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Mass and weight                [En Español]

Are mass and weight the same?

Mass is a property of bodies which is related to the number and type of particles that make up that body. Mass is measured in kilograms (kg) and also in grammes, tonnes , pounds, ounces, etc.

The weight of a body is the force with which the Earth attracts it and depends on the mass that body has. A body with twice the mass of another has twice the weight. Weight is measured in Newtons (N) and also in kilograms-force, dynes, pounds-force, ounces-force, etc.

kg is therefore a unit of mass, not of weight. However, many devices which measure weight (scales, for example) have got scales graduated in kg instead of kg-force. This is usually no problem because 1 kg-force is the weight on the surface of the earth of a body of 1 kg of mass. Therefore, a person with a mass of 60 kg weighs on the surface of the earth 60 kg-force. However, that same person would weigh only 10 kg-force on the surface of the moon, even though their mass would still be 60 kg. (The weight of a body on the moon represents the force with which the moon attracts that body.)

If we put on two identical scales 1 kg of lead and 1 kg of straw, will the two scales measure the same?

As we have seen above 1 kg of lead and 1 kg of straw weigh the same: 1 kg-force. Therefore it seems common sense that both scales should measure the same. However, that is not the case, scales do not tell you the weight of the object you put on them but the force that object exerts on the scales.

What would the scales measure if we put a balloon on them? Obviously and in spite of the fact that it has weight (Earth exerts a force on it as does on all objects with mass) the scales would not measure anything, because the balloon would fly away and would not exert any force on the scales.

Lead and straw do not exert the same force on the scales even though their weight is the same. That is due to the fact that air pushes them upwards with different force.

Air, like all fluids (gases, liquids), exerts a force upwards, called buoyancy on all bodies submerged in it. The greater the volume of the body the greater the force.

Therefore, as 1 kg of straw has a volume much greater than 1 kg of lead, the force air exerts on the straw is also much greater than the force it exerts on the lead.

The scales the straw is on will measure slightly less.

The difference is small, 1g-force approximately.

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