How is mass different from weight?

Question

Somebody said they are different because of gravity.

In: 33

Answer 1

If you use a balance beam to “weigh” your sample. That means you put it on one side of a fulcrum and you put a known mass on the other side until it balances. Example, your sample is 7 grams. On the other side of the balance you put a calibrated 5 g and 2 g mass. The balance looks even.

If you bring your balance to the moon and try again, your 7 g mass weighs less because gravity pulls on it less. However, the 5 and 2 g masses also weigh less by the same factor, so your balance will still remain balanced and you will get the same answer of 7 g. This works because the force pushing down on the calibrated side changes with gravity.

A scale, on the other hand, uses a spring. The more you compress a spring, the harder it pushes back. Or more appropriately for this example, the harder you push a spring the more it compresses. The scale basically measures how much that spring compresses (in inches or millimeters or whatever) and does math to convert that to weight. (Sometimes, it will tell you kilograms or grams which is mass, but that ONLY works on Earth under Earth’s gravity).

If you take this scale to the moon and put the same sample on it that you did on earth, the sample is under less gravity, so it puts less force on the spring, so the spring compresses less, so the scale reads a lower number. If you’re reading in pounds or Newtons, these are measures of force (well, there’s pound-mass and pound-force because imperial is awful, but you get the idea), which means the answer is correct. That is the force your sample is putting on the scale. If it’s reading out grams or kilograms, the answer is incorrect because the scale is calibrated to tell you what mass object would produce that force *IF* it were on Earth.

So weight is a force. If you apply a force to a mass, it will accelerate. The higher the mass, the harder it is to accelerate, so the same force will result in less acceleration. This is what is meant by an object in motion tends to stay in motion and an object at rest tends to stay at rest, or inertia. The exact relation between force, mass, and acceleration is Newton’s second law F=m*a and this makes sense because if you jump out of a plane, your weight (force) begins accelerating your mass towards the Earth.