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Tension in the rope must equal the weight of the supported mass, as we can prove by using Newton’s second law. If the 5.00 kg mass in the figure is stationary, then its acceleration is zero, so F n e t = 0 . The only external forces acting on the mass are its weight W and the tension T supplied by the rope. Summing the external forces to find the net force, we obtain

F n e t = T - W = 0
where T and W are the magnitudes of the tension and weight and their signs indicate direction, with up being positive. By substituting mg for Fnet and rearranging the equation, the tension equals the weight of the supported mass, just as you would expect:
T = W = m g

For a 5.00 kg mass (neglecting the mass of the rope), we see that

T = m g = ( 5 . 00 k g ) ( 9 . 80 m / s 2 ) = 49 . 0 N

Another example of Newton’s third law in action is thrust. Rockets move forward by expelling gas backward at high velocity. This means that the rocket exerts a large force backward on the gas in the rocket combustion chamber, and the gas in turn exerts a large force forward on the rocket in response. This reaction force is called thrust.

A common misconception is that rockets propel themselves by pushing on the ground or on the air behind them. They actually work better in a vacuum, where they can expel exhaust gases more easily.

Newton’s third law of motion

This video explains Newton’s third law of motion through examples involving push, normal force, and thrust (the force that propels a rocket or a jet). Think about this equation as you watch: F n e t = F f l o o r - f = 150 N - 24 . 0 N = 126 N

    Words defined in the video:

  1. Force
  2. Push
  3. Normal force
  4. Thrust

A physics teacher pushes a cart of demonstration equipment to a classroom, as in Image 4.12 Her mass is 65.0 kg, the cart’s mass is 12.0 kg, and the equipment’s mass is 7.0 kg. To push the cart forward, the teacher’s foot applies a force F foot of 150 N in the opposite direction (backward) on the floor. Calculate the acceleration produced by the teacher. The force of friction, which opposes the motion, is 24.0 N.

Alt text
A teacher pushes a cart of demonstration equipment.

We should not include the forces F teacher , F cart , or F foot because these are exerted by the system, not on the system. We find the net external force by adding together the external forces acting on the system (see free-body diagram in the figure) and then use Newton’s second law to find the acceleration.

    Forces that shouldn’t be included:

  1. F teacher (m/s 2 )
  2. F cart
  3. F foot ( F n e t = F f l o o r - f = 150 N - 24 . 0 N = 126 N )

Newton’s second law is a = F n e t m

The net external force on the system is the sum of the external forces: the force of the floor acting on the teacher, cart, and equipment (in the horizontal direction) and the force of friction. Because friction acts in the opposite direction, we assign it a negative value. Thus, for the net force, we obtain F n e t = F f l o o r - f = 150 N - 24 . 0 N = 126 N

The mass of the system is the sum of the mass of the teacher, cart, and equipment: m = ( 65 . 0 + 12 . 0 + 7 . 0 ) k g = 84 k g

Insert these values of net F and m into Newton’s second law to obtain the acceleration of the system:

  1. a = 126 N 84 k g = 1 . 5 m / s 2
    1. F net
      1. equipment
      2. teacher
      3. cart
    2. m
    3. F floor
  2. a = F n e t m
  3. a = 126 N 84 k g = 1 . 5 m / s 2

Section summary

  • Newton’s third law of motion states that, when 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 it exerts.
  • When objects rest on a surface, the surface applies a force on the object that opposes the weight of the object. This force acts perpendicular to the surface and is called the normal force.
  • The pulling force that acts along a stretched flexible connector, such as a rope or cable, is called tension. When a rope supports the weight of an object at rest, the tension in the rope is equal to the weight of the object.
  • Thrust is a force that pushes an object forward in response to the backward ejection of mass by the object. Rockets and airplanes are pushed forward by thrust.

Key equations

Normal force for a non-accelerating horizontal surface:

N = m g

Tension for an object at rest:

T = m g

Check your understanding

Concept items

Performance task

To investigate how mass affects tension in a connector, find a rubber band and some objects to hang from the end of the rubber band. How much does the rubber band stretch when a light object is hung from it?How much does it stretch when a heavier object is suspended? What does this show?Measure the mass of the object and the corresponding length of the rubber band in each case and plot a graph of mass vs length. (15 min) [link]

Questions & Answers

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 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
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Updated tutor hs physics content - legacy. OpenStax CNX. Mar 16, 2015 Download for free at https://legacy.cnx.org/content/col11768/1.4
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