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1. Assuming that the dart was not deformed as it was forced out of the barrel of the gun, the potential energy of the dart is given by


Enter the following into the Google search box:

(0.1 kg) * (9.8 (m / (s^2))) * (1 m)

The result should be:

Potential energy = 0.98 joules

2. The kinetic energy of the dart is given by


Enter the following into the Google search box:


The result should be:

kinetic energy = 5 joules

3. The total mechanical energy of the dart is the simple sum of the potential energy and the kinetic energy, which is:

Total mechanical energy = 5.98 joules

4. When the dart exits the gun, the gravitational potential energy of the gun is reduced because the total mass of the gun and the dart is reduced by the massof the dart.

In addition, the elastic potential energy stored in the spring is imparted into the dart in the form of kinetic energy.

Therefore, the loss in mechanical energy of the gun is equal to the total mechanical energy of the dart immediately upon exit from the gun barrel.Therefore, the total mechanical energy of the gun is reduced by 5.98 joules when the dart exits the gun.

A crate on a ski run

A crate containing soft drinks with a mass of 5 kg is accidentally released at the top of a ski run and slides down the ski run to the valley below. Theheight of the point where the crate is released is 100 m above the valley floor. The crate goes through numerous dips and over many small hills on the way down but never stops.

Assuming there is no friction, no air resistance, no deformation, and no loss of energy in any form during the trip, what is the magnitude of the crate's velocitywhen it reaches the valley floor?


As presented, this is a simple case of the conversion of gravitational potential energy into kinetic energy. The fact that the crate slowed down andsped up several times during the trip while negotiating little dips and hills doesn't matter. All that really matters is the balance of energy between the starting point and point where the cratereached the valley floor. With no energy loss during the trip, the total mechanical energy at the end of the trip must equal the total mechanical energy at thebeginning of the trip.

At the top of the hill, the crate's gravitational potential energy was equal to

m*g*h = 5kg*(9.8m/s^2)*100m = 4900 joules

Therefore, at the bottom of the hill, with no remaining potential energy, the crate's kinetic energy must be equal to

0.5*m*v^2 = 4900 joules

Rearranging terms gives us

v^2 = (4900 joules)/(0.5*m), or

v = sqrt((4900 joules)/(0.5*m)), or

v = sqrt((4900 joules)/(0.5*5kg))

Entering this expression into the Google calculator gives us the crate's velocity when it reached the valley floor as

v = 44.3 m/s

Do the calculations

I encourage you to repeat the calculations that I have presented in this lesson to confirm that you get the same results. Experiment with the scenarios, making changes, and observing the results of your changes. Make certain that you can explain why your changes behave as they do.


I will publish a module containing consolidated links to resources on my Connexions web page and will update and add to the list as additional modulesin this collection are published.


This section contains a variety of miscellaneous information.

Housekeeping material
  • Module name: Energy -- Kinetic and Mechanical Energy
  • File: Phy1190.htm
  • Revised: 10/02/15
  • Keywords:
    • physics
    • accessible
    • accessibility
    • blind
    • graph board
    • protractor
    • screen reader
    • refreshable Braille display
    • JavaScript
    • trigonometry
    • potential energy
    • work
    • gravitational potential energy
    • elastic potential energy
    • kinetic energy
    • mechanical energy
    • total mechanical energy

Financial : Although the openstax CNX site makes it possible for you to download a PDF file for the collection that contains thismodule at no charge, and also makes it possible for you to purchase a pre-printed version of the PDF file, you should beaware that some of the HTML elements in this module may not translate well into PDF.

You also need to know that Prof. Baldwin receives no financial compensation from openstax CNX even if you purchase the PDF version of the collection.

In the past, unknown individuals have copied Prof. Baldwin's modules from cnx.org, converted them to Kindle books, and placed them for sale on Amazon.com showing Prof. Baldwin as the author.Prof. Baldwin neither receives compensation for those sales nor does he know who doesreceive compensation. If you purchase such a book, please be aware that it is a copy of a collection that is freelyavailable on openstax CNX and that it was made and published without the prior knowledge of Prof. Baldwin.

Affiliation : Prof. Baldwin is a professor of Computer Information Technology at Austin Community College in Austin, TX.


Questions & Answers

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
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
How can I make nanorobot?
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
how can I make nanorobot?
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
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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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