We begin this section by putting gravity in context with the other forces around and within us and we'll end the chapter by putting Newtonian mechanics in context and mentioning its limitations. We see the effects of gravity all around us yet we don't feel it. My hands are supporting my weight now but the forces I feel in my hands are due to the forces the bench exerts, forces which are only indirectly due to gravity. Contact forces, that's normal plus friction, are the result of electrical forces as are spring forces and nearly all of the forces we notice directly. Magnetic forces are related to electrical forces. We can think of magnetism as a small correction we make to electrical forces when the electric charges are moving with respect to the observer. And yes, we'll give you a link about that. As our calculations have told us, gravity is an extremely weak force. I was joking just then. Consider two electrons. They attract each other by gravity but they repel because of the electric force which is stronger than the gravitational attraction by a ratio of four by 10 to the 42. Yes, 10 to the 42. That's huge. Which raises the question - why then does gravity beat electricity on the astronomical scale? Yes, both gravity and electric forces have very large, perhaps infinite range. However, macroscopic objects always have approximately equal amounts of positive and negative charge so electric forces almost completely cancel on a large scale. There are also nuclear forces. These have a tiny range which is why we never experience or observe them directly. They're important, however. Without them, the only stable nucleus would be hydrogen. So, no stars, no planets, no physicists. Help! Turn those nuclear forces back on! Thank you. On the scale of planets and stars, all we need are Newton's laws of motion and his law of gravity. All of our space exploration has been calculated to fabulous precision using just Newton's laws. But now it's time to warn you about the limitations to Newton's laws and to give you an idea of when it's safe to use them. Newtonian mechanics is fine provided that the speeds are very much less than that of light. At speeds comparable with c, we must use Einstein's relativity. And to put that in perspective, a jet airliner travels at a bit less than a millionth of the speed of light. Newton's gravity also becomes imprecise in extreme conditions. It's fine providing that the magnitude of the gravitational potential energy is much less than mc squared. Otherwise, we must use Einstein's theory of gravity called general relativity. And to put that in perspective, potential energy over mc squared at the Earth's surface is less than one in a billion. Important to note however, that applications like satellite navigation require much higher precisionthan one part in a billion. So relativistic calculations are absolutely necessary. On the small scale of the quantum world, Newtonian mechanics is not so much erroneous as irrelevant. Quantum calculations introduce Planck's constant h. Quantum phenomenon become important when momentum times size is comparable with Planck's constant. This is usually okay for whole molecules but it's almost never okay for electrons. Further, the last calculation that you did shows a problem on a galactic scale. To explain the rotation of galaxies we have to imagine some new form of matter, dark matter, or else abandon Newtonian mechanics on that scale. Astronomers and cosmologists generally favor the former. Finally, on the largest observable scale it seems that the rate of expansion of the universe is accelerating, which is exactly opposite to the prediction of Newtonian gravity. Don't be worried by these limitations; instead be excited. There is still more interesting physics to be discovered perhaps by you. In week one, I mentioned four interviews I did to put Newtonian mechanics in context. Brian Schmidt is one of the discoverers of the accelerating expansion of the universe. Michelle Simmons works in quantum electronics. Both outside the applicability of Newton's laws. And I also interviewed Alex Bulgakov and Jasper Wolfe, two engineers who confidently used Newtonian mechanics in some very interesting situations. Have a look at those if you haven't done so already. Well, this is the last lesson. There's a quiz and a test to come but that's the end of this course. Wow! What are we gonna do? In a normal physics course Newtonian mechanics would be followed by sections on oscillations, waves, sound, light, et cetera. We do have multimedia resources in these areas and we'll give you links to those. By the way, waves and sound takes you to my area of research on the physics of the voice, the ear, and musical instruments and we have a big website on that, too. But of course, there's a whole universe of physics and its applications. And we hope that you will be looking at the physics around you with a new, analytical eye. Perhaps you're doing this course because you will study to become a scientist, an engineer, technologist, or a teacher, which is great, because the world needs those. However, whatever you do after this, we wish you good studies, a good career, and a good life.
