Work
So far, the problems that we have studied have had either a constant
force, or one that is time dependent.
In these cases we have been able to solve
for the velocity, and from that the position as a function of time.
However, in
many of the problems that we face, we only know the force as a function of
position.
In these cases, our "standard" methods do not work well and new
methods are needed.
The most important method is the use of work and energy
conservation.
We can define
energy
as a measurement of the capacity of an object to
do work, where
work
is a measurement of the amount of force applied through a
distance.
Mathematically, this can be written as
∫
⋅
=
2
1
x
x
x
d
F
W
(10.1)
where
x
is the vector tangent to the path that the object traverses.
Conservation Principles
One of the most important concepts that is connected to energy is that of
conservation of energy
.
Conservation of energy is one of the major
conservation laws in physics.
What do we mean by a conservation law?
Whenever we attempt to describe a physical system, we create a mathematical
model of it.
This model uses various parameters to describe the state of the
system at any given time.
Most of these parameters can vary when the system
undergoes a transformation or an interaction, but some of the parameters remain
constant.
These parameters are referred to as having been
conserved
by the
transformation or interaction.
There are three major conservation principles in
physics today:
conservation of energymomentum
,
conservation of angular
momentum
, and
conservation of charge
.
Conservation of energymomentum
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 Spring '09
 Knott
 Physics, Energy, Force, Work, Position Dependent Forces

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