16.17 Weight

Before you read this, I suggest that you read posts 16.13 and 16.16.

In science the weight of an object is the force exerted on it by a gravitational field (post 16.16). We measure mass in kilogrammes (post 16.13) and weight in newtons (post 16.13) because it is a force.

In everyday English we say that an astronaut is “weightless” when he is drifting in space – this is the same as the scientific use of the word “weight”. Unfortunately we also say that a bag of potatoes “weighs” 4 kg. However, this isn’t the weight of the potatoes; it’s their mass.

So, in everyday English we use the word “weight” to mean both “mass” and “weight”. This shouldn’t be a problem if we remember to use these words correctly when we’re thinking about science. The mass of our potatoes depends only on the quantity of stuff in them – so it’s the same here and on the surface of the moon. However, the gravitational field of the moon is only 1.6 m.s-2 compared with 9.8 m.s-2 on the surface of the earth. So the weight of our potatoes is 4 × 9.8 = 40 N on earth but only 4 × 1.6 = 6 N on the moon! (You might want to look at post 16.7 to see why I haven’t given the answers to these simple calculations as 39.2 N and 6.4 N).

Why is everyday English potentially confusing? It may arise because of the way we measure mass. Nowadays we usually measure the mass of an object using a device that converts a force into an electrical signal (a force transducer); in order to do this our device contains a battery. We still sometimes use devices where we measure this force by measuring the distortion of a spring, either by things pulling it (a “spring balance”) or by things pushing down on it; these devices do not need batteries. In either case we measure the force exerted on the object by the earth’s gravitational field. However, the device displays the weight of the object divided by the strength of the earth’s gravitational field to show us its mass (in kilogrammes).

Measurement of mass is a bit more confusing when we think of using a device called a “balance” or “scales”, shown in the picture above. The balance is a horizontal beam with a pivot at its centre. At each end of the beam is a pan of equal mass. When we place an object of unknown mass in one pan, it is pulled downwards by the earth’s gravitational field and the beam is no longer horizontal. We then add objects of known mass (unfortunately called “weights”) to the other pan until the beam is horizontal again. Then the forces acting on the objects in both pans are the same so their masses must be equal. The mass of the unknown object is then the sum of the masses of the objects of known mass. If we repeat this procedure on the surface of the moon, we will get the same results as we obtain on earth. This is because both the object of unknown mass and the objects of known mass are in the same gravitational field which exerts the same force on both of them. You may need to think about this for a while!

It might be a good idea if scientists stopped using the word “weight” and always used “gravitational force” instead!

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