Homeschool Physics Curriculum

Today's topic, mass and weight, is a beefy one, so I've got two classes scheduled for it. I hope this can clear up any confusion that exists between these two different units of measure, maybe even before any confusion gets started. Mass, as we learned in the beginning of the course, is the amount of matter an object contains, while weight is generated by the force of gravity pulling an object's mass down towards the center of the Earth. On Earth, of course, the object that generates gravitational pull, and so generates weight, is the Earth itself. Now, the more matter something has, the more matter the force of gravity has to pull downward on, and so the more weight that generates. A car weighs more than a tennis ball because the car contains more matter for gravity to pull down on than the tennis ball has. The SI unit for the amount of matter is the gram and also the kilogram, while the SI unit for weight is newton. If we were in any country other than America and I asked you how much you weighed, you'd go and step on a scale that looks like this. Note though, that the units are in kilograms. If kilograms are units for the amount of matter something contains, why are scales, which measure weight, marked in units of kilograms everywhere on the planet besides the United States? And in weightlifting, powerlifting and Olympic lifting competitions around the world, including the United States, the amount of weight lifted is reported in kilograms. So why? Well, the answer leads us into a great foundational understanding of physics, and we'll spend the rest of the class learning why. An important aspect of this matter and mass discussion is to keep in mind how important density is. The bale of cotton on the left and the gold bar on the right give a great visual of how density relates to mass and volume that the mass occupies. Both the gold bar and the bale of cotton contain the exact same quantity of mass, 250 kilograms, and I have these pictures scaled properly. At first blush, then, it seems like there must be way more cotton than gold, since the cotton occupies a much larger volume than the gold. That would be true if cotton and gold have the same density, but they don't. Cotton’s density is 1.55 grams per cubic centimeter, while gold’s is 12.5 times denser at 19.32 grams per cubic centimeter. Gold packs way more matter into the same amount of space, so the same amount of cotton matter, 250 kilograms, takes up more than 12 times the volume compared to gold. That's an important relationship to keep in mind when considering matter and mass. Okay, so back to the conundrum I raised before. If I were to tell someone who knows nothing about physics that I just got off the scale and I weigh 100 kilograms, that person would likely say, “Okay, great, whatever.” But if I said that same thing to my physics buddy, he would say, “No, you don't weigh 100 kilograms. Amount of matter is measured in kilograms. Weight is measured in newtons. You contain 100 kilograms of matter. You don't weigh 100 kilograms.” He would be correct, and yet scales that measure weight are marked in kilograms, and that's okay. There's a specific relationship between mass and weight that, while it's not technically correct, makes it okay to report weights in units of mass. Now, a short digression. I've said several times that you measure weight with the scale, but haven't said anything about how to measure mass. That's done with a balance. As the diagram shows, a balance has two plates suspended from a lever arm attached to an upright, which allows the lever arm to rotate clockwise or counterclockwise depending on the amount of mass in each plate. You place an object on one of the trays and then add calibrated mass standards to the other plate until the two plates are even horizontally, they balance out. Calibrated mass standards come in one gram, five gram, ten gram, 25 gram, etc. values, and you simply put them on until the balance is balanced. Add up the amount of mass standards it took to achieve balance and that's the mass of the object. This is done frequently in science labs all over the world, but as is probably obvious, it isn't really very practical in everyday life. Weight, on the other hand, is a lot faster and easier because all you need is a scale. Here we're measuring the weight of a moose at 4,903 newtons and a dog at 245 newtons. Again, remember what a scale measures is the force that gravity pulls down on the mass of the object with. So Earth's gravity pulls down on the moose with 4,903 newton's of force, and on the dog with 245 newtons of force. And since we know that the more weight something has the more matter it contains, we can, in our minds, determine that since the moose is heavier than the dog it also has more mass than the dog. And in fact, the moose has 500 kilograms of mass, while the dog has 25 kilograms of mass. Interestingly, if we divide the moose's weight of 4,903 newtons by its mass of 500 kilograms, we get 9.8. If we divide the dog's weight of 245 newtons by its mass of 25 kilograms, we get 9.8. In fact, if you divide the weight of any object by its mass, you get 9.8. No matter where on earth you are, the way that gravity and mass work is that an object's weight in newtons is always 9.8 times more than its mass in kilograms. And that's why in day to day life, when you're not interacting in physics class, it's okay to report weight in units of mass, kilograms, instead of units of newtons. Now, it is true that the further you move away from the center of the Earth, the weaker gravity gets. So let's consider that now. If the strength of Earth's gravity pull decreases the farther away you get from the center of Earth, that means that the Earth's gravity pull is weaker on top of a mountain than it is at sea level. And if Earth's gravity pull is weaker, that means it won't generate as much pulling down force on an object, and so that object will weigh less at the top of a mountain than it does at sea level. That is true, but the practical effects are way, way too little to make any difference. Here's what I mean. If I weighed our 500 kilogram moose friend here at sea level, he's 4,903 newtons. And if I weigh his same 500 kilogram mass on top of a 5,000 meter mountain, he'd weigh 4,900 newtons. So yes, it is less, but practically, it's barely off and likely within the margin of error of more scales. So technically, an object does weigh less at altitude than it does at sea level, but the difference is so small that practically the weight is the same. And again, that's why it's okay, on Earth, to report an object's weight in the units technically reserved for mass. But wait a second, I just use the qualifier “on Earth.” That's why it's okay on Earth to report an object's weight in units of mass instead of units of weight. Why would I say that, though? And lest you think it's because gravity isn't really that big of a deal, it isn't that strong of a force, think again. The sun, which is far more massive than any of the planets and so has far stronger gravity, has enough gravity to keep the planets in place orbiting the sun. If it wasn't for the sun's constant force of gravity pull on the planets towards the sun, they would all shoot off into space. Even the effects of the moon's gravity is pretty impressive. The moon is less massive than the Earth, and way, way less massive than the sun, yet the effects of the moon's gravity pull on the Earth's oceans does this. This is high tide, and here's low tide in the same harbor. Even though the moon is about 250,000 miles away, its gravity is still strong enough to cause the ocean's waters to rise and fall more than 15 feet in the same day. Gravity is a force to be reckoned with. So now, here's specifically why in physics it's important that we know the difference between mass and weight. Gravity does not affect mass, but it has great effects on weight since it is, in fact, the pull of gravity that causes weight to exist. As we know, the moose with 500 kilograms weighs 4,903 newtons at sea level. And if we took him to the moon and weighed him there, he would weigh 818.8 newtons. Now that we are operating off Earth, out in space, it's clear that we are no longer working under the same assumptions that we had on Earth. We're operating in physics space, and we must remember that and use terms and units appropriately. By that I mean, if I continue to operate under the assumption that, on the moon, it's fine to report weights in kilograms and not newtons, and then told my physics friend that when I weighed the moose on the moon he weighed 83 kilograms, what have I really just told him in physics terms? I told him that my moose lost more than 400 kilograms of his mass. He isn't a complete moose anymore. The moon's force of gravity is only 16.7% as strong as Earth's gravity, which means the moose's weight is a lot less on the moon than on Earth, but his mass doesn't change. He still contains 500 kilograms of mass because mass is not dependent upon gravitational force. Weight is, though, and that's why I made the qualifier of “on Earth.” If I weigh myself on Earth on my kilogram scale and report it as 100 kilograms, and then I got on a rocket with my kilogram scale and weighed myself on the moon and reported it as 32 kilograms, a physicist will understand that to mean that during the trip to the moon, I lost 68 kilograms of mass, of me. That clearly isn't correct. Mass is not affected by gravity. Weight is. I am 100 kilograms of mass on the Earth and 100 kilograms on the moon, but my weight is a lot less on the moon because the moon's gravity is less than Earth's. So let me summarize the important concepts from this discussion today. Mass is the amount of matter an object contains. Weight is created by the force of gravity pulling on an object's mass. Mass is reported in grams or kilograms. Weight is reported in newtons. On Earth, there is a constant relationship between mass and the Earth's gravitational pull, so that no matter where you are on Earth, an object's weight in newtons is 9.8 times its mass in kilograms. The amount of mass something contains is not affected by gravity, but an object's weight is.