mass vs weight


Conceptually I understand that mass is a measure of the amount of stuff present in an object, while weight is a measure of the force of gravity applied to that object. An object of a given mass will have a bigger weight on Earth than on the moon because Earth’s gravity is stronger. But… mass is determined by weighing an object on a scale. And there is a simple mathematical conversion between grams (mass) and pounds (weight), implying that they’re just different units for the same concept. So what gives? (Also this is a question that applies to so many fields, I had no idea which flair to apply.)

In: 53

>But… mass is determined by weighing an object on a scale.

In the circumstances you’re familiar with, sure. But you can also measure an object’s mass by applying a known amount of force to it and observing its acceleration, or in some astronomical cases, measuring its gravitational effect on other objects (which objects, in a cool way, you don’t even have to observe directly, sometimes).

>And there is a simple mathematical conversion between grams (mass) and pounds (weight)

Again, *under familiar conditions.* Objects in freefall (ie, orbit) have zero weight, but positive mass: that usual conversion doesn’t work in space.

>But… mass is determined by weighing an object on a scale.

The scale experiences the force of your weight (w=mg), but since acceleration due to gravity (g) is constant, it is calibrated to show you the mass (m) of the object that should be producing the weight (w) it is experiencing

In other words, the scale is a sort of a calculator for mass

Bob and Alice use kilos for weight, and they’re incorrect. They should use newtons, but since everyone knows what they mean then it doesn’t matter (until you get to physics class or go to the Moon).

Strictly speaking pounds measure mass, so the same applies as for kilograms. If you want to be specific, use “pound-mass” or “pound-force”.

Your mass is the same everywhere in the universe. On the moon your mass is, say, 75kg, on mars it’s 75kg, in microgravity it’s 75kg, on earth it’s 75kg, on the surface of a neutron star it’s 75kg.

This mass doesn’t change. The work needed to move that mass also doesn’t change. If you want to accelerate 1000kg on earth (~~parallel~~ *perpendicular* to gravity so it’s not helping you) that takes the same effort as accelerating it on the moon, on mars, in space, etc.

Once accelerated and moving at a constant velocity it has the same kinetic energy on earth, the moon, mars, etc.

Along the same lines – put a mass on a strong and spin it in a circle at a given speed. The centripetal force in the string is going to be the same on earth, mars, the moon, etc (well, almost as long as it’s going fast enough the forces from local gravity aren’t significant, or if it’s on a surface that supports its weight).

Your weight however is the force your body experiences due to gravity. On the moon your weight is less than on earth. Ditto on mars. Your weight is not directly tied to momentum, kinetic energy, acceleration, etc. It’s just your mass multiplied by local gravitational force – it affects how much work you need to do to move through gravity (Eg stand up) but it does not affect kinetic energy; momentum, acceleration, etc.

You know how it’s much easier to lift people when they’re in swimming pools? Why is that? It’s not like parts of their bodies are missing when they get in the water. The person’s body has a fixed mass (ie they didn’t lose anything when they got in the pool), but their weight has been offset by the weight of the water they’ve displaced. If they were to stand on a submerged scale it would show truly profound weight loss… until they got out and dried off. Yet, the amount of force it would take you to accelerate them would not decrease.

You’ve doubtlessly seen people on the ISS experiencing weightlessness, and you’d surely find it preposterous if the force of a sneeze accelerated them to lightspeed, so clearly they still resist acceleration (which is all that mass is), so what gives? How could someone lose their weight but not their mass if the two are the same thing?

What you think is a simple conversion is not so simple. It depends on a lot of factors.