The person responsible for the law of conservation of energy is James Prescott Joule, for whom the SI unit of energy is named. Joule worked in the family brewery and became interested in reducing the waste heat in the brewing process. Before he had finished his work, he had determined the mechanical equivalent of heat.; that is, there is a definite numerical connection between mechanical energy dumped into a system and heat energy removed from the system, and conversely. In modern terms, 4.185 Joules of mechanical energy equals one calorie of heat energy. 

These sites pertain to biographical
data about JP Joule. http://physics.hallym.ac.kr/reference/physicist/joule.htm http://www.answersingenesis.org/docs/3277.asp 
Work & Energy
It is useful to define a quantity called work. .
This form is formally known as the scalar product of two vectors
but is also commonly known as the dot product. We can define work as
the product of a force acting through a distance. It is important to note that while F
and X are vectors, W is a scalar. Furthermore, by convention,
the dot product operator causes the magnitude of W to be W = F
x cos q, where q is the angle
between F and x. In most applications the force and the distance
through which the force acts are collinear and pointed in the
same direction; q = 0 and the cos 0 = 1. Things get a little
tricky when a force is applied to an object that is moving some
distance in a direction perpendicular to the force. In this situation
the angle q between F and x is 90, the cos 90 = 0
and the force does no work.
The unit for work is the Nm (Newtonmeter) which is renamed
the Joule in honor of the man.
A useful applet on the scalar
product of two vectors can be seen at
http://www.loncapa.org/~mmp/kap17/scalar/scalar.htm
Kinetic energy
What happens to the work done if I throw a ball. I exert a
force F( assumed constant in magnitude for this
argument) through some distance x in the wind
up and delivery. Thus I do work such that W = F X
. Check out the derivation in the box
Our work in kinematics suggests that if the ball starts from rest (initially at wind up), equation 4 (page 1) yields 

Multiply both sides of the equation by m (mass) and by 1/2  
Kinetic energy is given by the expression , where m is the mass of the object and v is its speed.  

The fact that the expression for kinetic energy shows the speed of the object squared is significant. At any given speed for an automobile, doubling the speed means increasing its Kinetic Energy by 2 squared = 4; the engine has to work four times harder. And if stopping a car at a given speed takes a given distance X, then the stopping distance from the doubled speed means 4 times the stopping distance.
Gravitational
potential energy
We can do work on a block to lift it to some high place. At
the end of the trip, we have done work in moving the block but
the kinetic energy of the block is zero at the upper location.
If we release the block, it falls toward the floor and has acquired
kinetic energy just before hitting the floor. Where did that energy
come from?
We say that the work done in lifting the block was stored in the Earth's gravitational field and was retrieved when the block was released. Close to the surface of the Earth, gravitational potential energy is given by PEg = mgh, where h is the height through which the block was raised and g is taken as a constant 9.8 m/s/s for the entire distance h.
PEg manifests itself as the energy a) stored behind the dam at a hydropower station; b) stored in counter weights in elevators or in older doublehung windows (the ones with sash cords); c) stored in counterweights in some grandfather clocks.
Elastic potential
energy
It is possible to apply a stressing force to a spring to stretch
or compress it some distance. It is our common experience that
the spring will return to its original rest position when the
stressing force is removed. Robert Hooke, Newton's venerable nemesis,
determined the force needed to stretch a spring some distance
is not a constant but varies directly with the distance stretched.
We can write this as F = kx. k is
called the force constant (units: N/m) and is constant over a
relatively short span of compression or extension. If the object
is stretched beyond a point called the elastic limit,
Hooke's law no longer prevails. Ever stretch the spring of a retractable
ball point pen too far? What once passed for a spring becomes
a twisted piece of wire.
Body builders who need an alternative to lifting weights will often stretch springs. Larger values of k mean that it will take a large force to stretch the spring a small distance
In applying a force acting through a distance, we have done work on the system. Where did it go? We say that the work done is stored in the spring as elastic potential eneregy and can be retrieved when the spring is released. Because the force varies from zero to some large number, we must average the initial and final forces. W = 1/2 (F + 0) x. = 1/2 (kx + 0) x. PEelas = 1/2 k x^{2}.
You can find elastic PE ready to work for you in the following applications: the springs in mouse traps and in wind up toys and nonbattery wrist watches, the bend in a pole vaulter's fiber glass pole.
We need to add here that nonconservative forces such as friction may act on the object as it moves and convert its mechanical energy to heat. The reader must understand that the conservation law is still intact. Friction has simply made the energy irretrievable for any mechanical purpose.
http://www.dti.gov.uk/renewable/ed_pack/games/1216/
http://www.stagnes.org/~lstinson/webpages/kinpot.htm
This site shows an interactive, animated version of a car negotiating first a hill, then a loop
http://www.funderstanding.com/k12/coaster/
http://www.suite101.com/article.cfm/12/54640
This site under the title "Angular Momentum: The
CounterIntuitive Conservation Law" includes information
relating to how
orientation affects the conservation of energy, different definitions
for
terms relating to the conservation of energy.
This site claims to be an online
classroom containing
all the basics such as termonology of Potential
Energy, Kenitic Energy, Mechanical Energy and Power.
There are pictures and easy to understand
descriptions.
http://www.phys.virginia.edu/classes/581/MostlyPE.html
Summary of the work energy
business. Obviously comes
from the University of Virginia (reliable site).
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38 
http://www.mcasco.com/p1wke.html http://www.mcasco.com/p1pef.html 
And what if the conservation laws did not always prevail? The
result would be perpetual
motion machines.
A famous example of such a
device is "Waterfall" by M.C, Escher shown at left.
What's wrong with this picture?
A hallmark of Mechanics is the consideration of word problems. Useful relationships are published here in a page called EQUATIONS. The reader should consult this page before attempting the problems assigned.
Go to supplementary problems  energy
Go to problems at U Oregon
http://zebu.uoregon.edu/~dmason/probs/mech/work.html
Does the object that travels
the shorter distance win the race? Try the racing balls applet
http://www.phy.ntnu.edu.tw/~hwang/racingBall/racingBall.html
Page last modified 11/25/05