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## What is the difference between mass and weight?

Some people find these ideas confusing because in daily life there is no distinction between weight and mass. They are treated as the same thing.

Mass corresponds to the amount of matter present. A bus has more mass than a car, an elephant has more mass than an ant, etc ...

The weight is proportional to the mass, but is not the same thing. It is a force. The weight is a result of the gravity pull. ##### g = acceleration of gravity m = mass

All objects on the planet are being pulled towards its center.According to the law of gravity, the bigger the mass, the bigger the pull, the bigger the weight. That is why stuff that have a big mass also are heavy. The force that pulls objects down is called weight, and it is a result of gravity..

If there was no gravity, objects would have no weight, but they would still have mass. We know that when astronauts are on the moon, they are able to do big jumps because they weigh less in there. Furthermore, the moon has no atmosphere (no air), because a stronger gravity is needed to pull air molecules. That is because the gravity pull on the moon is smaller than in the earth, because the moon is smaller (gravity is proportional to mass). If astronauts in or around the space station their weight is zero, although their mass is still the same as in the Earth.

Formulae and calculations

Mass (m) is measured in kilograms (kg) and weight is measured in newtons (N). These are the SI units and you must make sure that you use those when calculationg something because otherwise you may get it wrong.

The weight is a force, and it will be represented as F . You could use W for weight, but we will leave W to be used for work. Note that weight is a force but not every force is weight, because there are also other forces.

Force (F) = mass (m) x acceleration of gravity (g)

F = m x g

Let's assume that g = 10 m/s2 . Sometimes it is taken as 9.8, but we will use 10 to make calculations simpler.

Examples

a) What is the weight of a person of mass 60 kg? (assuming that the person is on the earth)

F = 60 * 10 = 600 N

b) What is the weight of a person of mass 60 kg, standing on the surface of the moon? gmoon = 1.6 m/s2

F = 60 * 1.6 = 96 N

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