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p 1 + p 2 = constant , size 12{p rSub { size 8{1} } +p rSub { size 8{2} } =" constant"} {}
p 1 + p 2 = p 1 + p 2 , size 12{p rSub { size 8{1} } +p rSub { size 8{2} } = { {p}} sup { ' } rSub { size 8{1} } + { {p}} sup { ' } rSub { size 8{2} } } {}

where p 1 size 12{ { {p}} sup { ' } rSub { size 8{1} } } {} and p 2 size 12{ { {p}} sup { ' } rSub { size 8{2} } } {} are the momenta of cars 1 and 2 after the collision. (We often use primes to denote the final state.)

This result—that momentum is conserved—has validity far beyond the preceding one-dimensional case. It can be similarly shown that total momentum is conserved for any isolated system, with any number of objects in it. In equation form, the conservation of momentum principle    for an isolated system is written

p tot = constant , size 12{p rSub { size 8{"tot"} } ="constant"} {}

or

p tot = p tot , size 12{p rSub { size 8{"tot"} } =p' rSub { size 8{"tot"} } } {}

where p tot size 12{p rSub { size 8{"tot"} } } {} is the total momentum (the sum of the momenta of the individual objects in the system) and p tot size 12{ ital "p'" rSub { size 8{"tot"} } } {} is the total momentum some time later. (The total momentum can be shown to be the momentum of the center of mass of the system.) An isolated system    is defined to be one for which the net external force is zero F net = 0 . size 12{ left (F rSub { size 8{ ital "net"} } =0 right ) "." } {}

Conservation of momentum principle

p tot = constant p tot = p tot ( isolated system )

Isolated system

An isolated system is defined to be one for which the net external force is zero F net = 0 . size 12{ left (F rSub { size 8{ ital "net"} } =0 right ) "." } {}

Perhaps an easier way to see that momentum is conserved for an isolated system is to consider Newton’s second law in terms of momentum, F net = Δ p tot Δ t . For an isolated system, F net = 0 ; thus, Δ p tot = 0 size 12{?p rSub { size 8{"tot"} } =0} {} , and p tot is constant.

We have noted that the three length dimensions in nature— x size 12{x} {} , y size 12{y} {} , and z size 12{z} {} —are independent, and it is interesting to note that momentum can be conserved in different ways along each dimension. For example, during projectile motion and where air resistance is negligible, momentum is conserved in the horizontal direction because horizontal forces are zero and momentum is unchanged. But along the vertical direction, the net vertical force is not zero and the momentum of the projectile is not conserved. (See [link] .) However, if the momentum of the projectile-Earth system is considered in the vertical direction, we find that the total momentum is conserved.

A space probe is projected upward. It takes a parabolic path. No horizontal net force acts on. The horizontal component of momentum remains conserved. The vertical net force is not zero and the vertical component of momentum is not a constant. When the space probe separates, the horizontal net force remains zero as the force causing separation is internal to the system. The vertical net force is not zero and the vertical component of momentum is also not a constant after separation. The centre of mass however continues in the same parabolic path.
The horizontal component of a projectile’s momentum is conserved if air resistance is negligible, even in this case where a space probe separates. The forces causing the separation are internal to the system, so that the net external horizontal force F x net is still zero. The vertical component of the momentum is not conserved, because the net vertical force F y net is not zero. In the vertical direction, the space probe-Earth system needs to be considered and we find that the total momentum is conserved. The center of mass of the space probe takes the same path it would if the separation did not occur.

The conservation of momentum principle can be applied to systems as different as a comet striking Earth and a gas containing huge numbers of atoms and molecules. Conservation of momentum is violated only when the net external force is not zero. But another larger system can always be considered in which momentum is conserved by simply including the source of the external force. For example, in the collision of two cars considered above, the two-car system conserves momentum while each one-car system does not.

Making connections: take-home investigation—drop of tennis ball and a basketball

Hold a tennis ball side by side and in contact with a basketball. Drop the balls together. (Be careful!) What happens? Explain your observations. Now hold the tennis ball above and in contact with the basketball. What happened? Explain your observations. What do you think will happen if the basketball ball is held above and in contact with the tennis ball?

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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.
Bharti
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
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
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?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
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
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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 ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
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
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Physics of the world around us. OpenStax CNX. May 21, 2015 Download for free at http://legacy.cnx.org/content/col11797/1.1
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