As I get ready for classes to start tomorrow I felt it was time for another physics teaching moment. (and I have re-read and re-written this a few times, and I still feel like I ramble too much).
Most of us out there think that these two words are the same thing. I can’t blame you, or my students, for thinking this. It happens all over the place: books, conversations, the news, classrooms, even in science classes and from some scientist. Most people have never had explained to them correctly. They have either had it explained incorrectly; given a definition that is too specific and therefore created confusion, or have never had it explained and have created a definition based on its usage. And as I just said the usage is such that it is easy to think they are the same thing.
Well, they aren’t.
So, what are they? Well let’s tackle them separately.
Mass – to me, this is the easy one. It is stuff. It is the amount of stuff that makes up an object. It is measured in kilograms, or grams if you are a chemistry person, but kilograms is the proper scientific unit. That is it. There is nothing more to it. If it exists*, then it has mass. You exist therefore you have mass. Mass is a given for an object no matter where you are in the universe. You can be here on Earth, on Mars, floating in the void of space, floating in a spaceship just above the Earth, on the Sun, ANYWHERE, and your mass is the same. Let Q bounce you around to all those places and you will find that your mass stays the same (and protect you from burning up on the sun and the whole need air thing in the other places). You can change you mass by eating, not eating, exercising, etc. That changes the amount of stuff in you.
Weight – this is the trickier one, and where people tend to get things mixed up. Frist off, weight is a force. It isn’t a given by existing, it requires more. I am going to start with the most common mistake because it isn’t exactly a mistake. Student M says, “Weight is how hard gravity pulls you down.” Well, that is a force, good. But it is the force of gravity pulling you towards the Earth, and this is the start of a right answer, but it is missing something key. What is gravity doing? Where do we get this idea that gravity is weight? Well, it comes from our bathroom scales. You, me, whoever can get on a scale and read their weight. Where does that value come from? It comes from the fact that gravity is pulling you onto the scale. But what is the scale actually telling you? It isn’t telling you how hard gravity is acting on you. If you place the scale on a vertical wall, go ahead and try it, and push against it, will it give you a reading? Yes, it will. Is that a weight? Is it your full weight? Well, if scales tell you weight then that value must be a weight, right? But where is gravity here? It isn’t causing a value on the scale, your pushing into it is giving you the value. Gravity is downward and the scale is working in and out from the wall, so gravity doesn’t affect the scale here in its value reading, only your push does.
So, what is the scale telling you? It is telling you how hard you are pushing right? Yes, sort of. It is telling you how hard it has to push BACK on you. This comes straight from Newton’s third law of motion: For every force there is an equal and opposite force. So, when you push on the scale, the scale pushes back on you with an equal amount, but in the opposite direction (toward you). This means that a scale reads what is called a normal force (sometimes called a contact force, but I like normal force better). That is what weight truly is. Weight is a normal force. It is that “simple.” So, when you stand on a scale, on flat ground, on Earth, and not accelerating, then the scale is telling you how hard gravity is pulling you down since the scale is preventing you from accelerating through it by applying a normal force up (back) on you. If you put the scale on an incline, it still pushes back on you, but it won’t read your full weight anymore, it will read less since you have shifted the axis from straight down and gravity is now acting in a different direction on your than the scale is (you may need a rope to hold you on the scale to prevent you from falling off if the incline is too steep). Your mass hasn’t changed, but your weight has. So, the scale is reading a normal force.
Space is another great place to go and look at this. People on the international space station (ISS) are said to be “weightless”, and they are. But it isn’t because there is no gravity. There is gravity, in fact there is still a lot of gravity. The acceleration of gravity on Earth’s surface is around 9.8m/s2. And it gets weaker the further you are from the center of the Earth. At the altitude of the ISS the acceleration due to the Earth’s gravity is still 8.72m/s2. That is still 89% of what it is at sea level. So, they should have weight if weight is tied to gravity. But they are weightless because no surface can push back on them to give them a weight, this is because everything, including the astronauts, are all accelerating at the same rate toward the Earth. It is like being in an elevator, if you take a scale on an elevator you will find that when it accelerates up or down your weight will change while it is accelerating.
Gravity is not the cause of weight. Weight is due to a normal force acting on you. We tend to only think of the total normal force acting on an object as that object’s weight. This again leads back to reasons why weight and mass tend to be tied together. They are totals, but they don’t need to be.
So, weight is a force and it measure in Newtons or Pounds. Mass is measured in kilograms. They are not the same thing. Scales tell you weight not mass**.
Speaking of pounds. You got to love the USA don’t you. We use pounds for telling us weight, and never tell people that pounds is a measure of force. Unless you are a mechanic, scientist, or engineer, you probably haven’t realized this. Ok, anyone who understands a torque wrench and what the units of foot*pounds (ft*lbs) means will understand that pounds is a force. Pounds is a measure of how HARD something pushes. Our issue is that pounds is so tied to the concept of how much stuff something is made of that it again muddies the waters of the difference between mass and weight. If only we could switch to Newtons as the unit of force we use, but that would mean using the metric system, and we all know that the USA is too stubborn to ever do that… (well we can ray can’t we).
* photons are the exception to the rule here. They exist but they don’t have mass. They must exist so you can read this blog; unless you are having it read to you or you are reading it using brail (that is cool if you are). You can blame special relativity for this fact.
** scales in some parts of the world give you your “weight” in kilograms. They are calibrated to work with an acceleration of 9.8m/s2 and then do the conversion to kilograms from the Newtons that it is measuring. If you take one of those scales to a very high mountain or to another planet without calibrating it, then it will give you an incorrect number (so will pound scales as well, but that is a different issue).