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Newton’s second law is given by

a = F net m size 12{a = { {F rSub { size 8{"net"} } } over {m} } } {} .

The net external force on System 1 is deduced from [link] and the discussion above to be

F net = F floor f = 150 N 24 . 0 N = 126 N size 12{F rSub { size 8{"net"} } = F rSub { size 8{"floor"} } -f ="150 N"-"24" "." "0 N"="126 N"} {} .

The mass of System 1 is

m = ( 65 . 0 + 12 . 0 + 7 . 0 ) kg = 84 kg size 12{m = \( "65" "." "0 "+" 12" "." "0 "+" 7" "." 0 \) " kg "=" 84 kg"} {} .

These values of F net size 12{F} {} and m size 12{m} {} produce an acceleration of

a = F net m , a = 1 26 N 84 kg = 1 . 5 m/s 2 . alignl { stack { size 12{a= { {F rSub { size 8{"net"} } } over {m} } ,} {} #a = { {1"26 N"} over {"84"" kg"} } =" 1" "." "5 m/s" rSup { size 8{2} } "." {} } } {}


None of the forces between components of System 1, such as between the professor’s hands and the cart, contribute to the net external force because they are internal to System 1. Another way to look at this is to note that forces between components of a system cancel because they are equal in magnitude and opposite in direction. For example, the force exerted by the professor on the cart results in an equal and opposite force back on her. In this case both forces act on the same system and, therefore, cancel. Thus internal forces (between components of a system) cancel. Choosing System 1 was crucial to solving this problem.

Force on the cart—choosing a new system

Calculate the force the professor exerts on the cart in [link] using data from the previous example if needed.


If we now define the system of interest to be the cart plus equipment (System 2 in [link] ), then the net external force on System 2 is the force the professor exerts on the cart minus friction. The force she exerts on the cart, F prof size 12{F rSub { size 8{"prof"} } } {} , is an external force acting on System 2. F prof size 12{F rSub { size 8{"prof"} } } {} was internal to System 1, but it is external to System 2 and will enter Newton’s second law for System 2.


Newton’s second law can be used to find F prof size 12{F rSub { size 8{"prof"} } } {} . Starting with

a = F net m size 12{a = { {F rSub { size 8{"net"} } } over {m} } } {}

and noting that the magnitude of the net external force on System 2 is

F net = F prof f size 12{F rSub { size 8{"net"} } = F rSub { size 8{"prof"} } -f} {} ,

we solve for F prof size 12{F rSub { size 8{"prof"} } } {} , the desired quantity:

F prof = F net + f . size 12{F rSub { size 8{"prof"} } = F rSub { size 8{"net"} } + f} {}

The value of f size 12{f} {} is given, so we must calculate net F net size 12{F} {} . That can be done since both the acceleration and mass of System 2 are known. Using Newton’s second law we see that

F net = ma size 12{F rSub { size 8{"net"} } = ital "ma"} {} ,

where the mass of System 2 is 19.0 kg ( m size 12{m} {} = 12.0 kg + 7.0 kg) and its acceleration was found to be a = 1.5 m/s 2 size 12{a=1 "." "50"" m/s" rSup { size 8{2} } } {} in the previous example. Thus,

F net = ma size 12{F rSub { size 8{"net"} } = ital "ma"} {} ,

F net = ( 19 . 0 kg ) ( 1.5 m/s 2 ) = 29 N size 12{F rSub { size 8{"net"} } = \( "19" "." "0 kg" \) \( 1 "." "50 m/s" rSup { size 8{2} } \) ="28" "." 5" N"} {} .

Now we can find the desired force:

F prof = F net + f size 12{F rSub { size 8{"prof"} } =F rSub { size 8{"net"} } +f} {} ,

F prof = 29 N + 24.0 N = 53 N size 12{F rSub { size 8{"prof"} } ="28" "." 5" N "+"24" "." "0 N "="52" "." "5 N"} {} .


It is interesting that this force is significantly less than the 150-N force the professor exerted backward on the floor. Not all of that 150-N force is transmitted to the cart; some of it accelerates the professor.

The choice of a system is an important analytical step both in solving problems and in thoroughly understanding the physics of the situation (which is not necessarily the same thing).

Phet explorations: gravity force lab

Visualize the gravitational force that two objects exert on each other. Change properties of the objects in order to see how it changes the gravity force.

Gravity Force Lab

Section summary

  • Newton’s third law of motion    represents a basic symmetry in nature. It states: Whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that the first body exerts.
  • A thrust    is a reaction force that pushes a body forward in response to a backward force. Rockets, airplanes, and cars are pushed forward by a thrust reaction force.

Conceptual questions

When you take off in a jet aircraft, there is a sensation of being pushed back into the seat. Explain why you move backward in the seat—is there really a force backward on you? (The same reasoning explains whiplash injuries, in which the head is apparently thrown backward.)

A device used since the 1940s to measure the kick or recoil of the body due to heart beats is the “ballistocardiograph.” What physics principle(s) are involved here to measure the force of cardiac contraction? How might we construct such a device?

Describe a situation in which one system exerts a force on another and, as a consequence, experiences a force that is equal in magnitude and opposite in direction. Which of Newton’s laws of motion apply?

Why does an ordinary rifle recoil (kick backward) when fired? The barrel of a recoilless rifle is open at both ends. Describe how Newton’s third law applies when one is fired. Can you safely stand close behind one when it is fired?

An American football lineman reasons that it is senseless to try to out-push the opposing player, since no matter how hard he pushes he will experience an equal and opposite force from the other player. Use Newton’s laws and draw a free-body diagram of an appropriate system to explain how he can still out-push the opposition if he is strong enough.

Newton’s third law of motion tells us that forces always occur in pairs of equal and opposite magnitude. Explain how the choice of the “system of interest” affects whether one such pair of forces cancels.

Problem exercises

What net external force is exerted on a 1100-kg artillery shell fired from a battleship if the shell is accelerated at 2 . 40 × 10 4 m/s 2 size 12{2 "." "40"´"10" rSup { size 8{4} } " m/s" rSup { size 8{2} } } {} ? What is the magnitude of the force exerted on the ship by the artillery shell?

Force on shell: 2 . 64 × 10 7 N size 12{2 "." "64" times "10" rSup { size 8{7} } `N} {}

Force exerted on ship = 2 . 64 × 10 7 N size 12{ - 2 "." "64" times "10" rSup { size 8{7} } `N} {} , by Newton’s third law

A brave but inadequate rugby player is being pushed backward by an opposing player who is exerting a force of 800 N on him. The mass of the losing player plus equipment is 90.0 kg, and he is accelerating at 1 . 20 m/s 2 size 12{1 "." "20"" m/s" rSup { size 8{2} } } {} backward. (a) What is the force of friction between the losing player’s feet and the grass? (b) What force does the winning player exert on the ground to move forward if his mass plus equipment is 110 kg? (c) Draw a sketch of the situation showing the system of interest used to solve each part. For this situation, draw a free-body diagram and write the net force equation.

Questions & Answers

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 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
characteristics of micro business
for teaching engĺish at school how nano technology help us
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
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
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, College physics arranged for cpslo phys141. OpenStax CNX. Dec 23, 2014 Download for free at http://legacy.cnx.org/content/col11718/1.4
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