The Difference between Mass and Weight (a rough analysis of)

I feel like blogging today, so you, my kind readers, get two posts today, whether you like it or not. After all, the first post was kind of cheating. Mostly cut and paste work.

 

So! What is the difference between mass and weight? This question was thrown to me by Google Instant. Try typing typing "The difference between" in the Google Search Bar, and you'll see what I mean. Coincidentally, I'm also studying Physics right now, so this doubles as a kind of revision for me. Although, all of my friends who study Physics already know, when answering quesiton, what the difference between mass and weight is. If you want to find the weight of an object, multiply the mass of the object by 10. So simple. And yet, so very inaccurate. We'll get to that in a moment.

 

First, to get a definition of "mass" and "weight", we turn to our old friend Wiktionary. According to Wiktionary, "mass" is "The quantity of matter which a body contains, irrespective of its bulk or volume." In other words, "mass" measures how much there is in your body. Fair enough, right? On the other hand, Wiktionary cites "weight" as meaning "The force on an object due to the gravitational attraction between it and the Earth." In short, how much you feel gravity.

 

Let's keep things nice and simple, now. "Mass" refers to how much "flesh" you have in your body, for want of a better term. "Weight" on the other hand refers to how much gravity affects you. All nice and clear now, right? In Physics, we can say that "mass" is a measurement of matter, and "weight" is a measurement of force. But that's just Physics, of course.

 

Before I start boring you with a lot of Physics, let me get right down to the main point: The difference between mass and weight. Mass will never change wherever you are, since it measure your "flesh". Your mass only changes if you put on some fat, or have some of it removed. Your weight, on the other hand, depends on gravity. If gravity were to suddenly become weaker, your weight would be less. But your mass, or "fleshiness", would still be the same. You haven't burned any carbs yet, after all. In short, if you were to go to the Moon where gravity is weaker, your weight would decrease. You've still got all your flesh on you though, so your mass does not decrease.

It would be great if you would keep on reading, but if you feel like you've learned enough, now would be an okay time to exit the blog. However, if you decide to leave here, please scroll down to the "important note" before you do.

 

Then what is the relationship between mass and weight? For that, let's take a quick look at the law of gravity. Wikipedia: "Gravitation, or gravity, is a natural phenomenon by which physical bodies attract each other with a force proportional to their masses." In the layman's terms, big objects attract bigger objects better. The Law of Gravity hence states that the greater your mass, or "fleshiness", the bigger the effect of gravity on your body.

 

So how do we arrive at calculating weight out of mass? Well, Earth's gravity is fixed at a certain strength, and all objects on earth experience a "gravitational accelaration" of approximately 10 meters per second per second - or m/s^2. In other words, if you were standing still in a helicopter in the air (not falling at all), and you were to step out onto thin air, you would accelarate at approximately 10 m/s^2. In short, if you were to walk out of a helicopter, 1 second later you would be falling at about 10 m/s, and another second after that you would be falling at about 20 m/s, and another second after that you would be falling at about 30  m/s... and so on, until you reach a maximum speed (or terminal velocity) of about 195 km/h, or 54 m/s. That's gravity for you. It's one of the few laws that cannot be broken.

 

But I'm dawdling, aren't I? Let's get back to getting weight out of mass. The formula for finding force is: Force is equal to mass multiplied by acceleration, or F=ma. Also discovered by Newton. Now, take a close look at that equation, and compare it to what we have learned so far. Force = mass x acceleation? Hey! Weight is gravitational force, isn't it? And that's what we want to find! As for mass... well, that depends on the object we're looking at, right? Let's take me as a sample. My mass is around 60kg. Not that you should tell that to the whole world or anything. Now, our equation says my gravitational force, or Weight = 60kg x accelaration. But wait! Weight is about gravity, and gravitational acceleration on Earth is 10 m/s^-2, isn't it? Well, let's put that in there! Now, my Weight is equal to my Mass multiplied by gravitational acceleration, or Weight = 60kg x 10m/s^-2. That means I weigh 600! But 600 what? Force is measured in Newtons (what? him again?), or N. So my mass is 60 kg, and my weight is 600 N.

 

For all practical purposes, acceleration due to gravity is always 10 m/s^-2 anywhere on earth. So when finding the weight of an object, you only need to determine it's mass, and multiply it by 10, or the gravitational acceleration. Now, what if you were to go to the Moon, where the force of gravity is weaker? The acceleration due to gravity on the Moon is only 1.6 m/s^-2. But remember what I said about you still having all your fleshiness on you? On the Moon, my mass would still be 60 kg. But when you multiply it by the gravity, 1.6, you find that I only weigh 96 N, less than a sixth of my weight on Earth. My mass has not changed, because mass is not affected by gravity. But my weight has decreased to a mere fraction of its previous reading. But I'm still as fleshy as ever as 60 kg, so even though I can say my weight has decreased, it doesn't mean I can quit my diet yet.

 

Important Note:

According to Physics, if the question asks "What is the weight of Ali?", your answer should be in Newtons, and if it asks for his mass instead, then you give your answer in kilograms. However, in modern everyday usage, people will ask you for your weight, and yes, they are referring to your "fleshiness", not your gravitational force. This slight inaccuracy of terminology is allowed because it has become the norm over many years, and when people ask you "How much do you weigh?" You are expected to give your answer in kilograms. Feel free to say "I weigh 60 kilograms", because even though it is technically inaccurate, it is expected in most social circles. Please do not say "Oh, you want my weight? Well, while I'm on Earth, I weigh 600N." That will just make you socially awkward. Of course, it still makes a good joke to tell your Physics teacher.

 

That's the end of the important note. Now, since you already know the difference between mass and weight, here's something for you to think about: When I stand on a weighing scale in an elevator, it gives a reading of 60 kg. The elevator then moves downwards with an acceleration. The reading of the weighing scale decreases. I do not need to tell you that my mass has not changed a hair. But the question is, has my weight actually decreased?

 

Well, the answer to that can be both yes and no. For instance, consider that after jogging, your legs feel tired, and that's when you really feel the weight of your body stressing on your legs. But you're not actually feeling the gravity on your legs. What you're feeling is the "reaction force" of the ground on your legs. This is what weighing scales measure. Consider the scenario of falling out of a helicopter, and that of standing still on the ground. In falling, gravitational force acts freely on you, and you're legs won't feel so tired. But when you're on the ground, the floor supports you with an upwards "reaction force" that prevents you from going any lower. It is this reaction force that you actually feel as weight. Meaning that when you are falling out of a helicopter, you don't feel any reaction force, and hence, you don't really feel weight. This is where the term "experience weightlessness" comes from. If you were to jump out of a plane with a weighing scale under your feet, you will find that you weigh 0 kg. A perfect dream.

 

But that's if we look at weight as the reaction force. The weighing scale actually measure reaction force, which is why it reads 0 in a free-fall, when there is no reaction force. In the scenario of the moving elevator, the downwards force of the accelerating elevator acts against and decreases the upward reaction force, thus creating an illusion of decreased weight. But in point of actual fact, the force of gravity acting on your body hasn't really decreased, has it? When you're falling from the sky, you don't actually feel any weight. But you're still falling aren't you? Because of gravity. Gravity very much still has power over you and is exerting downwards force on you, towards Earth. In that sense, you still weigh the same as you did when you were standing still. This become especially evident when you hit the ground travelling at 195 km/h. So much for experiencing weightlessness.

 

In conclusion, to recap: Mass measures fleshiness. It does not change on the Moon. It is represented in kilograms. Weight measure how much gravity you feel. It decreases on the Moon. It is represented in Newtons. But when people ask you for your weight, you tell them your fleshiness, in kilograms. Don't tell them your gravity. Unless you really want to.

P.S. I almost forgot to mention something very important. Weighing scales do not exactly measure your mass. They measure your weight, and then divide by Earth's gravity to get an accurate measurement of your mass, in kg. I don't know if there is any elaborate scientific apparatus that lets you actually measure your mass at a sub-atomic level, but hey, science can do anything.