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# Our Physicist Explains The Deal With Mass And Weight Once And For All

If people in glass houses shouldn’t throw rocks, then I’m a pitching machine crammed with gravel and I live in Philip Johnson’s summer house. You see, I’m a brutal little bitch when I find stupid mistakes in articles about cars, and then just the other day I made one of the most basic physics mistakes you can make. I need to make this right!

Let me explain why I’m such an idiot. I was all pumped full of geeky excitement about the New Horizons probe’s flyby of Pluto, and I wanted to commemorate the event with some sort of Pluto/automotive based article. I thought it would be fun to try and figure out how your car would perform on Pluto.

Some initial research and quick math showed me that Pluto has a gravitational pull about 1/12 that of earth. This is where I made my mistake. I immediately thought of gravitational pull in terms of weight, and weight made me think of power-to-weight ratios, and then I calculated and found that my 60HP Beetle with 1/12 its weight would have the same power-to-weight ratio as an Ariel Atom.

At that fun fact, my brain shut down and excitement took over, and I made that chart without the scrutiny and thought that it needed and that you, my readers, deserve. I conflated weight and mass. A number of commenters smarter than me pointed this out, and I quickly realized what I did.

What I also realized is that while I did recall that weight and mass are not equivalents, I wasn’t really equipped to fully understand or explain just why that is. Happily, a dipshit like myself doesn’t have to. This is exactly the sort of thing Jalopnik’s tame physicist, Stephen Granade, is good at, so I admitted my sin and asked him for help.

He obliged:

Oh, Jason. You’ve mixed up mass and weight. That’s easy to do since they’re connected to each other, but it can lead you to some wrong conclusions, like the ones in your original article. So let’s talk about how mass and weight are different, and why power-to-weight ratios aren’t the best way to compare cars.

Mass is a fundamental property of matter, while weight is the force of gravity pulling on an object. The two are related, because weight is directly proportional to mass. Double an object’s mass and you double its weight. But mass doesn’t change depending on where you are, while weight does. Way out in interstellar space, where you’ll feel almost no force of gravity, your weight is zero. But you still have mass! Just ask an astronaut who spent hours moving “weightless” construction materials around to build the International Space Station.

Think about your age. We decide whether or not you can vote based on how old you are. But your age is a fundamental property, while being able to vote is derived from your age. The voting age is different depending on where you live. It can even be changed, like how the USA lowered the voting age from 21 to 18 in 1971. That change didn’t affect anyone’s age. It just changed how old you had to be to vote.

That’s all well and good, you say, but what is mass? Where does it come from? For the stuff that makes up us, it comes from the Higgs field[1]. Every particle that we’re made up of interacts with something called the Higgs field, which fills the universe. The particles that we’re made of interact with the Higgs field by swapping Higgs bosons with it. The more a particle swaps bosons with the Higgs field, the more mass it has.

What does mass do? Mass determines inertia, which is how much an object resists being accelerated. That’s expressed by Newton’s second law of motion.

F = ma

The more massive an object is (m), the more force (F) you have to apply to make it speed up or slow down (a). And remember that I said that weight is a force! Newton’s second law relates weight (a force) to mass.

That’s half of what we need. The other half is how much acceleration we experience due to gravity. On the surface of the Earth, that acceleration is roughly 9.8 meters per second squared. More generally, the gravitational acceleration due to any object is given by

a = g M / r^2,

where g is the gravitational constant (a fundamental constant of the universe), M is the mass of the object, and r is the distance between us and the object’s center of mass. If you plug the Earth’s mass and its radius into the above formula, you get about 9.8 m/s^2 of acceleration.

That shows something else about mass: it gives rise to gravity[2]. Each of us exerts a gravitational force on everything around us. It’s small, but it’s there. Right now I’m producing enough gravitational force to accelerate the coffee cup on my desk at a whopping 20 nanometers per second squared. That’d get it to 60 MPH in over 42 years, if only my personal gravitational force were enough to overcome the static friction holding the cup in place.

Scientists use the metric system, which gives mass in kilograms and force in a unit called Newtons. (That’s us scientists: always creative with the names.) But since we started out measuring weight in pounds before the metric system was created, we’ve stuck with that unit. If we wanted to be consistent, we’d either need to give weight in Newtons or use the Imperial unit for mass: the slug.

(And how awesome is it that there’s a unit called “slug”? Answer: very awesome.)

Even though mass is the fundamental property, we mostly deal with weight in our day-to-day life. That’s because we don’t measure mass directly. Instead, we step on a scale to measure our weight and figure out mass from that. Since weight is the gravitational force, and we know the acceleration due to gravity, we can calculate mass from weight.

But we don’t do a good job of keeping mass and weight as separate concepts, so I understand mixing them up. Ever given your weight in kilograms? But the kilogram is a unit of mass, not weight! Since we mostly deal with mass and weight on the surface of the earth, it’s convenient for us to talk about there being 2.2 pounds in a kilogram. But that’s like saying that, when I’m driving, there are 60 miles in an hour. That’s true if I go 60 MPH, but not if I go slower or faster, or stop for gas. 1 kilogram is only equivalent 2.2 pounds of weight on Earth’s surface.

And that’s where Jason got tripped up. Car performance is often measured in power-to-weight because that lets you compare how powerful cars are while taking into account how much force is required to shove the car around. But that ratio’s more properly power-to-mass, because the mass determines the car’s inertia and therefore how much force you need to accelerate the car. The engine’s availble power, and thus force, isn’t changing, and neither is its mass. You’ll get the same acceleration on Pluto that you will on Earth, even though the cars will weigh less on Pluto, because their mass doesn’t change.

What will change is the car tires’ traction. Traction comes from the tire’s static friction, which depends on the coefficient of static friction between tires and surface and how much force the car bears down on the tires with. The lower weight means less force on the tires, which means less static friction, which means that the tires will slip more easily. Plus Pluto’s surface is mostly ice, which is a lot slippier than our roads. On the plus side, there’s not much atmosphere, so drag won’t be a problem. (That also means we can’t add spoilers to create downforce and increase the cars’ traction.)

Normally you can mix up mass and weight because most of us don’t work in space or on planets other than Earth. But if you’re going to get your ass to Pluto and drive around, you’ll have to treat mass and weight as separate concepts.

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[1] I’m lying to you a bit here. It turns out that mass and energy are related because of relativity. That’s Einstein’s famous equation E = mc^2, which says that energy E and mass m are related by the speed of light c. Making matters more complex, according to relativity, mass depends on how fast an object is moving relative to whatever’s observing the object.

We’re made up of atoms. Most of an atom’s mass comes from its protons and neutrons, which are bags of quarks whizzing around very very fast. The energy of their velocity translates into extra mass. So part of our atoms’ masses come from the Higgs field, but another part of their masses comes from the energy of the quarks zipping around.

[2] I’m lying again. If you need mass to create or interact with gravity, how can gravity bend light? (Which it does!) And just like in my previous lie, the answer is “relativity”. Mass, speed, energy, and gravity are all bound together in a wibbly-wobbly kind of way. But for our purposes right now, we can live in Newton-land and just talk about mass causing gravity.