# Kinetic Energy

Energy is the essence of the universe.  In the moments after creation there was both according to creation accounts and according to physics, a great deal of light.  Light is pure energy in the form of electromagnetic radiation.  We will actually mathematically derive light in our second semester studies.  [br][br]In the present era of the universe, there are many manifestations of energy.  Light is still around, but so is mass, and the motion of that mass, and gravitation, and other forces.  Soon we will see that there is energy associated with all of these.[br][br]In this chapter we will restrict our focus to single mass systems - meaning systems that we'll assume move as rigid bodies.  Macroscopic object are never really single masses since all the atoms can wiggle, but these details will be ignored for now. A single mass can only possess two types of energy really - either [b]rest energy[/b] associated with its mass [br][center]$E_0=mc^2, \\[br]\text{(c=3.0\times 10^8 m/s is the speed of light in vacuum)}[br]$[/center] or [b]kinetic energy[/b] due to motion through space at some speed. [br][br][center]$K=\frac{1}{2}mv^2.$[/center]  [br]We will not discuss rest energy in much detail, but will postpone that discussion until third semester.  One thing worth saying about it is that there is a tremendous amount of energy associated with even little masses. In this sense you can think of mass as some sort of condensed energy. For instance, it can easily be calculated that a standard aspirin tablet (325mg) has the energy equivalent of over 240,000 gallons of gasoline! (A gallon of gasoline contains $1.2\times 10^8J$ of energy.)[br][br]It is worth noting that kinetic energy is not a property of an object apart from an observer.  After all, if you and I are measuring the kinetic energy of a moving ball and if I am moving with respect to you, we won't agree on the ball's speed.  This makes kinetic energy a relative quantity - one that is only meaningfully measured relative to some observer.  Usually we will assume the earth's reference frame to be the frame of the observer unless otherwise specified.[br][br][i]EXAMPLE:  Consider the kinetic energy of a $1200kg$ car traveling at $20m/s$ down a roadway, and how it changes if the car were to double its speed.  In the first case $K=\frac{1}{2}mv^2=\frac{1}{2}1200kg\,(20m/s)^2=2.4\times 10^5 J$.  If the speed doubles, we get $K=\frac{1}{2}mv^2=\frac{1}{2}1200kg\,(40m/s)^2=9.6\times 10^5 J.$[/i][br][br]Doubling the mass makes the kinetic energy grow only two-fold, but doubling the speed makes it grow four-fold.  That's obvious from the equation, but I just wanted to be sure that you didn't miss that point.  [br][br]One other thing that's worth mentioning is that this present form of our kinetic energy expression is only an approximation of the truth.  It is a very good approximation, but one that breaks down as speeds approach the speed of light.  The real equation for kinetic energy is more complicated, and asymptotically approaches $\infty$ as $v\rightarrow c,$ where $c=3.0\times 10^8m/s,$ (speed of light in vacuum).  As a loose rule, we should be wary of describing kinetic energy with the equation from this chapter if the speed of an object v>c/10, or 10% the speed of light in vacuum.  We will discuss the details of how to quantify kinetic energy at speeds higher than this during our third semester of studies.