
30:25So we get four phases.
30:26Right now, I'm my normal weight
30:29if I stand on a bathroom scale.
30:30I jump for half a second, weightless
30:33hit the floor for about two-tenths of a second
30:36maybe close to 600 pounds.
30:38And then after that I will have my normal weight again.
30:42Now, you're going to have only half a second to see
30:46that this bottle, as I jump, is floating above my hands.
30:49I will pull my hands off
30:51so you will see that I no longer have to push it.
30:55That means it's weightless.
30:59Are you ready? I'm ready.
31:02Three, two, one, zero.
31:06Did you see it floating above my hands?
31:08We were both weightless.
31:11Now, I have been thinking about this
31:16for a long, long time.
31:18I have been thinking whether
31:19perhaps this could not be shown in a more dramatic way
31:25perhaps even a more convincing way.
31:28And so I thought of the idea
31:30of putting a bathroom scale under my feet
31:33tying it very loosely so that it wouldn't fall off when I jump
31:36and then show you that while I am half a second in free fall
31:40that the bathroom scale indeed indicates zero.
31:45And don't think that I haven't tried it.
31:46I've tried it many times with many bathroom scales.
31:49I made many jumps.
31:50There is a problem, and the problem is
31:53the bathroom scales that you buy--
31:55that you normally get commercially--
31:57they indeed want to go to zero.
31:59It takes them a long time.
32:01They have a lot of inertia, their response time is slow.
32:05But even if they make it to zero by the time you hit the floor
32:09then immediately the weight increases
32:13because you hit the floor
32:14and your weight comes up by 3½ times.
32:16So it begins to swing back and forth
32:18and it becomes completely chaotic
32:19and you can no longer see what's happening.
32:22And it just so happened that about six months ago, Dave...
32:26I had dinner with Professor Dave Trumper
32:28and I explained it to him that it is just unfortunate
32:32that you can never really show it
32:34that you jump off the table, have a bathroom scale under you
32:37and see that weight go down to zero when you are in free fall.
32:39And he said, "Duck soup-- I can do that."
32:43He says, "I can make you a scale
32:45"which has a response time of maybe 10 milliseconds
32:49"so when you jump off the table
32:51in 10 milliseconds you will see that thing go down to zero."
32:56And he delivered, he came through.
33:00He built this wonderful device
33:02which he and I are going to demonstrate to you.
33:06Let me first give you some reasonable light for this.
33:14And I would like to show you on the scale there
33:19what this scale that he built is indicating.
33:23Here is the scale, I have it in my hands.
33:27And on top of this scale is a little platform
33:30just like on your scale.
33:31This platform weighs 4½ pounds.
33:35And you can see that, it says about 4½.
33:39Now, you will say
33:40"Hmm! I wouldn't want that kind of a bathroom scale.
33:44"I mean, if I want to see my bathroom scale
33:46"I want to see a zero before I want to go up.
33:48"I'm heavy enough all by myself.
33:49I don't want to get another 4½ pounds."
33:52The manufacturer has simply zeroed that scale for you
33:56but obviously also your bathroom scale has a cover on it.
34:00Once you have seen these demonstrations
34:02you will be able to answer for yourself why we don't zero this
34:07why we really leave this to be 4½.
34:09That's the actual mass which is on top of the spring.
34:13But it's not really a spring--
34:15it is a pressure gauge, but think of it as a spring.
34:184½ pounds.
34:21Here we have a weight
34:24which is a barbell weight, which is 10 pounds.
34:31Is this from one of your children, Dave
34:34or were you doing it yourself?
34:3610 pounds... we put it on top here.
34:41What do you see? Roughly 14½ pounds.
34:45All right, we are going to tape it down.
34:53There we go.
34:55And we're going to drop it
34:57from about 1½, two meters
35:00and we drop it in here, well-cushioned
35:03because we don't want to break this beautiful device.
35:09When we drop it, the response is so fast
35:12that you will see, indeed, that pointer go to zero.
35:16Now, keep in mind, when it hits the cushion
35:20that the weight will go up.
35:22For now, I want you to concentrate
35:24only on the thing going to zero and not what comes later.
35:28We will deal with that within a minute.
35:33Okay... 14½ pounds.
35:41You know why the thing is actually jiggling
35:43back and forth?
35:44I can't hold it exactly still
35:46and so I slightly accelerate it upwards and downwards
35:50and when I accelerate it slightly upwards
35:51it weighs a little more
35:53and when I accelerate it downwards, it weighs less.
35:55It's interesting.
35:56You can see I'm nervous.
35:57That's my nervous tension meter there.
36:00Okay, we're ready?
36:03Look and... don't look at me, now, look at that pointer.
36:07Three, two, one, zero.
36:11Did you see it go to zero? All the way to zero.
36:15Now comes something even more remarkable.
36:19He said to me, "I can also make the students see the response
36:28on a time scale of about a fraction of a second."
36:31By the way, this is the hero who made all this stuff.
36:35He's fantastic.
36:36(class applauds)
36:43LEWIN: He can show you the weight on an electronic scale
36:50and this weight you will see as a function of time.
36:56I will put the ten pounds back on again...
37:00tape it a little tighter
37:05and so the level that you see now is 14½ pounds.
37:11This is 14½ pounds and this is zero, this mark is zero.
37:17I'm going to hold it in my hand.
37:25And notice, if I can hold it still
37:26you're back to your 14½ pounds.
37:30Now I'm going to drop it.
37:33You will see it go down to zero.
37:35It will hit the floor, the cushion.
37:38It will get an acceleration upwards.
37:40It will become way heavier than it was before
37:44and then it will even be bounced back up in the air
37:47and it goes again into free fall.
37:49We will freeze that for you, and you will be able...
37:52we will be able to analyze it, then, after it all happens.
37:57So, 14½ pounds... three, two, one, zero.
38:06And now Professor Trumper is freezing it for you.
38:08Now look at this, look at this incredible picture.
38:12This is truly an eye-opener for me, when I saw it.
38:15The physics in here is unbelievable.
38:18Here is your 14½ pounds.
38:21Tick marks from here to here are half a second.
38:24It was half a second in free fall
38:27and it goes to zero, that's no weight.
38:29Now it hits the floor, the cushion
38:31and its weight goes up
38:33in something like a tenth of a second.
38:35Look, this is about one, two, three...
38:38It's about 3½ times its weight now.
38:41So the 14½ has to be multiplied
38:43by 3½ or four
38:44which is exactly what we predicted--
38:46that it would be much higher.
38:48But now it's being...
38:49it bounces off, because it's a very nice cushion.
38:51It throws it back up.
38:53So it goes back into the air
38:54so it goes immediately to weightlessness again
38:56and then it oscillates back and forth.
38:59And then here you would expect
39:01that this level, 14½ pounds, would be the same as this.
39:05And the only reason why that's not the case is
39:07there's a little cable that fell with it
39:09which is pushing a little bit up
39:11on the upper... on the upper disc that is there
39:14so it's making it a little lighter.
39:16Isn't it incredible?
39:17You see here in front of you the weightlessness
39:20and you see the extra weight when it hits
39:23and again followed by weightlessness.
39:26Dave, A-plus, you passed the course.
39:32There is a great interest
39:35in doing experiments under weightless conditions.
39:40NASA was very interested in it.
39:42And if you would jump 100 meters up in the sky
39:47you would only be nine seconds up.
39:49You wouldn't even be weightless because of air drag.
39:52However, if you could jump up
39:54way near the top of the atmosphere--
39:57where the air drag is negligible--
39:59then you would be weightless for quite some time.
40:03And that is what people have been doing
40:06for the past few decades.
40:08Professor Young and Professor Oman here
40:09at the Aeronautics Department
40:12have done what they call "zero gravity experiments"
40:16from airplanes-- and I will explain that in detail--
40:18but first I want you to appreciate
40:21that "zero gravity" is a complete misnomer.
40:25"Zero weight," yes-- "zero gravity," no.
40:29If you have an airplane anywhere near Earth, flying
40:32whether the engines are on or whether the engines are off
40:34or whether it is free-falling doesn't matter.
40:36There is never zero gravity.
40:38There is always gravity-- thank goodness.
40:40But if you are in free fall, indeed, there is no weight.
40:45Apart from that, they call them "zero gravity experiments"
40:50and why not?
40:51Maybe it sells better.
40:55They fly an airplane, which is the KC-135
41:01and they do these experiments
41:03at an altitude of about 30,000 feet.
41:09If I could clean this as best as I can...
41:13The plane comes in at one point in time
41:20at an angle of about 45 degrees.
41:23There's nothing special about that 45 degrees.
41:26It's just... that's the way it's done.
41:28You have to also think of the convenience--
41:30convenience for the passengers.
41:32The speed is then about 425 miles per hour
41:41so the horizontal component is about 300 miles per hour
41:45and the vertical component is also 300.
41:50The air drag is very little.
41:51Let's assume, for the sake of the argument
41:53that the engines are cut
41:56and the plane goes into free fall.
41:59It's no different from this tennis ball--
42:01(makes whooshing sound)
42:03the same thing.
42:03You're going to see a parabola.
42:06And so this plane is going to free-fall
42:09and comes back to this level.
42:13And let's analyze this arc, this parabola.
42:17Right here at the top, clearly
42:20there will still be 300 meters per second
42:22in the absence of any air drag.
42:24You should be able to calculate
42:26with all the tools that you have available
42:28how high this goes from this level.
42:32In other words, what is the time
42:34that the velocity in the y direction comes to zero?
42:37You can calculate that
42:38and then you know how much it has traveled.
42:41Very crude number, this is about 900 meters.
42:45And it will take about 15 seconds to reach this point
42:48so it will take about 30 seconds to go from here to here
42:52and in those 30 seconds
42:55the horizontal displacement is about 3½ kilometers.
43:00And all these numbers you should be able to confirm.
43:04Right here, the engines are restarted.
43:10During this free fall, everyone in the airplane is weightless
43:14including the airplane itself.
43:16Now the engines start, and the engine is sort of...
43:19The plane is going to pull up, it goes into this phase
43:22and then the plane flies horizontally for a while.
43:25During this phase, as we just discussed
43:28it's like hitting the floor.
43:30You need an acceleration in this direction.
43:32There will be weight increase
43:36so there is here an acceleration upwards.
43:39And during this time, very roughly
43:41people have about twice their weight.
43:45And then here, they have again normal weight.
43:47And then the plane pulls up again
43:50and here it goes and repeats the whole thing
43:55again going into free fall.
43:58So again here, people have more than their normal weight.
44:04Zero weight, more than normal weight
44:06normal weight, more than normal weight, free fall.
44:09And the whole cycle takes about 90 seconds.
44:15You can imagine that it is very important
44:17when you are here in free fall, when you have no weight
44:21that when your weight comes back and your weight doubles--
44:24and Professor Oman told me that this change from zero
44:27to twice your weight takes less than a second--
44:30that you better know where your feet are and where your head is
44:33because if your head is down
44:35and you all of a sudden double your weight
44:38you crush your skull, so you have to be sure
44:41that you are standing straight up in the plane
44:44when your weight begins to double
44:46and we will see that very shortly, how that works.
44:50I want to show you first some slides from these experiments.
44:55So here you see the situation that we just described.
45:01Let us start here, that is where I started with you.
45:05The plane turns the engines off.
45:07This is the parabola.
45:09Here the engines are restarted.
45:11This is the free-fall period.
45:14This is about 30 seconds.
45:16The engine is restarted, and during this time
45:19there is an acceleration upwards and they call it "2g peak."
45:23Well, they really mean 1g.
45:25What they really mean, that my weight doubles.
45:27They call that "2g"
45:29but, of course, they call this "0g"
45:31which is equally incorrect.
45:33It's not 0g-- you have no weight.
45:36This is weightless, here your weight is double
45:38here your weight is normal, here your weight roughly doubles
45:41and you go into another free-fall period
45:45and the cycle from here to here is about 90 seconds.
45:49Now, the irony has it
45:51that the reason why these flights are done
45:55is to study motion sickness under weightless conditions.
45:59Astronauts were complaining about motion sickness.
46:02And so Professor Young and Oman have done
46:04lots and lots of experiments with airplanes
46:07and later, also, in the shuttle to study this motion sickness.
46:10I find it rather ironic
46:12because if you and I were part of these experiments
46:17we would get terribly sick because of the experiments.
46:20Just imagine that you go from weightlessness
46:23into twice your weight, back to weightlessness.
46:25We would be puking all day!
46:27How can you study people who are sick?
46:30How can you study the sickness due to weightlessness?
46:34Well, they must have found a way.
46:37They do this about 50 times per day.
46:40And now I want to show you some real data
46:43which were kindly given to me by Professor Young
46:48where you see them actually in the plane.
46:53I believe I have to put this on one and start the...
47:02Can you turn off the slide projector?
47:07So here you see them in the plane.
47:10They are not weightless, they are climbing up.
47:21I think this is Professor Young.
47:24The guys lying on the floor must be a bit tired.
47:26The light will shortly go on, and when the light goes on
47:30that's an indication that the weightlessness is coming up.
47:34It already went on, I must have missed it, I wasn't looking.
47:39And there they go into weightlessness.
47:44See, this person is upside down here.
47:46You better get straight up before your weight doubles
47:49because you'll crash into the floor.
47:52(class laughs)
48:04LEWIN: And now it takes 60 seconds
48:07because the whole cycle is 90 seconds
48:10and in these 60 seconds
48:14they get ready for the next free fall--
48:18for the next weightlessness.
48:20And you will see very shortly
48:21the light will go on again, and that will tell them
48:24that the weightlessness is coming up
48:27and then they will be weightless for another 30 seconds.
48:34The sound that you hear is obviously
48:36the engines of the plane.
48:43There you go-- light goes on,
48:45they get a warning, they take their headphones off
48:47and everything becomes weightless.
48:49They may not like that
48:51and so they put their headphones in a secure place.
48:55You see that here Professor Young takes his off.
48:59And there they go again... swimming in mid-air.
49:05(class laughs)
49:0930 seconds weightless.
49:16(class laughs)
49:19LEWIN: And the plane in which this happens...
49:20(class laughs)
49:25LEWIN: Yeah, these things happen.
49:28I'd like to show you a last slide of the plane
49:31that they do these experiments from.
49:34This is the plane while it is in free fall.
49:40About 45-degree angle
49:42and these people have done a tremendous job
49:46in indeed making a major contribution
49:48to the airsickness due to weightlessness.
49:54All right, see you Friday.

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