# 0.3 Gravity and mechanical energy

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## Weight

Weight is the gravitational force that the Earth exerts on any object. The weight of an objects gives you an indication of how strongly the Earth attracts that body towards its centre. Weight is calculated as follows:

$\mathrm{Weight}=mg$

where $m$ = mass of the object (in kg)

and $g$ = the acceleration due to gravity ( $9,8\phantom{\rule{2pt}{0ex}}m·$ s ${}^{-2}$ )

For example, what is Sarah's weight if her mass is $50\phantom{\rule{4pt}{0ex}}\mathrm{kg}$ . Sarah's weight is calculated according to:

$\begin{array}{ccc}\hfill \mathrm{Weight}& =& mg\hfill \\ & =& \left(50\phantom{\rule{4pt}{0ex}}\mathrm{kg}\right)\left(9,8\phantom{\rule{0.166667em}{0ex}}\mathrm{m}·{\mathrm{s}}^{-2}\right)\hfill \\ & =& 490\phantom{\rule{4pt}{0ex}}\mathrm{kg}·\phantom{\rule{0.166667em}{0ex}}\mathrm{m}·{\mathrm{s}}^{-2}\hfill \\ & =& 490\phantom{\rule{4pt}{0ex}}\mathrm{N}\hfill \end{array}$

Weight is sometimes abbreviated as ${F}_{g}$ which refers to the force of gravity. Do not use the abbreviation $W$ for weight as it refers to `Work'.

Now, we have said that the value of $g$ is approximately $9,8\phantom{\rule{4pt}{0ex}}m·s{}^{-2}$ on the surface of the Earth. The actual value varies slightly over the surface of the Earth. Each planet in our Solar System has its own value for $g$ . These values are listed as multiples of $g$ on Earth in [link]

 Planet Gravitational Acceleration (multiples of $g$ on Earth) Mercury 0,376 Venus 0,903 Earth 1 Mars 0,38 Jupiter 2,34 Saturn 1,16 Uranus 1,15 Neptune 1,19 Pluto 0,066

Sarah's mass on Earth is $50\phantom{\rule{4pt}{0ex}}\mathrm{kg}$ . What is her mass and weight on Mars?

1. m (on Earth) = $50\phantom{\rule{4pt}{0ex}}\mathrm{kg}$

m (on Mars) = ?

Weight (on Mars) = ?

2. Sarah's mass does not change because she is still made up of the same amount of matter. Her mass on Mars is therefore $50\phantom{\rule{4pt}{0ex}}\mathrm{kg}$ .

3. $\begin{array}{ccc}\hfill {\mathrm{Sarah}}^{\text{'}}\mathrm{s}\phantom{\rule{3.33333pt}{0ex}}\mathrm{weight}& =& 50×0,38×9,8\hfill \\ & =& 186,2\phantom{\rule{3.33333pt}{0ex}}\mathrm{N}\hfill \end{array}$

## Differences between mass and weight

Mass is measured in kilograms (kg) and is the amount of matter in an object. An object's mass does not change unless matter is added or removed from the object.

The differences between mass and weight can be summarised in the following table:

 Mass Weight 1. is a measure of how much matter there is in an object. 1. is the force with which the Earth attracts an object. 2. is measured in kilograms. 2. is measured in newtons 3. is the same on any planet. 3. is different on different planets. 4. is a scalar. 4. is a vector.

## Weight

1. A bag of sugar has a mass of $1\phantom{\rule{4pt}{0ex}}\mathrm{kg}$ . How much does it weigh:
1. on Earth?
2. on Jupiter?
3. on Pluto?
2. Neil Armstrong was the first man to walk on the surface of the Moon. The gravitational acceleration on the Moon is $\frac{1}{6}$ of the gravitational acceleration on Earth, and there is negligible gravitational acceleration in outer space. If Neil's mass was $90\phantom{\rule{4pt}{0ex}}\mathrm{kg}$ , what was his weight:
1. on Earth?
2. on the Moon?
3. in outer space?
3. A monkey has a mass of $15\phantom{\rule{4pt}{0ex}}\mathrm{kg}$ on Earth. The monkey travels to Mars. What is his mass and weight on Mars?
4. Determine your mass by using a bathroom scale and calculate your weight for each planet in the Solar System, using the values given in [link]

## Gravitational fields

A field is a region of space in which a mass experiences a force. Therefore, a gravitational field is a region of space in which a mass experiences a gravitational force.

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