[MUSIC] In this week's lesson, weight, contactforces including friction, and the forces involved in stretching and compressingsprings, and other elastic materials. Contact forces are familiar,because we can feel them almost directly. But, we'll come backto this example later. But, we'll start by lookingmore closely at weight. We don't sense weight directly. I know that this apple has weightbecause of the contact force on my hand. However, the two are notnecessarily equal. The contact force could even be zero. The weight of an object isthe gravitational force exerted on it by a nearby astronomical object,such as the earth. See, it even works down under. More on gravity in week eight. But first, some revision. How big are the accelerations dueto the rotation of the earth and due to its orbit around the sun? Yes, those centripetalaccelerations are much smaller than gravitational acceleration. So, for this week, let's neglectthose centripetal accelerations. With that approximation and if we neededthe surface of the earth and if we can neglect air resistance, all objects fallwith the same acceleration, g, downwards. We've written Newton's first andsecond laws in a single equation. If total equals ma where m is the mass. Mass is a property of a bodywhich we defined last week by its resistance to acceleration or its inertia. The mass actually depends on how many and what sort of atoms make up the body,and almost nothing else. Let's apply Newton's secondlaw to our falling body. In free fall, no other force, objects accelerate downwards at g equals9.8 meters per second per second. As we saw, it follows that near the earth's surface an object'sweight is approximately mg downwards. You might like to reflecton why that same constant mass is involved in both gravitation andinertia. We'll give you a link ifyou want to think about it. Weight is related to mass andsome people do confuse them. But in fact,they're conceptually very different. Mass is a scale of quantity. Its units are kilograms. An object's mass doesn'tdepend on gravity. On the other hand, weight is a force, theforce produced by gravity, it's a vector. Its units are newtons andits direction is down. An object's weight isproportional to its mass, but it depends on what planet your on. It's proportional to the strengthof the local gravitational field. An astronaut's mass is the sameon the earth or on the moon. But, his weight is six times smaller on the moon [LAUGH] which partlyexplains his unusual motion. One of the reasons that people oftenconfuse mass and weight is simple. The dial on this gadgetis marked in kilograms. But it doesn't measure mass,it measures force. I push with a force of, say,300 newtons, and it reads 30 kilograms. So it just measures the force,divides by 9.8, and calls that mass. When I stand on the scales and if I'm in mechanical equilibrium,then here's my free body diagram. No acceleration, sothe magnitude of the force applied by the scales equals the magnitude ofmy weight, which is 700 newtons. The scales read 72 kilograms. The scale displays the measuredforce divided by g. Note that it only works inmechanical equilibrium. Here, I'm varying the force andthe machine shows that it's varying. It's certainly not showing my mass,which is constant. On the moon, my mass would still be 72kilograms, but I'd weigh 120 newtons. [LAUGH] So these stupid scaleswould read 12 kilograms. Well in practice thatdoesn't cause problems, because scales like theseare only ever used on earth. We'll talk about the peculiarsituation of astronauts in orbit when we discuss gravity. But for now, let's summarize. Mass, in kilograms, is defined by how muchan object is accelerated by a given force. Weight, in newtons,is proportional to mass, but it's also proportional tothe local gravitational field. It depends on what planet you're on. Simple, but important. Let's check out thoseideas with a short quiz. Now for another puzzle. My weight is 700 newtons,but I'm not accelerating. So, for Newton's second law,the total force on me is zero. Therefore, at the moment, the floor must be exertingan upwards force of 700 newtons. The floor force is not always 700 newtons. It can be greater than 700 newtons whenI'm accelerating upwards during takeoff or also landing. It can even be zero when I'm airborne. Seven hundred, greater zero, greater,and then back to 700 Newtons. [SOUND] So there's the puzzle. Why is the floor force 700 Newtonsnow when I'm standing still? For me, it's important. If the floor force wereconsistently greater, say 800 newtons, I'd accelerate upwards. If it were 600 newtons,I'd fall through the floor. So, puzzle for you. Why does the floor force equal my weight? If you said Newton's third law,then you'd better go back and revise that part of last week's lesson. Newton's third law just says thatmy feet exert a force equal and opposite to the floor's force. And we've seen that that can be greaterthan 700 Newtons when I take off or land or even zero. Newton's third law also tells me that theweight of the Earth in my gravitational field is equal and opposite to myweight in its gravitational field. I attract the earth upwardswith a force of 700 Newtons. You'll be happy to know that mygravitational attraction of the earth is balanced by the averageforce exerted by my feet. So the earth's orbit is not affected,not even slightly. But, back to the original problem, why dothe external forces on me average to zero? How does the floor knowto exert 700 newtons. I mean, how smart can a floor be? Does, does it know what I had forbreakfast this morning? I promise we'll come back to thispuzzle after the next section. But, to keep the suspense up,it's time for a quiz.