# Mass and weight

Imagine pulling a 50 kg crate across a smooth floor. It's difficult because the mass of the crate is large, 50 kg.

Now think about what happens when you take the same box to the Moon and try to drag it across a floor of just the same type as the one on the Earth – it will be just as difficult because the MASS of the box has not changed. It is still 50 kg.

(Ignore any friction between the box and the floor)

Now imagine LIFTING the crate on the Earth. This time the important thing is the force of the Earth's gravity on the crate. As you know gravity acts downwards. So, lifting up the crate means that we have to move it against the force of the Earth's gravity.

The force of the Earth’s gravity on every kilogram is about 10 N.

Put another way the gravitational attraction of the Earth is about 10 N/kg. (At sea level this attraction is nearer 9.8 N/kg).

We call the force of attraction of the Earth’s gravity on an object the WEIGHT of the object

The weight of an object is a force and is so is measured in Newtons, while the mass of an object is measured in kilograms.

To find the weight of an object you simply multiply its mass (in kilograms) by the force of the Earth's gravity on 1 kg (10N).

Weight (W, Newtons) = Mass (m, kg) x Gravitational field strength (g, N/kg)

On the Earth the weight of our crate will be 50x10 = 500 N

Now imagine taking the crate to the Moon and lifting it up there. Its mass is still 50 kg but the Moon's gravitational pull is only about 1/6 of the Earth's – in other words about 1.6 N/kg. This means that the weight of our crate on the Moon will be 50x1.6 = 80 N and so it will be much easier to lift up.

Since Force = mass x acceleration we could also find the weight of an object by multiplying its mass by the acceleration of free fall. You would get the same numbers as in the examples above because the acceleration in free fall is 10 m/s2 on the Earth and 1.6 m/s2 on the Moon.

Some examples of other masses are shown in the table.

 Mass on the Earth Weight on the Earth Mass on the Moon Weight on the Moon 100 g 1 N 100 g 0.16 N 60 kg 600 N 60 kg 9.6 N 100 kg 1000 N 100 kg 160 N 1000 kg 10 000 N 1000 kg 1600 N

On other planets the strength of the gravitational field and the acceleration in free fall is different from that on the Earth and so our crate would weigh different amounts if taken to these planets. The table below gives you some weights of our 50 kg crate on other planets.

 Planet Weight of the 50 kg crate Mercury 190 N Venus 440 N Earth 500 N Mars 190 N Jupiter 1245 N Saturn 520 N Uranus 520 N Neptune 690 N (Pluto) 14.5 N

(Remember that its MASS is the same everywhere including in deep space or in orbit round any planet where it would be weightless!)

It's interesting to look at the weights of our crate on Earth and on Saturn or Uranus. They are almost the same. That means if you were to go to Saturn or Uranus you would weigh just about the same as you do here. However on Pluto you would be lighter than on the Moon. What do you think that means about astronauts' athletic records on Pluto?

On the surface of our Sun the gravity pull is so strong that our crate would weigh an enormous 13 700 N!

The mass of an object stays the same no matter where it is in the Universe. The weight of an object changes depending on the gravitational pull at the place where it is.

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© Keith Gibbs 2020