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Potential energy versus stretch or compression

There is an equation for springs that relates the amount of elastic potential energy to the amount of stretch (or compression) and the spring constant. The equation is

PEs = 0.5 * k * x^2


  • PEs represents the elastic potential energy stored in the spring
  • k is the spring constant for the material from which the spring is made
  • x is the amount of compression or stretch relative to the equilibrium state.


Gravitational potential energy can be stored in an object by moving it further away from the center of the earth. As a practical matter, this usuallymeans moving it to a higher position relative to the ground, the floor, or a tabletop.

Elastic potential energy can be stored in an object by deforming it within its elastic limit. Usually, but not always, this involves stretching orcompressing the object, but it could also mean twisting it or deforming it in some other way. If the deformation doesn't exceed the elastic limit of theobject, it will return to its original shape when the load is removed.

Some materials, such as the spring material in a fisherman's scale, can sustain considerable deformation before reaching the elastic limit. Othermaterials, such as toasted bread, not only reach their elastic limit, but also reach their structural limit and break at the slightest amount of deformation.

Other materials, such as fresh bread and modeling clay have a low elastic limit but a relatively high structural limit. In other words, they doesn'treturn to their original shape when deformed, but they also don't easily break when deformed.

Sample Calculations

The rock and the tree

You pick a flat rock with a 10kg mass off the ground and balance it on a tree limb 2 meters above the ground.

What was the gravitational potential energy of the rock before your arrival and what change in gravitational potential energy did you impart to the rock byyour actions?


Assuming that the rock was flat and the ground was flat and there was essentially no chance the the rock could roll downhill, the gravitationalpotential energy of the rock before you picked it up was zero.

Using the Google calculator to do the arithmetic and handle the units, after you balanced the rock on the tree limb, the potential energy was:

(10 kg) * (9.8 (m / (s^2))) * (2 m) = 196 joules

Therefore, the change in gravitational potential energy was 196 joules.

A crate and a ramp

You push a 100 kg mass up a 5 meter-long ramp and onto a platform at the upper end of the ramp. The ramp makes an angle of 36.9 degrees relative to theground on which it is setting.

What change in gravitational potential energy did you impart to the crate?


First compute the height of the platform at the upper end of the ramp.

height = 5 * sin(36.9 degrees) = 3m

Now compute the change in gravitational potential energy.

(100 kg) * (9.8 (m / (s^2))) * (3 m) = 2940 joules

All that matters insofar as the change in gravitational potential energy is concerned is that the crate was lifted 3 meters higher than its initial position.How that lift was accomplished doesn't matter. It could be accomplished with a ramp, a pulley, or with brute strength and the change in gravitational potential energy would be the same.

Questions & Answers

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
Do somebody tell me a best nano engineering book for beginners?
s. Reply
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?
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
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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