Wonders of Life by Brian Cox & Andrew Cohen

Author:Brian Cox & Andrew Cohen
Language: eng
Format: epub
Publisher: HarperCollins

It seems obvious, because of our experience, that small things should bounce whereas big things splash. But why is this? At first glance, one might not expect there to be any difference. All objects fall at the same rate in a gravitational field in a vacuum. The deep explanation for this is that they are following geodesics – that is ‘straight lines’ – in spacetime curved by the presence of the Earth. Since their paths have everything to do with the spacetime and nothing to do with their mass, it should be obvious that all objects (including, note, light itself, which has no mass at all) fall towards the ground at the same rate. This is graphically demonstrated in orbit, where astronauts and water droplets float happily together inside a spacecraft, all of which might be described as plummeting towards the Earth. In the presence of air, however, all things do not fall at the same rate. This, as Haldane notes in his essay, is due to the increasing effects of air resistance as animals get smaller. This is a consequence of the scaling laws we discussed earlier in the chapter. If we think in more Newtonian language, for a moment, which is appropriate, then we can picture two forces acting on a falling animal. The gravitational force, acting downwards towards the Earth, is proportional to the mass of the animal, which is proportional to the cube of its size. The drag force (air resistance) acts in the opposite direction to slow the animal down, and this is proportional to the surface area of the animal, which is proportional to the square of its size. As an animal gets smaller, therefore, air resistance becomes more important. If the animal falls for long enough, it reaches what is known as terminal velocity, which is given by

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