# 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.

#### Questions & Answers

how can chip be made from sand
Eke Reply
is this allso about nanoscale material
Almas
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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Source:  OpenStax, Maths test. OpenStax CNX. Feb 09, 2011 Download for free at http://cnx.org/content/col11236/1.2
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