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Physics: Weight vs Mass


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About this Lesson

  • Type: Video Tutorial
  • Length: 9:16
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 99 MB
  • Posted: 07/01/2009

This lesson is part of the following series:

Physics (147 lessons, $198.00)
Physics: Dynamics (15 lessons, $24.75)
Physics: Newton's Three Laws (7 lessons, $8.91)

This lesson was selected from a broader, comprehensive course, Physics I. This course and others are available from Thinkwell, Inc. The full course can be found at The full course covers kinematics, dynamics, energy, momentum, the physics of extended objects, gravity, fluids, relativity, oscillatory motion, waves, and more. The course features two renowned professors: Steven Pollock, an associate professor of Physics at he University of Colorado at Boulder and Ephraim Fischbach, a professor of physics at Purdue University.

Steven Pollock earned a Bachelor of Science in physics from the Massachusetts Institute of Technology and a Ph.D. from Stanford University. Prof. Pollock wears two research hats: he studies theoretical nuclear physics, and does physics education research. Currently, his research activities focus on questions of replication and sustainability of reformed teaching techniques in (very) large introductory courses. He received an Alfred P. Sloan Research Fellowship in 1994 and a Boulder Faculty Assembly (CU campus-wide) Teaching Excellence Award in 1998. He is the author of two Teaching Company video courses: “Particle Physics for Non-Physicists: a Tour of the Microcosmos” and “The Great Ideas of Classical Physics”. Prof. Pollock regularly gives public presentations in which he brings physics alive at conferences, seminars, colloquia, and for community audiences.

Ephraim Fischbach earned a B.A. in physics from Columbia University and a Ph.D. from the University of Pennsylvania. In Thinkwell Physics I, he delivers the "Physics in Action" video lectures and demonstrates numerous laboratory techniques and real-world applications. As part of his mission to encourage an interest in physics wherever he goes, Prof. Fischbach coordinates Physics on the Road, an Outreach/Funfest program. He is the author or coauthor of more than 180 publications including a recent book, “The Search for Non-Newtonian Gravity”, and was made a Fellow of the American Physical Society in 2001. He also serves as a referee for a number of journals including “Physical Review” and “Physical Review Letters”.

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In everyday language, the words "mass" and "weight" are often used interchangeably. If you go to England and you ask the grocer, "How much sugar am I getting?" They might say, "Oh, let me weigh it. Yeah, it weighs about a kilogram," and that seems like perfectly ordinary use of language, and as a physicist we have to be a little bit careful. Mass and weight really need to be distinguished. They are different things. Newton's second law says F = ma. The quantity which you're interested in when you're working dynamics problems is the mass of the object.
So mass, it's a familiar concept. We've talked about how you compare this mass to a standard kilogram, and you say, "Oh yes, this is a mass of 1 kilogram," and you can then calibrate others and say, "This is a mass of .2 kilograms," and that's exactly what we mean by the mass in this formula. It's a measure of how much stuff there is. Here you can think of it as a measure of the inertia, how hard it is to get it accelerating from a given force.
Weight is something different. Weight is what you obtain - when you put something on a scale, for instance, you are measuring its weight, and this scale is calibrated in metric, and it says 10 - this was one kilogram - and then I look carefully and it says 10 Newtons. And I say, "Oh, I think that makes sense." Let's define the word "weight." We need to come up with a rigorous definition, and various people have various different definitions, but the one that's most commonly used is this. Weight is defined to be the force of gravity exerted on an object. So it's a little bit of a subtle story about what's going on in this scale and we need to think about it. This scale is measuring the force on a spring and the weight of the object is defined to be the force of gravity exerted on the object.
Let's think about what Newton's law tells us about weight. Newton's law says F = ma, and supposing that I were to take an object, a 1 kilogram object, and release it. Imagine no air friction, so it's in free fall, and Galileo tells us that like any object near the surface of the earth, it will begin to accelerate downwards, and the magnitude of acceleration will be 9.8. So I look at Newton's second law and I say, "What is the force of gravity on this object?" If I let it go it's the only force acting on it of any significance, and so the force will be the force of gravity. That would be the weight, and the right-hand side would be m times its acceleration, which is g, so the weight of an object is just - we call it W for weight, it's a vector, and it's got magnitude mg and how shall I write its direction? I can sort of symbolically give you an indication that it's towards the center of the earth. Weight is a force. It's got a magnitude and a direction. This object's weight is - you can think of it as an arrow which points towards the center of the earth.
So my mass is 60 kilograms, and what do I weigh? Well, my weight is m times g, so you take 60 kilograms and you multiply it by 9.8, which is roughly 10. So my weight is approximately 600 Newtons. This sugar, which we weighed, its weight is 10 Newtons and weight is equal to mg, so 10 Newtons is equal to m times... Well, it's a little bit less than 10. In fact, it's about 9.8. Its mass is almost exactly one kilogram, and that's what it's supposed to be. Its mass is a kilogram, its weight is 9.8 Newtons.
In the old-fashioned British system, weight, that's a force, was measured in units of pounds, so you would properly say that my weight is 138 something pounds and my mass is - well, in the metric system it's 60 kilograms, in the British system you measure mass in slugs. It's a great unit. We'll never use one.
If you were to go off into the space shuttle and hold some lead bricks and try to juggle them - it would be kind of sideways juggling, because everything's floating around in there - what would it feel like? Are they heavy on the space shuttle? That's an interesting question. If you set them on a scale they float away. So it would appear that they were weightless. We'd say the apparent weight on the space shuttle is zero; however, there is still gravity acting, even when you're up in the space shuttle. It's a little bit less than it is down here on earth, but there's still gravity. There is still a weight. If you start to juggle them, you'd say to yourself, "Yeah, but come on, they're floating around. Isn't it easy to juggle them?" And irrespective of what the force of gravity is on them - that's actually quite irrelevant when you're sliding them back and forth between your hands sideways - what matters is their mass. It's a universal property of an object. It's got a certain mass, it's got that mass here on earth, they're hard to juggle on the earth because of two things, because they've got a lot of inertia so it's hard to get them moving, and because there's this extra force of gravity pulling them down.
When you're on the space shuttle they still have the same mass, and if it's a large mass, they still have a lot of inertia up there. And so it's hard to get them moving, even though you don't have to worry so much about the effect of gravity, you still have to worry about the fact that they're massive. If I was to go on the moon and walk around - you've seen pictures of astronauts, they're bouncing around up there. They have a weight which is approximately 1/6 of their weight on the earth. Why is that? Well, this formula is only true near the surface of the earth where objects accelerate with 9.8 . When you go near the surface of the moon, the force of gravity there is different and it's smaller. The moon is smaller than the earth, and so the idea of this formula would still be correct, but you would have to use the correct acceleration of gravity on the moon, and so you would discover that if I go up there with my mass, that's still 60 kilograms. My weight would be about 1/6 of my weight on earth. So instead of 600 Newtons I will weigh approximately 100 Newtons on the moon.
So the concept of weight is an important one. Distinguishing weight and mass is obviously important if you're going to use Newton's second law. You want to plug in the mass, not the weight on the right-hand side. Let me just do one quick example of a simple physical situation where we talk about forces and Newton's law. Here's an object, something sitting on the table. So here's my little picture, an object sitting on the table. What are the forces acting on this object? First of all, does it have a weight? The answer is absolutely yes. Our definition of weight is the force of gravity on the object. It's not accelerating, but it still has a weight. The weight is mg. It's the force of gravity on the object. So here's this object with a force of gravity, which we label weight, and the magnitude of that arrow, the magnitude of weight is given by the formula mg. Now, why isn't it accelerating down? Well, there's a table underneath it, and the table must be pushing up. When I push down on a table, the table pushes back up on me. There is definitely an upward force. I might call it the force on the object by the table, and we'll talk more about this kind of force in future lectures. How do I know it's there? I know it's there by Newton's second law. The net force on this object is equal to mass times its acceleration, and it's not accelerating. It's just sitting there. So the net force must be zero.
This force and this force are balancing. This one is there and it's just being balanced by another force. So when you think about weight, it's the force of gravity on an object. As long as you're near the surface of the earth, it's always going to be given by the simple formula, mg, no matter whether it's sitting still or moving around near the surface of the earth. The magnitude of weight is mg, and when you draw diagrams involving forces, it's always going to be there. You can't get away from gravity. You can't in any way hide from it. Every force diagram like this that we draw, you will almost always have, if you're being careful, a weight, which points down with negative energy.
Newton's Three Laws
Weight Page [2 of 2]

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