Mass and Weight

First of all, let’s agree that no matter whether you ever understand the difference between mass and weight we are NEVER going to talk about “stones”, “pounds” or “ounces” !!

Only people who are lost in time or who are literally in the “stone” age still use stones, pounds and ounces; apart, of course from Americans, who don’t use stones but do use pounds!

In the UK, for a long, long time we have used Kilograms for our measurement of…………(mass or weight?)

What are we measuring when we stand on our bathroom scales? Mass or weight?

When a person stands on a bathroom scale and announces to the world “my weight is 75kg.” they have got it….. .WRONG.

They should announce: “My mass is 75kg.”

Bathroom scales tell you your Mass, in Kilograms. That’s a fact. So, learn it.

They do not do not tell you your Weight.

OK, so we need to know what is really meant by Mass and by Weight.

Time for definitions again:

Mass is a measure of the amount of matter or stuff in an object, measured in Kg.

So Mass is purely a property of the object and it will NOT change if the object is moved from place to place in the universe (eg from Earth to the Moon). If your mass is 75kg on Earth, it will be 75kg on the Moon or if you were floating about on the International Space Station.

Weight is the force acting on an object due to gravity, measured in newtons (N).

So Weight depends on both the mass of the object and on the local gravitational field strength. It WILL change if the object is moved from place to place in the universe. We would all weigh less on the Moon, but we would all weigh a lot more on Jupiter (not that anyone plans to go there!).

Mass is easy, its just a measurement in Kg.

Weight, on the other hand, depends on two things or two factors.
The first is the mass of the object.

Not surprisingly, we find that the weight of an object is greater for objects with large masses; in fact weight and mass are directly proportional to each other.
(If you have already worked through 3.1.3 Contact Forces then you will have met the idea of "proprtional" and "directly proportional" before)

So, the first factor is: The Weight of an object is directly proportional to the mass of an object.

The second factor on which weight depends is: The Weight of an object is directly proportional to the size of the local gravitational field strength, which is all about how massive the planet is on which you are standing or are close to.

Most of the time we are on the surface of the Earth and the size of our local gravitational field strength is about 10 newtons of force on every 1kg of mass or to put it more neatly,

the gravitational field strength at the Earth’s surface is 10N/Kg.

The two quantities, mass and gravitational field strength, come together in the following formula which we use to calculate the weight of an object.

Notice that the unit for Weight is the newton.

This shouldn’t surprise you because we have said that weight is a Force, so never again shall you say that your weight is so many kilograms (or so many stones!!!)

Hopefully you managed to correctly answer all of the above questions.

You must learn the formula for weight and be able to recall the values of g on Earth (10N/Kg) and on the Moon (1.6N/Kg).

Let’s move on now to consider what causes weight?

Isaac Newton’s Universal Law of Gravity

In about 1660 Sir Isaac wrote his famous law of Gravity and this is what it stated;

“Every object in the universe pulls every other object with a gravitational force which increases as their masses increases and decreases as their separation increases.”

To help to understand this force, Newton spoke of a “field of gravity” around each mass and whenever any other mass entered this field it experienced a force.

Now, we have already been using the idea of a “gravitational field” because our formula for Weight involved the Gravitational Field Strength; do you remember?

We could think of this “field of gravity” as a “force field” around the object. So, every object, including us, has a force field around it! The force field is very weak for objects with a small mass, like us, but it is large for objects with a large mass, like a star such as our Sun or a planet.

For example, there is a significant force due to gravity between the Sun and the Earth.

Notice, Newton's Law tells us that whenever two objects interact, BOTH feel the same pull due to gravity, so in this diagram the force arrow lengths are the same. Also notice that in each case the force acts from the C.O.M, which is at the centre of each sphere.

Between the Sun and Venus there is also a force due to gravity, but because Venus is closer to the Sun than the Earth the force is LARGER, in accordance with Newton’s Law – as the distance between the objects decreases, the force increases.

Venus is similar in mass to the Earth but is closer to the Sun so the force of gravity is greater, so the force arrows here are longer, but still a pair of force arrows.

Newton's idea of a "gravitational field" or a "force field" around an object like the Earth helps to explain the behaviour of other objects which come close to it. For example, as meteors or small asteroids pass close to the Earth, they enter its gravitational field and get attracted towards the Earth which might cause them to veer off their origninal path and to crash through the Earth’s atmosphere where they burn up and we see them as “shooting stars”.

Even smaller objects like artificial satellites (eg those used for GPS systems or satellite TV) and space stations such as the International Space Station, are kept in orbit around the Earth by the force of gravity, though the size of the force is much smaller than between, say, the Sun and any of the planets.

Here the force of gravity between the Earth and a satellite is tiny compared to other astronomical objects, so the force arrows are drawn shorter. NB Their thickness is unimportant.

Let’s also mention the most common example of Newton’s Law Of Gravity, the force of gravity between each one of us and the Earth; the force which we tend to call our “weight” which we have already learnt a lot about.

The force of gravity between the Earth and a person is very small compared to all the others mentioned above, so the force arrows are the smallest, but still notice that the Earth is pulled just as much by you as you are pulled by it! Hence the two arrows, always.

Why don’t we notice this?

The reason is that the Earth’s mass is so unbelievably huge compared to our mass that it barely moves in the interaction between it and us; so, although we get noticeably pulled towards the Earth, the Earth does not get noticeably pulled towards us!

Finally, if you have already worked through 3.1.3 Contact Forces which was my suggestion at the top of this page, you will know that forces are either Contact Forces or Non-Contact Forces.
Well, to which type do you think Gravity belongs? Check

To end this section:
Now that we have an understanding of the cause of gravity and how it varies if we were to travel around in space, consider how we would cope if we did travel throughout our solar system.

We would start on Earth in "normal" gravity (g = 10 N/Kg) but fairly quickly, as we move away from the Earth, g would become very small and we would begin to feel such a small "weight" that we would describe ourselves as weightless.

If we travelled to the Moon we would re-gain weight but not as much as on Earth, and so on...

You can think of how such a journey would continue all the way past each planet and how your weight would vary as you approached and maybe landed on each one (those that are solid). Near Jupiter your weight would be huge etc.