Mass

Eitan asks me how to measure mass. As I consider his question I realise that I have no idea how to even describe mass. Here is Arthur's follow-up:

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OK, but this is not an easy one...

My thought is that you keep this answer "alive" over a period of time with Eitan because it's something that may take a while for him to truly grasp. Point out the concept when you see examples of it around you in the world.

Technically, mass is the reluctance of an object to move. More technically, it's the reluctance to CHANGE speed. If you start something moving or stop it moving, either way, how hard you have to push is aconsequence of its mass. The problem with this definition is that on earth, most of the time when we move or stop something, we are dealing with a lot of friction that gets in the way of seeing what's going on. For example, it is entirely possible for an ant to push a car. The car
would just speed up very, very slowly because of its large mass and the weak push from the ant. In real life, the friction in the tires and wheel bearings and so on make it impossible for an ant to move a car.

Even a single person has trouble getting much motion going. If you leave out friction, the greater the mass of an object, the harder you need to push to get a result. Twice the mass and you need to push twice as hard for the same change of speed. You may recall that there have been instances of astronauts manhandling satellites orbiting right next to the shuttle. The satellites may weigh a ton or more and it takes a very great effort to move them, but the astronauts can do so. I raise this example because in space, there's no friction.

On earth, one example that occurs to me is really heavy metal doors that some office buildings sometimes have. If you can find one that doesn't have a spring closure (The doors at Seymour center come to mind), you can see for yourself how hard it is to get them moving and then how hard
It is to stop them once they are moving. Maybe you can see a bit of a difference in the doors in your house. The front door is probably pretty solid. Compare that to interior doors, particularly if you can find one that is flimsy and hollow.

Here's something you could try if you have two skate boards. On a really smooth floor (definitely not on carpet), you and Eitan stand facing each other each on a skate board. Now push yourselves apart (push against each other) and you should see that because you are more massive, you move less than Eitan who is less massive. The moral is that for one push you shared, Eitan moved more than you did because of the difference in mass. You can also do this next time you're ice skating and probably get even better results.

Now for the clincher. It turns out that mass is proportional to weight. It's not sort-of or approximately proportional. It's exactly proportional. I remember reading some musings by Einstein in which he
pointed out that no one had ever really questioned why the pull of the earth is exactly proportional to mass (you have to ponder this a moment.

An object that has twice the mass is tugged on by the earth EXACTLY twice as hard - it has twice the weight - with the result that all objects fall towards the earth under the pull of gravity at the same
speed regardless of their mass. A bus and a coin fall at the same speed. The earth pulls on the bus much harder than it pulls on the coin (you can weigh them to see the difference in the earth's pull). Somehow the earth magically determines the mass of the objects (their reluctance to move) and adjusts the tug of gravity by just the right amount to get them moving at the same speed.) Einstein had to develop the theory of general relativity to fully explain this.

So the point of that last paragraph is to point out that you can exactly measure the mass of an object simply by weighing it! But you have to do it on earth. If you do it on the moon you will get a different weight because the pull of the moon's gravity is much less. Of course you can still use the weight on the moon to determine mass, but you need to take into account the weaker gravity.

Phew!

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