Differences Between Mass and Weight

 

Topics discussed:

·        The difference between mass and weight

·        Why the difference is so confusing

·        Why scales read the funny things that they do

·        What a scale would read if you took it to the Moon

·        How they ought to build scales to use the correct meaning of mass and weight

·        The concept of inertia

·        How heavy rocks behave in outer space where there is no gravity

 

 

Student:    Hey, Professor, I’m having a real hard time understanding the difference between mass and weight.  I mean, I thought they were the same thing.  They’re both measured in pounds in the English system and kilograms in the metric system.

Professor:  I agree that the difference is confusing – and I disagree with you saying that they’re both measured in pounds and kilograms. 

Student:    Well, what are they both measured in?  My digital scale in my kitchen tells me I weigh 156 pounds.  If I flip the little switch, it tells me I weigh 70.76 kilograms.  How can mass and weight not be measured in pounds and kilograms?

Professor:  Right, right – a confusing subject indeed.  I’ll get to the scale dilemma in a minute.  For now, let’s define mass.  Mass is a measure of how much stuff you have inside of you.  Weight is how hard the Earth’s gravity pulls on you.

Student:    But those are the same, aren’t they?

Professor:  Not necessarily.

Student:    Okay.  You’ve totally confused me now!

Professor:  First of all, I should make you aware of this fact: one of the reasons why the difference between mass and weight is so confusing is that lots of people use the word weight when they actually mean mass, and vice-versa.  Mass and weight are kind of like the words “affect” and “effect”.  They’re two really similar sounding words with similar (but distinct) meanings, and people mistakenly use one when they mean the other all the time.  Think about this – when you go to the Moon, don’t you weigh less?

Student:    Yeah, you do.  That’s because the Moon’s gravity isn’t as strong as the Earth’s gravity.  I’ve seen the footage of the Apollo astronauts on the Moon bouncing around like crazy.

Professor:  Right.  So you weigh less.  But it’s not because you lost a lot of fat off your body is it?  Your entire body is still there, isn’t it?

Student:    Yeah.  Nothing changes about my body when I go to the Moon.  The only thing that changes is how hard gravity is pulling on me.

Professor:  Okay, so the total amount of stuff inside your body stayed the same, but the downward force you exert on the ground decreased when you went to the Moon. 

Student:    Right.

Professor:  Well, since the total amount of stuff inside your body doesn’t always correlate exactly with how hard gravity pulls on you, physicists have different words for these two things.  Mass is the total amount of stuff inside your body.  Weight is how hard gravity is pulling on you.

Student:    But doesn’t gravity pull on everything the same amount?  I thought that was why a golf ball and a bowling ball hit the ground at the same time if you drop them from the same height at the same time.

Professor:  I agree that the bowling ball and the golf ball hit the ground that the same time, but it’s not because gravity is pulling on them with the same force.  The reason that the bowling ball and the golf ball hit the ground at the same time is because gravity makes everything accelerate at the same rate.  It’s not because gravity pulls on everything with the same force.

Student:    Oh, okay.  I didn’t know that.

Professor:  Okay, now back to mass and weight.  For a moment, I want you to pretend to forget about the English system and imagine that you only know about the metric system.  In the metric system, mass is measured in kilograms, and weight is measured in a unit called “Newtons”.

Student:    Oh yeah!  Newtons are also used to describe how strong a force is.  So I guess there’s two ways you can use Newtons.

Professor:  Well, if you think about it hard enough, weight is just a particular type of force, so really there’s nothing new about using Newtons to describe how much someone weighs.

Student:    I see.  But I’m still hung up on the pounds thing.  I know that earlier you told me to pretend like I don’t know anything about the English system, but I can’t go the rest of my life pretending not to know something.  I’m still buggered up on how we measure mass and weight in the English system.

Professor:  Pounds is the English unit for weight.  If you want to correctly measure mass in the English system, you use a unit called “slugs”.

Student:    Slugs?  I’ve never heard of that in my life.  And besides, where did that odd name come from.

Professor:  I think it comes from the idea of having small slugs of metal – a bullet that has been shot out of a gun and then found is called a slug too.  I don’t think it has anything to do with the little insect/creature.  And yes, most people do not use the term – they just get lazy and refer to mass in pounds.

Student:    Well, according to what you just said, it’s not right to measure mass in pounds.  I guess people just do it anyway.  So tell me, how do you convert from kilograms to Newtons?

Professor:  It depends on what planet you’re on.

Student:    Let’s say I’m on the Earth.

Professor:  In that case, to convert from kilograms to Newtons, you take the number of kilograms you have and multiply it by 9.8 m/s², the acceleration due to gravity here at the Earth’s surface.

Student:    Oh, that’s not too bad.  How would I do that if I were on the Moon.

Professor:  The acceleration due to gravity at the Moon’s surface is only 1.62 m/s².  So if your scale tells you that you “weigh” (even though that’s technically an incorrect usage of the term) 70.76 kilograms, that means that you “weigh” (using the term correctly this time) 693.448 Newtons on Earth (that’s 70.76 x 9.8 ).  On the Moon, you still have 70.76 kilograms’ worth of stuff inside of you, but the Moon’s gravity makes you weigh (using the term correctly) only 114.63 Newtons (that’s 70.76 x 1.63).

Student:    Oh! Okay!  I think I’m getting a little more comfortable with this now.  So what’s up with my kitchen scale at home?  Why does it say that I “weigh” 70.76 kilograms?

Professor:  Companies make scales according to the common and incorrect notions of weight and mass.  People who haven’t taken physics (which is most people out there) would be confused as hell if they stepped on their scale one morning and it told them that they had a mass of 21 slugs.  If an astronaut were to make a scale that was kosher with the true distinction between mass and weight, it would have four readings on it – your mass in slugs, your mass in kilograms, your weight in pounds and your weight in Newtons.  Also, it would have a little knob on it that you could move around to tell the scale what planet you were currently on, so it would know whether to use 9.8 for Earth, 1.62 for the Moon, or whatever, when calculating your mass.

Student:    Oh yeah, that reminds me – would my scale read incorrectly if I used it on the Moon?

Professor:  It depends.  What does your scale say when you set it to metric and use it here on Earth.

Student:    It tells me that my “weight” is 70.76 kilograms. 

Professor:  Well let’s keep this example simple and pretend that your scale tells you correctly that you seem to have a mass of 70.76 kilograms.  One of the things that we have to consider is the fact that the scale itself doesn’t actually measure your mass in a direct way.  It measures your weight in Newtons, with a spring – and in your case the weight is 693.448 Newtons.  The engineers who built the scale set the dial up to read “70.76 kg” whenever a person of weight 693.448 Newtons steps on the scale.  In essence, the engineers calibrated the scale to have 9.8 built into it.  Now when you take the scale to the Moon, the 9.8 is still built in to the scale, but is no longer correct.  Based on this, what do you think the scale will read?

Student:    Umm, let me think.  Uh, well, the scale takes my weight in Newtons, and divides that number by 9.8 to get my mass (even though it seems to mistake my mass for my weight, in a way).  On the Moon I have a weight of 114.63 Newtons.  The scale, unaware that it has been brought up to the Moon, will still continue to divide my weight by 9.8.  So the new reading on the scale would be 114.63 / 9.8 which is 11.69 kg. 

Professor:  See how it works now!

                If you were to use the astronaut’s scale that I was talking about a second ago, on Earth it would read:

Mass = 70.76 kg  :  4.875 slugs

Weight = 693.448 Newtons  :  156 lbs.

                Assuming that you had the knob set to “Earth”.  If you were to take that astronaut’s scale to the Moon, and set the knob to “Moon”, the scale would read:

Mass = 70.76 kg  :  4.875 slugs

Weight = 114.63 Newtons  :  25.89 lbs

                Notice that from Earth to Moon, your mass didn’t change, but your weight did.  The astronaut’s scale knew to take your weight in Newtons and divide it by 1.62 instead of 9.8 because you set the knob to “Moon”.

Student:    So what would happen if I had the scale on Earth, but set the knob to “Moon” and then stepped on the scale?

Professor:  In that case, the astronaut’s scale would still give you a correct “weight” reading in both Newtons and pounds.  The astronaut’s scale measures weight in a direct way regardless of what planet you’re on.  However, with the knob set to “Moon”, the scale would incorrectly divide your weight (in Newtons) by 1.62 and give you an artificially high number for your mass.

Student:    So can I pick up giant rocks on the Moon that I wouldn’t ordinarily be able to pick up on the Earth?

Professor:  It depends on how strong you are.  A 300 kg rock is a 300 kg rock no matter what planet you’re on.  But on Earth, a 300 kg rock has a weight of 2,940 Newtons, which is 660 lbs.  Can you pick up a 660 lb rock?

Student:    Uh, a champion weightlifter might be able to do that, but I couldn’t.

Professor:  Right, neither could I.  How much does a 300 kg rock weigh on the Moon?  Remember, the acceleration due to gravity on the Moon is 1.62 m/s².

Student:    Well, 300 x 1.62 = 486 Newtons.  The conversion between Newtons and pounds is 1 Newton = 0.2248 pounds.  So 486  x 0.2248  = 109.25 lbs.  I guess that I could pick up a 109 lb rock if I really had to and tried to be careful not to hurt my back.

Professor:  Yeah, I agree.  Now what if the rock on the Moon had a mass of 3,000 kg?

Student:    Wow!  A 3,000 kg rock would have a weight of 1,092.5 lbs on the Moon (using the conversions I just did for the 300 kg rock).  I still couldn’t pick that rock up even if it was on the Moon!

Professor:  Right.  So on the Moon, you can pick up bigger rocks, but there’s still an upper bound to your strength and what you can pick up.

Student:    I see!  So what if I had this 3,000 kg rock in the cargo bay of a spaceship out in space with no gravity?  Could I pick it up then?

Professor:  How much would it weigh in outer space?

Student:    That’s just it.  The rock wouldn’t have any weight out in outer space because there is no gravity.  I could just push this rock around like a toy with no problem!

Professor:  Actually, no.  I agree that the rock wouldn’t have any weight, but remember it would still have a mass of 3,000 kg.  It’s not like any part of the rock broke off.  In the cargo bay of your spaceship out in outer space with no gravity, you could pick the rock up, but it would still require some effort to get it moving.  It would be like trying to pull a 3,000 kg sled on ice.  And then once you got it going, it would be difficult to get the rock to stop moving.  You’d be banging this rock around the walls of your cargo bay if you weren’t careful.  This resistance to being pushed around and resistance to being stopped once you get going is called inertia.

Student:    Cool!  Or, not cool I guess.  And I’ve been wondering what inertia meant.  Anyways, thank you for explaining the difference between mass and weight to me.

Professor:  You’re welcome.