The acceleration due to gravity Mr. Ward European School Brussels 3 Download this presentation from morpheus.cc

If you were to drop two metal balls from the top of a high building, using ball of very different masses (say one ball five times heavier than the other) then what do you think would happen? A the heavy ball would hit the ground significantly before the lighter ball B the lighter ball would hit the ground significantly before the heavier ball C the two balls would hit the ground at almost exactly the same time

This is an experiment that was first done (it is said) by Galileo, who dropped two balls from the top of the leaning tower of Pisa. They were seen to fall side by side and hit the ground at the same time (if you put a metal plate on the ground then the experiment is even more convincing for you hear a ‘bang’ not a ‘bang-bang’).

In fact all objects falling near the earth’s surface have the same acceleration provided they are not significantly affected by air resistance. Something like a feather, a leaf or a sheet of paper would NOT have such a big acceleration for it would be significantly affected by air resistance.

On the moon there is no atmosphere so no vacuum tube is necessary. When astronauts went to the moon one of the experiments they did was to drop a hammer and feather together – they fell side by side and hit the lunar surface at the same time. However, if the metal ball is allowed to fall side by side with a feather in a tube from which the air has been removed (a vacuum tube) then they would fall side by side!

The acceleration of objects acted on by gravity ONLY (and not air resistance) is called the acceleration due to gravity or the acceleration of free fall or the gravitational field strength and is represented be ‘g’. At the surface of the earth g is equal to about 9.81 m/s² - we often round that to 10 m/s² to make calculations easier.

So ‘free fall motion’ is the motion of an object acted on by gravity alone (air resistance not significant). But what about an object that has been thrown straight up and is at the top of its motion and thus stationary for a moment – is it in free fall? Yes. Even an object that has been thrown up and is still rising fits the free fall definition above so the equations of free fall can be used (just be careful to use ‘+’ and ‘-’ signs to indicate direction properly).

The value of g varies slightly between different places on the earth’s surface – it’s a little higher at the poles and a little lower at the equator. Why? It’s because the spinning of the earth causes the shape of the earth to be a slightly squashed sphere, as if you had squeezed the earth between its two poles. Therefore when you are at the equator you are a little further away from the centre of the earth, making the gravity weaker.

As you go up above the earth’s surface the gravity (and the value of ‘g’) would weaken, but notice that even at the height that the International Space Station (ISS) orbits at the gravity isn’t much less than it is at the surface, since the ISS orbits about 400 km above the surface and this is a small distance compared to the radius of the earth itself (6366km). And of course the earth’s gravity extends all the way to the moon and beyond, for it is the earth’s gravity that pulls the moon’s motion into a circular orbit around the earth.

Imagine that a very deep mine shaft has been dug, all the way to the centre of the earth. In fact why not imagine the shaft going right through the earth from one side to the other! For this thought experiment, ignore the fact that inside the shaft it would be extremely hot, and ask yourself how the gravity would change as you go down the shaft towards the centre of the earth. Then ask yourself what the gravity would be like at the exact centre of the earth.

The answer is that as you go down beneath the surface of the earth the gravity would get weaker because there would be less and less ‘earth matter’ beneath you pulling you down. In fact there would be more and more earth matter above your head and this would be pulling you upwards. At the centre of the earth there would be no gravity at all and you would just float around. If you thought there WOULD be gravity at the centre of the earth then ask yourself which direction it would act in – does ‘down’ mean anything when you are at the centre of the earth??

Other celestial objects have gravity too – the gravity on the surface of the moon is about one sixth of the gravity at the surface of the earth, so at the surface of the moon g = 1.6 m/s² approx. Each planet has a different value of g at the surface, for example g = 3.70 m/s² the surface of Mars and g = m/s² at the surface of the gas planet Jupiter, the largest planet in our solar system.

One important use of ‘g’ is to calculate the WEIGHT of an object, for weight is defined as the pull of gravity on an object. Note that this means that weight is a force and is therefore measured in newtons and not kilograms. It is a VERY common mistake to express weight in kilograms – non- scientists make this mistake all the time. Mass is not the same as weight. Mass is the amount of matter in an object, measured in kilograms. Mass is a scalar quantity and weight is a vector quantity (like all forces). Mass does not depend on your location (i.e. on the strength of the gravity) whereas weight does. If you go to the moon then… your mass will be unchanged but your weight will be less. In outer space where there is no gravity you mass will still be same but your weight will be zero.

The equation that relates weight and mass is W = mg so a 1 kg object weighs about 10N on the surface of the earth, and a 100 gram object weighs about 1N. Note how I had to write the mass as 100 grams and not as 100 g otherwise you might confuse ‘g’ for grams with ‘g’ for gravity.) In fact a typical apple or hamburger has a mass of about 100 grams so the weight of an apple or a hamburger is about 1 N – think of a hamburger as a ‘newtonburger’ if you like.

Let’s go back to thinking about the International Space Station and the astronauts inside it. It’s often said that astronauts in an orbiting space craft are ‘weightless’ but is that scientifically correct? NO! We’ve already said that 400 km above the earth’s surface the gravity is almost as strong as it is at the surface, so according to W=mg the astronauts must have almost the same weight as at the surface.

But we see them floating around and we hear them saying they feel weightless… That’s the point – they FEEL weightless because there is nothing supporting them, nothing pushing up on them like the ground pushes up on them when they on the earth’s surface So there is the weight you FEEL, which we could call your APPARENT WEIGHT, and then there is your ‘true weight’ or ‘scientific weight’, the pull of gravity.

Scientists are really only interested in your ‘scientific weight’ because your apparent weight (the weight you feel) changes all the time. For example, if you jump from the top of a wall then for a moment you are not touching the ground – nothing is supporting you and you feel weightless like an astronaut, even though your true weight has not changed.

By now you should have realised that you cannot feel the force of gravity, only the contact forces that support you To convince yourself that you can’t feel the force of gravity, imagine being in a lift whose cable has broken, so the lift is in free fall – you would be floating around in the lift and feeling like an orbiting astronaut – you would not feel the force of gravity (and neither does the orbiting astronaut).

Two final more advanced notes about gravity, which you don’t need to know for any tests at this level: Gravity is not something that belongs only to very large objects like planets. In fact every object in the universe is attracted to every other object! The force depends on the masses and their separation, as shown in this equation F = Gm 1 m 2 /r² where G is a universal constant (not the same as g which changes from planet to planet), m 1 and m 2 are the two masses and r is the separation between their centres. G= 6.67 x SI units. If you want to, you can easily use the above equation to calculate the mass of planet earth, based on the fact that a 1kg object at the surface of the earth (6266 km from its centre) will be pulled down with a force of 9.81 N. It’s satisfying and impressive to be able to figure out the mass of something so huge!

Albert Einstein was very interested in gravity and spent much of his life trying to understand it better. He came to the conclusion that gravity is something of an illusion, actually caused by the ‘bending of the space-time continuum’.

He spent the second half of his life trying to figure out the connection between gravity and other basic force like electromagnetic forces, but he wasn’t able to do this and no one else has managed to do this either. It’s one of the great challenges still remaining in physics.