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In this case, the total mechanical energy is not conserved . Therefore, external forces are often referred to as non-conservative forces.

A quick review of internal forces

On the other hand, you also learned that if work is done on an object only by internal forces, the total mechanical energy possessed by the object cannot change. However, it can be transformed from potential energy to kineticenergy and vice versa.

In this case, the total mechanical energy is conserved . Therefore, internal forces are often referred to as conservative forces.

A quantitative relationship

The quantitative relationship between work and mechanical energy can be stated as follows:

MEf = MEi + We

where

  • MEf and MEi represent the final and initial total mechanical energy possessed by the object respectively.
  • We represents the work done on the object by external forces.

This equation states that the final amount of mechanical energy possessed by an object is equal to the initial mechanical energy plus the work done on theobject by external forces.

Potential energy plus kinetic energy

The total mechanical energy at any point in time can be the sum of potential energy (gravitational or elastic potential energy) and kinetic energy due to motion.

Given that, we can rewrite the earlier equation as:

KEf + PEf = KEi + PEi + We

where

  • KEf and PEf represent the final kinetic and potential energy respectively.
  • KEi and PEi represent the initial kinetic and potential energy respectively.
  • We represents the work done on the object by external forces.

As mentioned, the work done by external forces can be either positive or negative work. Whether the work is positive or negative depends on the cosine ofthe angle between the direction of the force and the direction of the displacement of the object.

An ideal rocket example

Consider the following scenario. The owners of an experimental rocket lift the rocket onto a platform above ground level and set it up for firing.

Later, when they fire the rocket, it goes straight up while the rocket engine is burning. When the rocketengine runs out of fuel and stops burning, the rocket coasts to its apex and stops climbing.Then it falls back to the surface of the earth in an unglamorous free fall.

Simplifying assumptions

We will make some simplifying assumptions:

  • The mass of the fuel is insignificant relative to the combined mass of the rocket and its payload. Therefore, expenditure of fuel doesn't affectthe mass of the rocket in a significant way.
  • Air resistance is negligible. The rocket acts as if in a vacuum.

Initial conditions

Here are the initial conditions for the rocket experiment:

  • Platform height = 15 meters.
  • Mass of rocket and payload = 10kg.
  • Thrust of rocket is constant at 150 newtons during burn.
  • Burn time for the rocket = 10 seconds.

Legs of the trip

We will analyze the rocket's round trip from the ground, into the air, and back to the ground in several legs as described below:

  • Leg A: Manually lifting the rocket from the ground to the platform.
  • Leg B: Displacement of the rocket under rocket-engine power straight up.
  • Leg C: Displacement of the rocket without power while coasting to the apex.
  • Leg D: Displacement of the rocket in free fall from the apex back to the ground.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
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
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
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.
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
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
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Source:  OpenStax, Accessible physics concepts for blind students. OpenStax CNX. Oct 02, 2015 Download for free at https://legacy.cnx.org/content/col11294/1.36
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