Instructor Are you ready for the last force in out unit on forces? I guess we ve saved the most common one for last. That s the force of gravity.

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1 Physics 505 Gravity (Read objectives on screen.) Are you ready for the last force in out unit on forces? I guess we ve saved the most common one for last. That s the force of gravity. Ouch! Legend has it that Isaac Newton discovered the force of gravity when an apple hit him on the head. Not true!! Newton did spend a lot of time in his family s apple orchard in His college was closed because of the great plague that year. Probably what happened is that Newton did observe apples falling in that orchard. And he did begin to ponder why apples fell to the ground but the moon didn t fall. These observations are what led him to his great discovery, not a knock on the noggin with an apple Newton did not discover the force of gravity. What he did discover is that the force of gravity is universal. The force that pulls an apple to the earth is the same force keeping the moon in orbit around the earth. In fact, there is an attractive force of gravity between this apple and me. It s very, very small, but it s there. The earth and I attract each other, too, and that force is not so small to me. It s called my weight. The fact that Newton discovered is that everything in the universe pulls on everything else. Why does this happen? No one knows. It s just one of those mysterious facts of the universe. And Newton s Law of Universal Gravitation is a beautifully simple rule that governs this attraction. (green chalkboard on screen) Isaac Newton discovered that gravity is universal. All objects attract each other to some degree. The force of attraction between two objects depends on two factors. First factor: Gravity is directly proportional to the masses of the objects. And, the second factor: Gravity is inversely proportional to the distance between the objects squared. In mathematical form, the law is F sub g equals capital G times m sub one times m sub two, divided by d squared. Capital G is called the universal gravitation constant. It is the same number, whether the objects are as large as planets or as small as marbles. The value of G is six point seven times ten to the negative eleventh power. The strange looking unit is necessary for all the units in the equation to cancel out so that newtons equals newtons. Let s look at this important equation more closely. First of all, G is called the universal gravitation constant for a reason. It s the same for the apple and me, for me and the earth, and for the earth and the moon. Notice how small the value is. Ten to the negative eleventh power is very, very small. This means that the force of gravity is relatively weak. Gravity is one of four fundamental forces in the universe. Another force is electromagnetic and the two others are kinds of nuclear forces. Of all these forces, gravity is the weakest. That probably comes as a surprise to you because the force of gravity is so familiar and important to you.

2 But watch how easy it is to overcome gravity. This magnet can easily overcome the force of gravity to make the paper clips jump off the table and stay attached to the magnet. The other thing I want you to notice about the equation is the d squared on the bottom. This tells us the force of gravity is inversely proportional to the distance between the two objects squared. If you double the distance, the force is one fourth as great. Now does this mean that if I climb a ladder from two feet above the earth to four feet, my weight would be divided by four? (diagram of earth on screen) Newton s Law of Universal Gravitation states that there is a force of attraction between any two particles. So every particle of mass in the man is attracted by every particle of mass in the earth and vice versa. The result is that an object acts as though all of its mass is concentrated at one point called the center of mass or center of gravity. The force of attraction between the man and earth are between his center of gravity and the earth s center of gravity. In the mathematical form of the law of gravity, the d represents the distance between the centers of gravity of the man and earth. Doubling d in the equation would mean doubling this already very large number. Now let me ask my question again. If I climb a ladder from two feet above the ground to four feet, will my weight be divided by two squared or four? No!! I haven t really doubled d, have I? That s because d is the distance between my center of mass, sometimes called center of gravity, and the earth s center of mass, which is at its center. I d have to climb a very tall ladder to double d, wouldn t I? Well, we have this important equation, so what should we do with it? I have an idea. Let s do some math!!! The problems we ll be doing are nothing new, so you try a couple and then we ll go over them. For one problem, you ll need the mass of the earth and its radius, so get these down in your notes. These are two of those numbers that will be given to you when you need them. (text on screen) Local Teachers: Turn off tape and give students problem set number one from facilitator's guide. (Pause Tape Now graphic) (text on screen) The first problem is just a plug and chug. We plug in the value of G here, the woman s mass here, the mass of the earth here, and the distance between the woman and the earth s center of mass here. You should chug out an answer of 550 newtons. Watch how the units cancel. Meters squared cancels on top and bottom, and so does kilogram squared. If you didn t get the right answer, chances are you forgot to square the distance and got a weight of 3.4 X 10 9 N. That would not be sane or reasonable would it? It s OK to make mistakes, but you should be able to catch many of them by doing a sanity check on your answer. 2

3 Now some of you may be wondering how we know the mass of the earth. You can read about different experiments performed by Henry Cavendish, and Phillip von Jolly to determine the value of G. Since d, the radius of the earth was known, once G was determined, the mass of the earth could be calculated using Newton s Law of Universal Gravitation. For now, let s check out the second problem. (text on screen) When an astronaut does a space walk far above the earth s surface, why does he or she feel weightless? The first part of this problem helps to explain. If the distance between the objects is multiplied by ten, the force of gravity is divided by 10 squared or 100. As the distance between the astronaut and the center of the earth increases, the gravitational attraction or weight decreases dramatically until it s so small that it s negligible. In part b, we double one mass, triple the other, and triple the distance. Two times three divided by three squared is six ninths or two-thirds the original force of gravity. Before I give you a chance to practice some universal gravitation problems, I want to tell you about a dramatic example of just how universal the force of gravity is. Put your pencils down and just listen. If everything in the universe pulls on everything else, then the planets pull on each other, too. This is evident when a planet in its orbit around the sun, gets close to another planet. When this happens, there is a small wobble in both planets orbits, called a perturbation. Well, a perturbation in the orbit of the planet Uranus could not be explained by the influences of the other planets close to it. In 1846 two astronomers took pencils and paper and applied good old Newton s Law of Universal Gravitation. And each predicted that the cause of the perturbation was an undiscovered planet beyond Uranus. They sent letters to their local observatories with instructions about where in the sky to look to discover the new planet. It took less than thirty minutes of searching to discover the planet Neptune. Isaac Newton would have been so proud! (Read Fact or Fiction statement on screen) That s it, as far as what you re required to know about gravity for the next test. But we have some really cool stuff we d like to tell you about g force, weightlessness, and artificial gravity. This won t be on the unit test, but just for your information. So how about this? After you show what you know, go ahead and practice solving more problems and take your unit test on forces. Then come back and we ll have some fun. And now it s time to SHOW WHAT YOU KNOW! Jot down your choice for each question. After the program, your local teacher will go over the correct answers with you. (Pause Tape Now graphic) 3

4 (Read Show What You Know questions on screen) (Pause Tape Now graphic) (astronaut on screen) Why do astronauts in orbit feel weightless? Without the force of gravity, would they even be in orbit? After all, the gravitational attraction of the earth furnishes the centripetal force needed to keep the satellite going in a circle. Why do you feel weightless on a free-fall ride at an amusement park? Without gravity, would you be falling? And why do you feel heavier when an elevator starts moving upward? If you stood on a bathroom scale in that elevator, would it record your actual weight or the weight you feel? Those are interesting questions, aren t they? It seems that our ideas of weight and weightlessness are a little confused. That s because we re almost always in contact with the earth and have been all our lives. So we take gravity for granted. In fact, we do not really feel the force of gravity. What do we feel and mistake for gravity or weight? Let me give you an example. Right now, I can feel myself pressing against the floor and I interpret this as weight. What I am actually feeling is the force being applied to me by the floor. It s an action-reaction thing. And as long as I stay at rest or even in uniform motion, the net force on me is zero. That means the support being applied to me by the floor is equal to my weight. Now let s pretend that I m in an elevator, and instead of standing on the floor, I m standing on a bathroom scale. The scale will read the force applied to support me. Sometimes this will equal my weight and sometimes it won t. It will show what I feel, sometimes heavier and sometimes lighter than my real weight, depending on what the elevator and I are doing. A force diagram will show what I mean! Remember, this is just for fun so put your pencils down and just watch. (drawing of man in elevator on screen) In this first picture the elevator is standing still or it is moving uniformly up or down. Unless the elevator is glass, our scientist won t be able to tell whether or not he is moving. Either way, the net force on him is zero, so the force applied by the scale will equal his weight. And remember, it s this applied force, represented by the red arrow, that the scale will show and that the scientist will feel. In the second picture, the elevator is accelerating upward. Notice that we ve drawn the same blue arrow down for the scientist s weight since that hasn t changed. But since acceleration is up, the net force must be up, too. That s Newton s Second Law. So the applied force up must be greater than the scientist s weight. He will feel heavier and the scale reading will be greater than his real weight. In the next situation, the elevator is accelerating down. You know how that feels. Let s see why. The net force must be down, so the weight is greater than the upward applied force. Our scientist feels lighter and the scale reading will be less than his real weight. 4

5 Now, heaven forbid, what if the cable breaks and the elevator, our scientist, and the scale are all in free-fall. Now the net force on the scientist is his weight, and the acceleration will be 9.8 m/s 2. The scale is falling, too, so it cannot apply any upward force to support the man. The scale reading will be zero and the scientist will feel weightless. If you ve ever been in free-fall, you know that feeling of your stomach in your throat. That s because your diaphragm, which usually supports your organs, is falling, too, so the support isn t there. So you see that accelerated motion produces situations where we feel different. Physicists call these non-inertial frames of reference. If you re in an accelerating vehicle, whether it s falling, speeding up, or turning a corner, you will experience feelings that seem very real, like the fictitious force that seems to push the passenger to the right when the car turns left. Test pilots describe g forces. Two g s means a pilot will feel twice as heavy as he or she actually is. This happens when the plane is accelerating so fast that the applied force upward is twice the pilot s weight. And zero g s means that the plane is falling so that the applied force upward is zero. (astronauts on screen) For the movie, Apollo Thirteen, the weightless scenes in the space capsule were filmed in an empty cargo plane, using what pilots call boom and zoom. They pull the nose of the plane way up as they boom up and then tip it down to zoom down, creating thirty seconds of zero g conditions. So the weightless scenes were filmed, thirty seconds at a time. Real astronauts were trained in the same kind of cargo plane, which they affectionately called the vomit comet. (diagram of space ship on screen) In space, far from the earth s gravitational pull, artificial gravity can be produced by acceleration. For example, if the ship is accelerating in this direction, and an astronaut releases a ball, it will stay still while the rocket ship accelerates out from under it. But to the astronaut, it will appear that the ball has fallen. And if the acceleration 9.8 m/s 2, it will seem as if the astronaut is back home on earth. And this end of the ship will always seem to be the ground, no matter which direction the ship is moving. Keeping the space ship accelerating to make the passengers feel normal would take too much fuel, but there s another way to simulate gravity. Let s pretend that a tiny boy is in this cup. If I spin the cup in a circle the boy will misinterpret his own inertia as a force pulling him toward the outside of the circle. To the boy, the bottom of the cup will seem like the ground. If he drops something, it will fall to this ground. People in the future may live in a space habitat that looks like a huge rotating bicycle wheel, about two kilometers in diameter. If the wheel spins with a centripetal acceleration of 9.8 m/s 2, the people in it will live under earth-like gravitational conditions of one g. It might be fun to discuss how life would be different, though. For instance, which direction would be up? Think about it. 5

6 Does all this talk of space colonies seem unthinkable to you? I wonder what Isaac Newton would have thought about the space travel we ve achieved so far. After all, it all started with his ideas.. In fact, these astronauts gave him credit in a transmission to earth. Watch. (astronauts on screen) I told Michael you guys are up there, and he said, Who s driving? That s a good question. I think Isaac Newton is doing most of the driving right now. That s it for this program. When you come back, we ll talk about some really fun subjects: collisions, explosions, karate chops, roller coasters and much more. And you ll learn how this fun toy works. It s all part of our study of work, energy, and momentum. See you soon. 6