<< Chapter < Page Chapter >> Page >

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 = 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 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 · 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:

F = G m 1 m 2 r 2 = ( 6 , 67 × 10 - 11 N · m 2 · kg - 2 ) ( ( 80 kg ) ( 65 kg ) ( 10 m ) 2 ) = 3 , 47 × 10 - 9 N

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

F = G m 1 m 2 r 2 = ( 6 , 67 × 10 - 11 N · m 2 · kg - 2 ) ( ( 80 kg ) ( 65 kg ) ( 1 m ) 2 ) = 3 , 47 × 10 - 7 N

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:

F = G m 1 m 2 r 2 = ( 6 , 67 × 10 - 11 N · m 2 · kg - 2 ) ( ( 5 , 98 × 10 24 kg ) ( 7 , 35 × 10 22 kg ) ( 0 , 38 × 10 9 m ) 2 ) = 2 , 03 × 10 20 N

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 = 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

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
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.
yes that's correct
I think
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Maths test. OpenStax CNX. Feb 09, 2011 Download for free at http://cnx.org/content/col11236/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Maths test' conversation and receive update notifications?