# 0.2 Force, momentum and impulse  (Page 20/35)

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The force exerted by a field of strength $g$ on an object of mass $m$ is given by:

$F=m·g$

This can be re-written in terms of $g$ as:

$g=\frac{F}{m}$

This means that $g$ can be understood to be a measure of force exerted per unit mass.

The force defined in  [link] is known as weight.

Objects in a gravitational field exert forces on each other without touching. The gravitational force is an example of a non-contact force.

Gravity is a force and therefore must be described by a vector - so remember thta gravity has both magnitude and direction.

## Newton's law of universal gravitation

Newton's Law of Universal Gravitation

Every point mass attracts every other point mass by a force directed along the line connecting the two. This force is proportional to the product of the masses and inversely proportional to the square of the distance between them.

The magnitude of the attractive gravitational force between the two point masses, $F$ is given by:

$F=G\frac{{m}_{1}{m}_{2}}{{r}^{2}}$

where: $G$ is the gravitational constant, ${m}_{1}$ is the mass of the first point mass, ${m}_{2}$ is the mass of the second point mass and $r$ is the distance between the two point masses.

Assuming SI units, $F$ is measured in newtons (N), ${m}_{1}$ and ${m}_{2}$ in kilograms (kg), $r$ in meters (m), and the constant $G$ is approximately equal to $6,67×{10}^{-11}N·{m}^{2}·\phantom{\rule{3.33333pt}{0ex}}k{g}^{-2}$ . Remember that this is a force of attraction.

For example, consider a man of mass 80 kg standing 10 m from a woman with a mass of 65 kg. The attractive gravitational force between them would be:

$\begin{array}{ccc}\hfill F& =& G\frac{{m}_{1}{m}_{2}}{{r}^{2}}\hfill \\ & =& \left(6,67×{10}^{-11}\phantom{\rule{0.166667em}{0ex}}\mathrm{N}·{\mathrm{m}}^{2}·\phantom{\rule{3.33333pt}{0ex}}{\mathrm{kg}}^{-2}\right)\left(\frac{\left(80\mathrm{kg}\right)\left(65\mathrm{kg}\right)}{{\left(10\mathrm{m}\right)}^{2}}\right)\hfill \\ & =& 3,47×{10}^{-9}\phantom{\rule{0.166667em}{0ex}}\mathrm{N}\hfill \end{array}$

If the man and woman move to 1 m apart, then the force is:

$\begin{array}{ccc}\hfill F& =& G\frac{{m}_{1}{m}_{2}}{{r}^{2}}\hfill \\ & =& \left(6,67×{10}^{-11}\phantom{\rule{0.166667em}{0ex}}\mathrm{N}·{\mathrm{m}}^{2}·\phantom{\rule{3.33333pt}{0ex}}{\mathrm{kg}}^{-2}\right)\left(\frac{\left(80\mathrm{kg}\right)\left(65\mathrm{kg}\right)}{{\left(1\mathrm{m}\right)}^{2}}\right)\hfill \\ & =& 3,47×{10}^{-7}\phantom{\rule{0.166667em}{0ex}}\mathrm{N}\hfill \end{array}$

As you can see, these forces are very small.

Now consider the gravitational force between the Earth and the Moon. The mass of the Earth is $5,98×{10}^{24}$  kg, the mass of the Moon is $7,35×{10}^{22}$  kg and the Earth and Moon are $3,8×{10}^{8}$  m apart. The gravitational force between the Earth and Moon is:

$\begin{array}{ccc}\hfill F& =& G\frac{{m}_{1}{m}_{2}}{{r}^{2}}\hfill \\ & =& \left(6,67×{10}^{-11}\phantom{\rule{0.166667em}{0ex}}\mathrm{N}·{\mathrm{m}}^{2}·\phantom{\rule{3.33333pt}{0ex}}{\mathrm{kg}}^{-2}\right)\left(\frac{\left(5,98×{10}^{24}\mathrm{kg}\right)\left(7,35×{10}^{22}\mathrm{kg}\right)}{{\left(0,38×{10}^{9}\mathrm{m}\right)}^{2}}\right)\hfill \\ & =& 2,03×{10}^{20}\phantom{\rule{0.166667em}{0ex}}\mathrm{N}\hfill \end{array}$

From this example you can see that the force is very large.

These two examples demonstrate that the greater the masses, the greater the force between them. The $1/{r}^{2}$ factor tells us that the distance between the two bodies plays a role as well. The closer two bodies are, the stronger the gravitational force between them is. We feel the gravitational attraction of the Earth most at the surface since that is the closest we can get to it, but if we were in outer-space, we would barely feel the effect of the Earth's gravity!

Remember that

$F=m·a$

which means that every object on Earth feels the same gravitational acceleration! That means whether you drop a pen or a book (from the same height), they will both take the same length of time to hit the ground... in fact they will be head to head for the entire fall if you drop them at the same time. We can show this easily by using the two equations above (Equations  [link] and [link] ). The force between the Earth (which has the mass ${m}_{e}$ ) and an object of mass ${m}_{o}$ is

$F=\frac{G{m}_{o}{m}_{e}}{{r}^{2}}$

and the acceleration of an object of mass ${m}_{o}$ (in terms of the force acting on it) is

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
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
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
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
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
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?
what is a peer
What is meant by 'nano scale'?
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 ?
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
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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