Gravity related to mass and 'weight'

Weight and weighing machines

There isn't a place on the face of the Earth where there is no gravity acting. This means that every object we ever come across is located in the Earth's gravitational field and is therefore acted upon by at least one force, the force due to gravity.

To keep the physical basis of the interaction in mind we suggest you call this the gravity force on the object (purists might prefer the gravitational force – but that's just much harder to spell. Gravity acts towards the centre of the Earth or, more simply, downwards. The force arrow representing the gravity force is best drawn from the centre of an object in a direction straight downwards.

The gravity story, of course, goes way beyond the Earth. Gravity is a universal force which acts between any two objects with mass wherever they might happen to be in the universe. (There is more on gravitational force in the Gravity and Space episode in the SPT: Earth in space topic.)

For most everyday purposes, there really is no need to distinguish between mass and weight. People understand equally well if you say that the mass of the bag of potatoes is 5 kilogram or if you call this the weight of the potatoes. However, in science, and particularly in physics, there is a clear distinction between the mass of an object and the pull of gravity acting on an object. If learners are to understand this area of science, they need to appreciate the difference between mass and force.

Over to you. Give it your best shot. Just what is the difference between mass and gravity force? Give yourself a minute to gather your thoughts. Try explaining this to a friend.

It may be that your thoughts involve ideas about forces, particles (or stuff), perhaps even the Moon – which makes a regular appearance in such explanations. It is a good idea to start with the force of gravity. It is within our everyday experience that some things weigh more than others. Just try lifting them. Weighing machines measure how much force you need to hold an object up steadily. So it seems simple, and helpful, to call this supporting force the weight.

For example, in supermarkets you'll find top pan scales and also hanging basket scales. Both instruments use the pull of gravity to measure the weight of groceries. They work on the principle of finding the upward force required to stop the groceries from falling to the ground. When a measurement is taken, the upward force from the weighing machine, or scales, balances the downward pull of gravity. This is an example of two forces in equilibrium. In school a newtonmeter will do the same job. The weight then is a supporting force, which is measured in newtons. Weighing machines show the magnitude of this force, which is often a tension force or a compression force.

Mass and weighing

What then of mass? The best place to start is to realise that you can't show mass with an arrow in a sketch. Mass doesn't have a direction. It is not about pushes or pulls. It is about how hard it is to change the motion.

Things with more mass are harder to get going and harder to stop once they are going. The mass is an inertial property. A 3 kilogram bag of potatoes will be harder to throw than a 5 kilogram bag. Mass is measured in units of kilograms. The number of particles in side something is measured in moles, and is the correct unit for quantity of matter.

There is a clear link between the mass of a bag of potatoes and the pull of gravity on the same bag. A 5 kilogram bag will weigh more than a 3 kilogram bag (the 5 kilogram bag has a force acting on it of about 50 newton at the Earth's surface and the 3 kilogram bag a a force acting on it of about 30 newton). The more the mass of something, the greater the a force acting on that thing. There is a deep connection between an object's reluctance to being accelerated and the gravity force acting on it.

Let's suppose you take a 5 kilogram bag of potatoes to the Moon. Don't ask why! If the bag felt heavy on the Earth it will be much easier to lift on the Moon. Can you explain why?

Everything weighs less on the Moon because the pull of gravity at the surface of the Moon is weaker than that on Earth. It is about 15 ^th that on the Earth. Thus the 5 kilogram bag of potatoes has a force of about 50 newton acting on it at the surface of the Earth and about 10 newton on the Moon. Everything feels lighter. This is simply because the Moon has a smaller mass than the Earth.

However there is still exactly the same number of potatoes in the bag, so it's just as hard to accelerate. The 5 kilogram mass has not changed but the gravity force (and so the weight) has. Therein lies the difference. Force depends on gravity; mass just depends on the object. Consider the force needed to bring an Earth-bound running rugby player to rest inside a metre. The same force would be needed to stop the same player, moving at the same speed, within the same distance, on the Moon. You are still faced with stopping the same mass moving at the same speed.

The essential point is that mass does not vary. If you measure the mass of an object here on Earth and on the Moon, you would find it is exactly the same. This is in line with common-sense. If you take an object to the Moon, it is the same object: Some properties should remain the same and mass is one of those intrinsic properties.

The 5 kilogram bag of potatoes would weigh about 120 newton on the surface of Jupiter (the strength of Jupiter's surface gravity is about 24 newton on every kilogram). Planets more massive than the Earth have stronger surface gravity. Stars, millions of times more massive than the Earth, have enormous surface gravity. Black holes, so massive it is almost impossible to imagine, have such strong surface gravity that even light rays are pulled inwards. This is why we can't see them. They appear black.

Finally, just to confuse us all, most everyday weighing machines don't give you a reading in newtons. For example, any set of bathroom scales that you are likely to use at home will be calibrated in kilograms (and stones and pounds!). In day-to-day life we find our weight in kilograms. In scientific contexts we measure force in newtons. This is a good example of a situation where everyday and scientific ways of talking and thinking differ from one another.

The supermarket weighing machine that tells you that a bag of bananas weighs 3 kilogram really measures the support force to be about 30 newton and then divides by ten to give you the mass of the bananas as 3 kilogram. It can be programmed to do this because on Earth gravity pulls every 1 kilogram down with a force of about 10 newton (actually about 9.8 newton, but 10 newton is close enough at this level). So something weighing(needing a support force – compression or tension) about 30 newton is going to have a mass of about 3 kilogram.