3.3 Mass, Weight, and Weightlessness

Critical Questions:

  • What is the difference between weight and mass?
  • Why do you weigh less on the moon?
  • Why does your stomach lurch when the elevator you’re in starts moving?

You might have noticed that in the last section, I used the words “mass” and “weight” interchangeably. If a certain type of physicist were reading that section, I might be in jail by now. At this point, I should placate the purists out there and be a bit more precise about all of these terms.

George Bluth in jail, from Arrested Development
At least there’ll be ice cream sandwiches.

Imagine stepping onto a simple bathroom scale and seeing the little needle turn. You might think that the way a scale works is obvious, but let’s Think Like a Physicist here and describe this situation technically. First of all, your body is pulled downwards by the gravitational attraction between yourself and the Earth. A coiled spring inside the scale compresses, providing you with more and more upwards force the more it is compressed. The whole thing adjusts itself, with a bit of wobbling, until it stops at a point when the upwards force from the spring is exactly equal to the force of gravity pulling you down. (At that point, the net force on you is zero, so you don’t accelerate.)

We know from the previous section that objects of greater mass experience a greater force of gravity, so heavier objects will stabilize with a more tightly compressed spring and thus a higher scale reading.

That may seem like a needlessly complicated way to describe what’s happening, but it reveals an interesting truth about weight. The scale isn’t directly measuring anything about you. It measures the amount a spring compresses, which measures the amount of gravitational force acting on your body.

This is the key point: the scale is measuring the strength of the force of gravity pulling you down. But as we now know, the strength of that force depends on both your own mass and the mass of the Earth, as well as the distance from you to the center of the planet.

So let’s say that a scale measures ‘weight’, which is really just another word for the strength of the force of gravity. Now grab the nearest scale and hop into a teleporter which sends you to the top of Mount Everest and stand on the scale again. What do you notice? Weight is the force of gravity, but we’ve already seen that gravity decreases the farther you get from the Earth. So the reading on the scale should now be smaller. And yet, if the teleporter was functioning correctly, you haven’t changed – there is still the same amount of ‘stuff’ (matter) in your body as there was previously. So we need another term to describe that quantity that didn’t change. This is ‘mass’.

On Earth, the two words are interchangeable for everyday use, because gravity has about the same strength everywhere on the surface of the planet. If an object has twice the mass, it will have twice the weight. But your weight changes depending on where you are in the universe. If you go to the moon, for example, you’ll weigh about one sixth of your weight on Earth. (This is due to the fact that the moon has a much smaller mass than the Earth does and so exerts a smaller gravitational force on you.) Your mass, on the other hand, won’t have changed.

Aldrin on the moon
Unless you survived only on freeze-dried potatoes and Tang on the way up.

Mass is a property of all matter[1. And, technically, of some particles that aren’t considered matter.]. It has two main effects: the first is to cause objects to resist acceleration when a force is applied; the other is to experience and apply gravitational forces when other objects are nearby. Today, physicists are actively researching what may seem like an unanswerable question: why does mass exist? One part of a possible answer to this question requires the existence of a particle called the Higgs Boson (check out a great animation about the Higgs in this previous post!). The Higgs Boson has been hyberbolically nicknamed the “God Particle” because its existence would help validate the Standard Model of particle physics (to be discussed later). As I write this, scientists in Europe are busily smashing particles together at the Large Hadron Collider, hoping that the Higgs boson might pop out of the resulting collisions.

But in some ways, this line of thinking answers more of the “how” then the “why”. For now, it seems that mass is just something we all have to deal with.

There are some particles (and by “some” I mean “two”) that are currently known to have no mass at all. The most commonly known of these is the photon, which is the particle that light is made out of. Because photons are not restricted by the limitations of mass, they only ever move at one speed – the fastest speed anything can move at, the speed of light.

We beings made out of matter will never know what it’s like to be a photon – we’ll never be able to experience masslessness. But we do have two ways of experiencing weightlessness, which is entirely different but still a lot of fun.

The easiest way to feel weightless is to go into outer space. As we already discussed, once you get far enough from any big planets or moons, there will be no strong gravity forces pulling you in any direction. You will simply float. This may feel a bit different than you’d imagine – it’s not exactly like floating underwater. Whenever you’re on Earth, certain parts of your body can sense which way is down by detecting the force of gravity. For example, a series of canals, comprising the vestibular system inside your inner ear, contain a fluid which moves around and tells your brain about how your body is accelerating. But when you’re floating in space, this fluid is floating around as well (rather than flowing to the lowest point). Your limbs and inner organs float too, of course – even your blood accumulates more in your brain than usual, as I mentioned in the introduction to this chapter.

If you can’t easily get to outer space, the other way to experience this sense of weightlessness is to be in freefall. To convince yourself of this, imagine standing inside an elevator whose cable has snapped, so that it’s accelerating downwards towards the ground.[2. In order to make this example work correctly, we’ll have to ignore air resistance here so that the elevator doesn’t end up moving at a terminal velocity.] Rather than panicking, pull an apple out of your pocket, hold it out to the side, and drop it. What happens?

Because the elevator and everything inside it all fall with the same rate of acceleration (just like the hammer and the feather from earlier), and because the apple cannot accelerate downwards more quickly than the elevator, the apple will not drop towards the floor. Instead, it’ll float next to your hand as if it were in outer space.

Everything around you and everything in your body is falling at exactly the same rate, and so you feel weightless: you can now float freely around inside the elevator, and even your inner ear fluids will float around inside your head.

To be clear, both you, the apple, and the fluids are not actually weightless – there is still a force of gravity pulling everything down. But you have no way to feel or detect this force unless there is a window that shows the outside world zooming past.

We can extend this line of thought to a few more related situations. First of all, you don’t have to be in an elevator to experience this kind of weightlessness – any freefall situation will do. But what about standing in an elevator that is accelerating downwards at some other rate? If its acceleration is slower than freefall, you’ll feel lighter than normal, but not completely weightless. This accounts for the strange swooping sensation you feel in your stomach when an elevator starts going down. Similarly, when an elevator starts accelerating upwards, you feel a bit heavier.

If you’re feeling very comfortable with the ideas of motion described in Chapter 1, you’ll now be able to explain why you feel strange at the beginning and end of an elevator trip but not in the middle. (If you’re not, this paragraph may hurt your brain.) Once an elevator has started to go down, it moves at a constant velocity for most of the time until it stops. But moving downwards at a constant velocity is very different from accelerating downwards: when an elevator is moving but not accelerating, a dropped object will fall to the ground, just like normal.

This is a surprisingly difficult set of ideas to come to terms with, but if you put together everything we’ve talked about so far, you should be able to convince yourself that it’s true.

Scientists often use this kind of apparent weightlessness to create artificial ‘microgravity’ situations. NASA’s famous “Weightless Wonder” (or “Vomit Comet”, depending on who you ask), is flown in parabolic arcs designed to match the path of a projectile moving in freefall – like how a baseball moves when you hit a home run.

Vomit Comet, By NASA [Public domain], via Wikimedia Commons
It’s ok, it’s supposed to do that.
For about 25 seconds during each six-mile-long arc, the passengers move in freefall with the plane and thus feel weightless.[3. The pilot doesn’t just cut the engine so that the plane hurtles through the sky for a while – the engine has to counter air reistance in order to match a true freefall trajectory. Another possible point of confusion is that the passengers feel weightless even on the upwards part of the arc. Just remember that an object can be accelerating downwards even while moving up. Freefall is freefall, no matter where you’re headed at the time.]

Big Ideas:

  • Weight is the amount of gravitational force acting on an object. It changes depending on where the object is located.
  • Mass is the amount of matter in an object. It can only change if some mass is added or removed.
  • When a person is accelerating, they feel either heavier or lighter (depending on the direction of acceleration).
  • A person in freefall has no sensation of gravity at all.

Next: 3.4 – Orbits

Previous: 3.2 – Gravity