Newton's Law of Gravitation
Earth and Space

Falling - physics narrative

Physics Narrative for 11-14 Supporting Physics Teaching

Falling at the same speed

One of the consequences of living in a gravitational field, where the force on an object depends on its mass, is that all objects fall at the same rate providing that there are no other forces acting.

A much-celebrated example of this occurred in 1971 when Apollo 15 astronaut Dave Scott dropped a hammer and a feather on the surface of the Moon.

The Moon's lack of atmosphere provided the ideal conditions to confirm what Galileo had anticipated centuries before. The hammer and feather fell together to hit the Moon's surface at the same instant and Dave Scott was able to report:

How about that, this proves that Mr. Galileo was correct in his findings.

Here on the surface of the Earth there is another force acting, which is air resistance. This has a significant effect on light objects (such as pieces of tissue paper or feathers) and balances out the gravitational force at relatively low speeds. The result is that most people, including most children, believe that heavier objects fall faster, which is true if air resistance has an effect and not true if this effect is removed or minimised (as it is on the Moon).

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How do we know that objects of different mass fall at the same rate?

Firstly, it is easy to repeat the experiment that Galileo is supposed to have carried out in dropping a musket ball and a cannon ball off the Leaning Tower of Pisa.

For a spectacular demonstration of this you might try dropping a melon and a peach simultaneously from the school roof or upstairs window.

For a less spectacular demonstration, try dropping a bunch of keys and an A4 sheet of paper. Naturally the keys get there first. Now repeat this process but this time, scrumple the piece of paper. Half of the class, at least, will not believe their eyes.

An approach through dialogue

Galileo used an alternative approach to argue the case, by using a thought experiment that involves two characters. Simplicio is characterised as being rather simple or dumb, whilst Salviatti is a bit of a know-all.

Salviatti asks Simplicio to consider two balls, one heavier than the other and asks:

Salviatti: Which will fall faster?

Simplicio states that it will be the heavier one. Salviatti then poses the following conundrum.

Salviatti: But if we tie them together, the larger stone will be slowed down by the smaller and the smaller stone speeded up by the larger, will it not?

Simplicio: Yes.

Salviatti: But what this means is that their joint speed is less than the speed of the larger stone on its own. Yet tied together they have an even bigger mass than the larger stone which would mean they should go faster. Should they not?

This conversation shows that the idea that heavier things fall faster is simply logically inconsistent and the conundrum exposes the weakness of this theory.

If all things fall at the same rate there is no inconsistency.

Newton's Law of Gravitation
is expressed by the relation F=G(m_1)(m_2)/r^2
can be used to derive Kepler's First Law
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