# 0.3 Gravity and mechanical energy  (Page 10/9)

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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.

#### Questions & Answers

what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
how did you get the value of 2000N.What calculations are needed to arrive at it
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