## Wednesday, April 6, 2016

### Mass versus Weight

The "bulk bag" of industrial powder massed over a ton (2,400 pounds to be exact). It was suspended from a chain and could turn easily. For some reason I wanted to turn it (I don't remember the reason why). So I pushed on it and got it spinning. When I wanted it to stop spinning, I tried to do so. And I found it nearly impossible. It was weightless, but it still had mass and therefore momentum and I couldn't stop its angular momentum as easily as I thought I should be able to.

That was a real-life practical experience for me dealing with mass versus weight.

Mass is a property of matter. All matter has mass. Mass is important. For example, in Newton's second law, force equals mass times acceleration (F=ma). And momentum is mass times velocity (p=mv).

("Force," "acceleration," "momentum," and "velocity" are all vectors but we'll ignore that for simplicity sake.)

Weight depends on a gravitational field. Weight equals mass times the force of gravity (W=mg). But the force of gravity is not a constant and is depended on mass of the two objects being acted upon, and the distance between them. But when one of the objects is the Earth (5,972,000,000,000,000,000,000,000 kg) and the other is you (say 100 kg), you can pretty much ignore your mass.

Earth's gravitational acceleration is 9.8 meters per second per second. That means in on second falling on Earth, you'll be going 9.8 meters per second (about 22 mph). After another second you'll be going 19.6 meters per second (44 mph). After five seconds you'll be going 49.0 meters per second (110 mph). (This assumes no air resistance).

So let's say you mass 100 kg. So your weight on Earth is (using F-ma) 980 Newtons. Nobody talks Newtons when it comes to weight. So how do you convert Newtons to kilograms? Divide by the acceleration of gravity) "g" which is 9.8 and, voila, you weigh 100 kg.

Now, on the moon, the acceleration of gravity is about 1/6th that of the acceleration of gravity on Earth, or 1.63 meters per second per second. So on the moon you weigh 100kg times 1.63 = 163 Newtons. divide that by g and you get 16.6 kilograms. Which is what you would weigh on the moon.

But you still mass 100 kg. Remember our equation for momentum was p=mv? On the moon, "m" is the same (100 kg) as on the Earth, on Venice, an Rigel IV, where ever. So a walk of say 4 mph on Earth is 1.8 meters per second. So you'd have a momentum of 180 kilogram meters per second. And on the moon, you'd have the exact same momentum.

Here's the tricky part. Fiction depends on weight. So you stop walking on Earth and the fiction you have is six times that you have on the moon. You stop quickly, but on the moon you'd probably bump into the wall because you couldn't stop as fast. You have less weight but you have mass and therefore momentum.

Clear as mud?