Is A Kilo of Iron Greater Than a Kilo of Wool?

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

30 October 2005

After last week’s article on the peculiar measurements used by Kenyans, a debate started simmering in my mailbox. The topic is; between, volume, mass and weight what is more reliable? One reader has revived the age-old question: which is greater, a kilo of wool or a kilo of iron?

Volume is the amount of space occupied by an object. It is the first quality we notice when we observe something. But it can be misleading: for example, a football looks very large but in reality it is made with very little material – the inside is hollow. Nevertheless, if a substance is fairly homogeneous (as in a liquid), volume can be a good measure of the quantity.

Mass is the quantity of matter in a substance. That is, the amount of elementary particles it contains. If two objects have equal mass, then they have equal quantities of matter, regardless of whether they are made of the same material.

Weight is the amount of gravitational force experienced by an object. It is measured in kilograms-force (kgf) and one kgf is the weight of a one-kilogram mass under one standard earth gravity. It is not the same thing as mass. Weight is measured on a spring balance while mass is determined from a scale balance.

One of the greatest differences between the two is that weight varies depending on which location it is measured from while mass remains constant. For example, a body that weighs 60kgf on Earth would weigh only 10kgf on the moon.

The reason is that the gravitational force on the moon is about one sixth that on the Earth. However, the mass of the body remains 60kg wherever it is measured. Indeed, before Einstein came to complicate things, scientists used to say that mass can neither be created nor destroyed…but that’s a story for another day.

Even here on earth, different places have different gravitational intensities thus the weight of an object varies from location to location. The force of gravity reduces as one moves farther away from the centre of the planet. Consequently, the weight of an object measure at Mombasa is about one percent more than that weighed at the top of Mount Kenya.

With this knowledge we can attempt to answer the question whether a kilo of iron is greater than a kilo of wool. Of course the wool would look bigger (has greater volume) than the piece of iron, but that doesn’t mean that it has more matter. Thus the answer is that none is greater than the other.

But things are not always straightforward: when you immerse your body in water, you feel lighter (it is said that this observation made Archimedes run naked through the streets of Syracuse shouting EUREKA! EUREKA!). This effect is observed every time an object is put in a fluid (i.e., liquid or gas) and the weight reduction is proportional to the volume.

Therefore the question arises: since we take our measurements in air, wouldn’t the wool experience greater reduction of weight due to Archimedes’ principle? Would that then mean that a kilo of wool is more than a kilo of iron? Hmm…