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# Mass and weight clarification

AP.PHYS:
FLD‑2.B (EU)
,
FLD‑2.B.1 (EK)
,
FLD‑2.B.1.1 (LO)

## Video transcript

in this video I want to clarify two ideas that we talk about on a regular basis but are really kind of muddled dumped in our popular language and these are the ideas of mass mass and weight and first I'll tell you what they are and then we'll talk about how they are muddled up so mass is literally there's a couple of ways to view mass one way to view mass is and this is not a technical definition it'll give you a sense of it is how much stuff how much stuff there is so this is similar to saying matter so if I have more molecules of a given mass or of a given mass I will have a total of more mass so if I have more atoms I will have more mass so how much stuff there is of something and I want to be careful with this definition right here because there are other things that aren't what would be what we would traditionally associate with a matter once we start going into more fancy physics that still will exhibit mass so another way to to define mass is how does how does something react to a specific force and we already learned from Newton's second law that if you have a if you have a given force and you have more mass you will accelerate less if you have less mass you will accelerate more so how something responds to force how something responds to force to a given force something with lower mass will accelerate more forgiven for something with higher mass will accelerate less now wait wait is the force of gravity on a mass or on an object so this is the force force of gravity gravity on on an object and just to think about the difference here let's think about let's think about I guess myself sitting on earth so if I'm on earth my mass is 70 kilograms my mass let me just in a new color so my mass my mass is 70 kilograms there's 70 kilograms of stuff that constitute salle but my weight is not 70 kilograms I mean you'll often hear people say I weigh 70 kilograms and that's all right in just conversational usage but that is not technically correct because weight is the force that earth is pulling down or I should say the force of gravity on my mass and so the my weight my weight think about the weight for a second the weight is going to be equal to the is going to be equal to and the gravitational field at earth let me just like we did hopefully you've watched the video on gravity if you haven't feel free to watch it but the gravitational attraction between two objects so the force of gravity between two objects is going to be big G the universal gravitational constant times the mass of the first object times the mass let me actually let me do it times the mass of the first object times the mass of the second object times the mass of the second object divided by the distance that separates the two objects squared and if you're on earth and if you take all of this stuff right over here combined so if you say that this right here is the mass of earth mass of Earth if you say this right here is the distance from the centre to the surface of Earth because that's where I'm sitting right now so distance distance from centre to surface of Earth then all of this stuff over here simplifies to simplifies to what sometimes called as lowercase G and lowercase G is and I'm just rounding it here 9.8 meters per second squared so the force of gravity for something near the surface of the earth is going to be is going to be this quantity right over here times times the mass times its mass so my weight my weight on the surface of the earth is this 9.8 meters per second squared 9.8 meters per second squared times my mast times seventy kilograms times seventy times seventy kilograms and so this is going to be and I could I won't do well I could get my calculator down why don't I just get my calculator out and do the math I was going to round it to ten and say it's about seven hundred but let's just actually calculate it so we have nine point eight times seventy kilograms so we have 686 so this gives me 686 and then the units are kilogram meters per second squared kilogram meters per second squared and these units kilogram meters per second squared are the same thing as a Newton as a Newton so my weight and you'll never hear people say this but my weight on the surface of the earth is 686 Newtons 686 Newtons and notice I just said that is my weight on the surface of the earth because as you can imagine weight is the force due to gravity on an object on a mass so if I go someplace else if I go if I go to the moon for example my weight will change but my mass will not so let's write this this is the weight this is the weight on earth if I were to take my weight on the moon the weight on the moon weight on the moon and I haven't looked this up before the video and you can verify this for me if you like but I've been told that the gravitational force on the moon or the gravitational attraction at the surface of the moon is about one-sixth that of the surface of the earth so on my weight on the moon will be roughly 1/6 roughly 1/6 of my weight on the earth times 686 Newtons so that gives me a little bit over what is that 100 and 114 maybe I'll just get the calculator out my brain is always operates a little bit slower while I'm recording videos yeah I got it right right 114 so that gives us 114 approximately 114 Newton's so this is the thing I really want to emphasize it weight is a force due to gravity on an object your weight changes from planet to planet you go on your weight would actually even change as you as you as if you went to a very high altitude because you're getting slightly further yet it would be immeasurably small but you're getting slightly further from the center of the earth your weight would change an imperceptible amount in fact because the earth is not a perfect sphere because the earth is not a perfect sphere it's slightly it's often referred to as an oblique spheroid your weight is actually slightly different your weight is actually slightly different on different parts of the earth if you went to the poles versus the equator you would have a slightly different a slightly different weight your mass does not change it doesn't matter where you go assuming that you don't have some type of nuclear reaction going on inside of you your mass does not change so your mass mass does not change it does not change depending on where you are now you might be saying hey look you know I don't deal with kilograms and Newtons and all of this I operate in America and in America we talk about pounds as pounds appropriate and yes pounds is a unit of weight so if I say if I say that I weigh 160 pounds 160 pounds this is indeed weight I'm saying that the force of gravity on me is 160 pounds but then you might say well what is mass then if you're talking about if you're talking about the English system or sometimes called the Imperial system and here I will introduce you to a concept that very few people know it's kind of a good trivial concept the unit of mass the unit of mass so let's just be clear here the unit of mass on in the imperial system mass is called the slug mass the unit of mass is called the slug so if you wanted to figure out how many slugs you are so your weight the force of gravity on you is 160 pounds 160 pounds this is going to be equal to if you were to take if you were to calculate you were to calculate all of this stuff the force of gravity on the surface of Earth but if you were to do it in if you're doing the imperial units instead of getting 9.8 meters per second squared you would get instead of 9.8 meters per second squared you would get 32 feet per second squared which is also the acceleration on near the surface of the earth due to gravity in feet and seconds as opposed to meters and seconds and then this is times your mass times your mass in slugs in in slugs so to figure it out you divide both sides by 32 feet per second squared so let's do that let's divide both sides by 32 feet per second squared divide both sides by 32 feet per second squared cancels out and then let me get my calculator out so I have 160 pounds divided by 32 feet per second squared and I get exactly 5 I should have been able to do that in my head so I get 5 and the unit's here in the numerator I have pounds I have pounds and then I'm dividing by feet per second squared that's the same thing as multiplying by second squared per feet and these units 5 pounds second Squared's over feet this is the same thing as a slug so if I weigh 160 pounds my mass is going to be equal to my mass is going to be equal to 5 slugs if my mass is 70 kilograms mass is 70 kilograms my weight is 686 Newtons so hopefully that clarifies things a little bit