[MUSIC] In this week's lesson, weight, contact forces including friction and the forces involved in stretching and compressing springs and other elastic materials. Contact forces are familiar because we can feel them almost directly. But will come back to this example later. But we will start by looking more closely at weight. We don't sense weight directly. I know this apple has weight because of the content force on my hand. However the two are not necessarily equal. The content force could even be zero. But weight of an object is the gravitational force exerted on it by a near by 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 due to the rotation of the earth and due to its orbit around the sun? Yes, those centripetal acceleration are much smaller than gravitational acceleration. So for this week, let's neglect those centripetal acceleration. With that approximation, and if we're near the surface of the Earth, and if we can neglect air resistance, all objects fall with the same acceleration, g, downwards. We've written Newton's first and second laws in a single equation, F total = ma. Where m is the mass. Mass is a property of a body, which 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 Second Law to our falling body. In free fall, no other falls, objects accelerate downwards at g equals 9.8 meters per second per second. As we saw, it follows that near the earth surface, an object's weight is approximately mg downwards. You might like to reflect on why that same constant mass is involved in both gravitation and inertia. We'll give a link if you ever think about it. Weight is related to mass and some people do confuse them. But, in fact, they are conceptually very different. Mass is a scalar quantity, its units are kilograms. An objects mass doesn't depend on gravity. On the other hand, weight is a force, the force produced by gravity, it's a vector It's units, a Newton and it's direction is down. An objects weight is proportional to its mass but it depends on what planet your on. It's proportional to the strength of the local gravitational field. An astronaut's mass is the same on Earth or on the moon. But his weight is six times smaller on the moon, which partly explains his unusual motion. One of the reasons that people often confuse mass and weight is simple. The dial on this gadget is 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, so the magnitude of the force applied by the scales equals the magnitude of my weight, which is 700 newtons. The scales read 72 kilograms. The scale displays the measured force divided by g. Note that it only works in mechanical equilibrium. Here I'm varying the force and the machine shows that it's varying. It's certainly not showing my mass, which is constant. On the moon, my mass would still be 72 kg. That I would weigh 120 newtons, [LAUGH]. So this stupid scales will read 12 kilograms, well, it practice that that doesn't cause problems because scales like this are only of the use on earth. We'll talk about the precarious situation of astronauts in orbit when we discuss gravity, but for now let's summarize. Mass, in kilograms is defined by how much an object is accelerated by a given force. Weight, in newtons, is proportional to mass but it's also proportional to the local gravitational field. It depends on what planet you're on. Simple, but important. Let's check out those ideas with a short quiz. Now for another puzzle, my weight is 700 Newtons but I'm not accelerating so from Newton's second law. The total force on me is 0. Therefore at the moment, the floor must be exerting an upwards force of 700 newtons. The floor force is not always 700 newtons. It can be greater than 700 newtons, when I'm exhilarating upwards during takeoff, or also landing. It can ever be zero, when I'm airborne. 700, greater, 0, greater and then, back to 700 Newtons. [SOUND] So there's the puzzle. Why is the floor force 700 Newtons now while I'm standing still? [LAUGH] For me it's important If the flow force was were consistently greater, let's say 100 Newton a hard accelerator upwards. If it were 600 Newton, I had fall through the floor. So puzzle for you, why does normal force equals my weight? If you said Newton's Third Law, then you'd better go back and revised that part of last week's lesson. Newtons Third Law just says, that my feet exert a force equal and opposite to the floor's force. We've seen that that can be greater than 700 newtons when I take off or land or even zero. Newton's third law also tells me that the weight of the Earth in my gravitational field is equal and opposite to my weight in its gravitational field. I attract the Earth upwards with a force of 700 newtons. You'll be happy to know that my gravitational attraction to the earth is balanced by the average force exerted by my feet. So the earth's orbit is not affected, not even slightly. But back to the original problem. Why do the external forces on me average to zero? How does the floor know to exert 700 newtons? I mean, how smart can a floor be? Does it know what I had for breakfast this morning. I promise we'll come back to this puzzle, after the next section. But to keep the suspense up, it's time for a quiz. [MUSIC]
