by Walter Lewin
It’s not easy for me to start and stop the timer while hanging on the pendulum without increasing my reaction time. However, I’ve practiced this so many times that I am quite sure that I can achieve an uncertainty in my measurements of ± 0.1 seconds. I swing ten times, with students counting the swings out loud—and laughing at the absurdity of my situation while I complain and groan loudly—and when after ten oscillations I turn off the timer, it reads 45.61 seconds. That’s a period of 4.56 ± 0.01 seconds. “Physics works!” I scream, and the students go bananas.
Grandmothers and Astronauts
Another tricky aspect of gravity is that we can be fooled into perceiving that it’s pulling from a different direction than it really is. Gravity always pulls toward the center of Earth—on Earth, that is, not on Pluto of course. But we can sometimes perceive that gravity is operating horizontally, and this artificial or perceived gravity, as we call it, can in fact seem to defy gravity itself.
You can demonstrate this artificial gravity easily by doing something my grandmother used to do every time she made a salad. My grandmother had such fantastic ideas—remember, she’s the one who taught me that you’re longer when you’re lying down than when you’re standing up. Well, when she made a salad, she really had a good time. She would wash the lettuce in a colander, and then rather than drying it in a cloth towel, which would damage the leaves, she had invented her own technique: she took the colander and put a dish towel over the top, holding it in place with a rubber band, and then she would swing it around furiously in a circle—I mean really fast.
That’s why when I demonstrate this in class, I make sure to tell the students in the first two rows to close their notebooks so their pages don’t get wet. I bring lettuce into the classroom, wash it carefully in the sink on my table, prepare it in the colander. “Get ready,” I tell them, and I swing my arm vigorously in a vertical circle. Water drops spray everywhere! Now, of course, we have boring plastic salad spinners to substitute for my grandmother’s method—a real pity in my book. So much of modern life seems to take the romance out of things.
This same artificial gravity is experienced by astronauts as they accelerate into orbit around the Earth. A friend and MIT colleague of mine, Jeffrey Hoffman, has flown five missions in the space shuttle, and he tells me that the crew experiences a range of different accelerations in the course of a launch, from about 0.5g initially, building to about 2.5g at the end of the solid fuel stage. Then it drops back down to about 1g briefly, at which point the liquid fuel starts burning, and acceleration builds back up to 3g for the last minute of the launch—which takes about eight and a half minutes total to obtain a speed of about 17,000 miles per hour. And it’s not at all comfortable. When they finally reach orbit they become weightless and they perceive this as zero gravity.
As you now know, both the lettuce, feeling the colander pushing against it, and the astronauts, feeling the seats pushing against them, are experiencing a kind of artificial gravity. My grandmother’s contraption—and our salad spinners—are of course versions of a centrifuge, separating the lettuce from the water clinging to its leaves, which shoots out through the colander’s holes. You don’t have to be an astronaut to experience this perceived gravity. Think of the fiendish ride at amusement parks called the Rotor, in which you stand at the edge of a large rotating turntable with your back against a metal fence. As it starts to rotate faster and faster, you feel more and more pushed into the fence, right? According to Newton’s third law, you push on the wall with the same force as the wall pushes on you.
This force with which the wall pushes on you is called the centripetal force. It provides the necessary acceleration for you to go around; the faster you go, the larger is the centripetal force. Remember, if you go around in a circle, a force (and therefore an acceleration) is required even if the speed remains unchanged. In similar fashion, gravity provides the centripetal force on planets to go around the Sun, as I discuss in appendix 2. The force with which you push on the wall is often called the centrifugal force. The centripetal force and the centrifugal force have the same magnitude but in opposite direction. Do not confuse the two. It’s only the centripetal force that acts on you (not the centrifugal force), and it is only the centrifugal force that acts on the wall (not the centripetal force).
Some Rotors can go so fast that they can lower the floor on which you stand and you won’t slide down. Why won’t you slide down?
Think about it. If the Rotor isn’t spinning at all the force of gravity on you will make you slide down as the frictional force between you and the wall (which will be upward) is not large enough to balance the force of gravity. However, the frictional force, with the floor lowered, will be higher when the Rotor spins, as it depends on the centripetal force. The larger the centripetal force (with the floor lowered), the larger the frictional force. Thus, if the Rotor spins fast enough with the floor lowered, the frictional force can be large enough that it will balance the force of gravity and thus you won’t slide down.
There are lots of ways to demonstrate artificial gravity. Here’s one you can try at home; well, in your backyard. Tie a rope to the handle of an empty paint can and fill the can with water—about half full, I’d say, otherwise it will be awfully heavy to spin—and then whip the can around as hard as you can up over your head in a circle. It might take some practice to get it going fast enough. Once you do, you’ll see that not a drop of water will fall out. I have students do this in my classes, and I must say it’s a complete riot! This little experiment also explains why, with some especially pernicious versions of the Rotor, it will gradually turn over until you are completely upside down at one point, and yet you don’t drop down to the ground (of course, for safety’s sake, you are also strapped into the thing).
The force with which a scale pushes on us determines what the scale tells us we weigh; it’s the force of gravity—not the lack of it—that makes astronauts weightless; and when an apple falls to Earth, the Earth falls to the apple. Newton’s laws are simple, far-reaching, profound, and utterly counterintuitive. In working out his famous laws, Sir Isaac Newton was contending with a truly mysterious universe, and we have all benefited enormously from his ability to unlock some of these mysteries and to make us see our world in a fundamentally new way.
CHAPTER 4
The Magic of Drinking with a Straw
One of my favorite in-class demonstrations involves two paint cans and a rifle. I fill one can to the rim with water and then bang the top on tightly. Then I fill the second can most of the way, but leaving an inch or so of space below the rim, and also seal that one. After placing them one in front of the other on a table, I walk over to a second table several yards away, on which rests a long white wooden box, clearly covering some kind of contraption. I lift up the box, revealing a rifle fastened onto a stand, pointing at the paint cans. The students’ eyes widen—am I going to fire a rifle in class?
“If we were to shoot a bullet through these paint cans, what would happen?” I ask them. I don’t wait for answers. I bend down to check the rifle’s aim, usually fiddling with the bolt a little. This is good for building up tension. I blow some dust out of the chamber, slide a bullet in, and announce, “All right, there goes the bullet. Are we ready for this?” Then standing alongside the rifle, I put my finger on the trigger, count “Three, two, one”—and fire. One paint can’s top instantly pops way up into the air, while the other one stays put. Which can do you think loses its top?
To know the answer, you first have to know that air is compressible and water isn’t; air molecules can be squished closer in toward one another, as can the molecules of any gas, but those of water—and of any liquid at all—cannot. It takes horrendous forces and pressures to change the density of a liquid. Now, when the bullet enters the paint cans, it brings a great deal of pressure with it. In the can with the air in it, the air acts like a cushion, or a shock absorber, so the water isn’t disturbed and the can doesn’t explode. But in the can full o
f water, the water can’t compress. So the extra pressure the bullet introduces in the water exerts a good deal of force on the walls and on the top of the can and the top blows off. As you may imagine, it’s really very dramatic and my students are always quite shocked.
Surrounded by Air Pressure
I always have a lot of fun with pressure in my classes, and air pressure is particularly entertaining because so much is so counterintuitive about it. We don’t even realize we are experiencing air pressure until we actually look for it, and then it’s just astonishing. Once we realize it’s there—and begin to understand it—we begin to see evidence for it everywhere, from balloons to barometers, to why a drinking straw works, to how deep you can swim and snorkel in the ocean.
The things we don’t see at first, and take for granted, like gravity and air pressure, turn out to be among the most fascinating of all phenomena. It’s like the joke about two fish swimming along happily in a river. One fish turns to the other, a skeptical look on its face, and says, “What’s all this new talk about ‘water’?”
In our case, we take the weight and density of our invisible atmosphere for granted. We live, in truth, at the bottom of a vast ocean of air, which exerts a great deal of pressure on us every second of every day. Suppose I hold my hand out in front of me, palm up. Now imagine a very long piece of square tubing that is 1 centimeter wide (on each side, of course) balanced on my hand and rising all the way to the top of the atmosphere. That’s more than a hundred miles. The weight of the air alone in the tube—forget about the tubing—would be about 1 kilogram, or about 2.2 pounds.* That’s one way to measure air pressure: 1.03 kilograms per square centimeter of pressure is called the standard atmosphere. (You may also know it as about 14.7 pounds per square inch.)
Another way to calculate air pressure—and any other kind of pressure—is with a fairly simple equation, one so simple that I’ve actually just put it in words without saying it was an equation. Pressure is force divided by area: P = F/A. So, air pressure at sea level is about 1 kilogram per square centimeter. Here’s another way to visualize the relationship between force, pressure, and area.
Suppose you are ice-skating on a pond and someone falls through. How do you approach the hole—by walking on the ice? No, you get down on your stomach and slowly inch forward, distributing the force of your body on the ice over a larger area, so that you put less pressure on the ice, making it much less likely to break. The difference in pressure on the ice when standing versus lying down is remarkable.
Say you weigh 70 kilograms and are standing on ice with two feet planted. If your two feet have a surface area of about 500 square centimeters (0.05 square meters), you are exerting 70/0.05 kilograms per square meter of pressure, or 1,400 kilograms per square meter. If you lift up one foot, you will have doubled the pressure to 2,800 kilograms per square meter. If you are about 6 feet tall, as I am, and lie down on the ice, what happens? Well, you spread the 70 kilograms over about 8,000 square centimeters, or about 0.8 square meters, and your body exerts just 87.5 kilograms per square meter of pressure, roughly thirty-two times less than while you were standing on one foot. The larger the area, the lower the pressure, and, conversely, the smaller the area, the larger the pressure. Much about pressure is counterintuitive.
For example, pressure has no direction. However, the force caused by pressure does have a direction; it’s perpendicular to the surface the pressure is acting on. Now stretch out your hand (palm up) and think about the force exerted on your hand—no more tube involved. The area of my hand is about 150 square centimeters, so there must be a 150-kilogram force, about 330 pounds, pushing down on it. Then why am I able to hold it up so easily? After all, I’m no weight lifter. Indeed, if this were the only force, you would not be able to carry that weight on your hand. But there is more. Because the pressure exerted by air surrounds us on all sides, there is also a force of 330 pounds upward on the back of your hand. Thus the net force on your hand is zero.
But why doesn’t your hand get crushed if so much force is pressing in on it? Clearly the bones in your hand are more than strong enough not to get crushed. Take a piece of wood of the size of your hand; it’s certainly not getting crushed by the atmospheric pressure.
But how about my chest? It has an area of about 1,000 square centimeters. Thus the net force exerted on it due to air pressure is about 1,000 kilograms: 1 metric ton. The net force on my back would also be about 1 ton. Why don’t my lungs collapse? The reason is that inside my lungs the air pressure is also 1 atmosphere; thus, there is no pressure difference between the air inside my lungs and the outside air pushing down on my chest. That’s why I can breathe easily. Take a cardboard or wooden or metal box of similar dimensions as your chest. Close the box. The air inside the box is the air you breathe—1 atmosphere. The box does not get crushed for the same reason that your lungs will not collapse. Houses do not collapse under atmospheric pressure because the air pressure inside is the same as outside; we call this pressure equilibrium. The situation would be very different if the air pressure inside a box (or a house) were much lower than 1 atmosphere; chances are it would then get crushed, as I demonstrate in class. More about this later.
The fact that we don’t normally notice air pressure doesn’t mean it’s not important to us. After all, weather forecasts are constantly referring to low-and high-pressure systems. And we all know that a high-pressure system will tend to bring nice clear days, and a low-pressure system means some kind of storm front is approaching. So measuring air pressure is something we very much want to do—but if we can’t feel it, how do we do that? You may know that we do it with a barometer, but of course that doesn’t explain much.
The Magic of Straws
Let’s begin with a little trick that you’ve probably done dozens of times. If you put a straw into a glass of water—or as I like to do in class, of cranberry juice—it fills up with juice. Then, if you put a finger over the top of the straw and start pulling it out of the glass, the juice stays in the straw; it’s almost like magic. Why is this? The explanation is not so simple.
In order to explain how this works, which will help us get to a barometer, we need to understand pressure in liquids. The pressure caused by liquid alone is called hydrostatic pressure (“hydrostatic” is derived from the Latin for “liquid at rest”). Note that the total pressure below the surface of a liquid—say, the ocean—is the total of the atmospheric pressure above the water’s surface (as with your outstretched hand) and the hydrostatic pressure. Now here’s a basic principle: In a given liquid that is stationary, the pressure is the same at the same levels. Thus the pressure is everywhere the same in horizontal planes.
So if you are in a swimming pool, and you put your hand 1 meter below the surface of the pool at the shallow end, the total pressure on your hand, which is the sum of the atmospheric pressure (1 atmosphere) and the hydrostatic pressure, will be identical to the pressure on your friend’s hand, also at 1 meter below the surface, at the deep end of the pool. But if you bring your hand down to 2 meters below the surface, it will experience a hydrostatic pressure that is twice as high. The more fluid there is above a given level, the greater the hydrostatic pressure at that level.
The same principle holds true for air pressure, by the way. Sometimes we talk about our atmosphere as being like an ocean of air, and at the bottom of this ocean, over most of Earth’s surface, the pressure is about 1 atmosphere. But if we were on top of a very tall mountain, there would be less air above us, so the atmospheric pressure would be less. At the summit of Mount Everest, the atmospheric pressure is only about one third of an atmosphere.
Now, if for some reason the pressure is not the same in a horizontal plane, then the liquid will flow until the pressure in the horizontal plane is equalized. Again, it’s the same with air, and we know the effect as wind—it’s caused by air moving from high pressure to low pressure to even out the differences, and it stops when the pressure is equalized.
So what’s hap
pening with the straw? When you lower a straw into liquid—for now with the straw open at the top—the liquid enters the straw until its surface reaches the same level as the surface of the liquid in the glass outside the straw; the pressure on both surfaces is the same: 1 atmosphere.
Now suppose I suck on the straw. I will take some of the air out of it, which lowers the pressure of the column of air above the liquid inside the straw. If the liquid inside the straw remained where it was, then the pressure at its surface would become lower than 1 atmosphere, because the air pressure above the liquid has decreased. Thus the pressure on the two surfaces, inside and outside the straw, which are at the same level (in the same horizontal plane) would differ, and that is not allowed. Consequently, the liquid in the straw rises until the pressure in the liquid inside the straw at the same level as the surface outside the straw again becomes 1 atmosphere. If by sucking, I lower the air pressure in the straw by 1 percent (thus from 1.00 atmosphere to 0.99 atmosphere) then just about any liquid we can think of drinking—water or cranberry juice or lemonade or beer or wine—would rise about 10 centimeters. How do I know?
Well, the liquid in the straw has to rise to make up for the 0.01-atmosphere loss of air pressure above the liquid in the straw. And from the formula for calculating the hydrostatic pressure in a liquid, which I won’t go into here, I know that a hydrostatic pressure of 0.01 atmosphere for water (or for any comparably dense liquid) is created by a column of 10 centimeters.
If the length of your straw was 20 centimeters, you would have to suck hard enough to lower the air pressure to 0.98 atmosphere in order for the juice to rise 20 centimeters and reach your mouth. Keep this in mind for later. Now that you know all about weightlessness in the space shuttle (chapter 3) and about how straws work (this chapter), I have an interesting problem for you: A ball of juice is floating in the shuttle. A glass is not needed as the juice is weightless. An astronaut carefully inserts a straw into the ball of juice, and he starts sucking on the straw. Will he be able to drink the juice this way? You may assume that the air pressure in the shuttle is about 1 atmosphere.
