Re: How does multiplying by lightspeed squared make any sense?

<actionintegral@xxxxxxxxx> wrote in message
news:1150316953.605029.292990@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Uno Lapideus wrote:
Can someone please advise me on how multiplying a number (representing
mass in kg) with another number (representing "speed" in km per second,
squared) can yield a third number that makes sense?

Your difficulty in understanding is not with relativity. The difficulty
is with Energy per se. Energy is not a visualizable concept like
velocity. Energy is a mathematical tool derived from visualizable
concepts like acceleration , velocity, and position.


Ordinary classical physics already has these units. Kinetic energy is 1/2
mv^2, which is a mass multiplied by a velocity squared.

Energy can be work, which is force * distance.

E = Fx

But if this force that acts on an object is used to accelerate it, then mass
an changes in velocity come into play. It takes some simple calculus, but
it can easily be proven that

x = x0 + v0*t + 1/2at^2

Where x is displacement, v is velocity and a is acceleration. We also know
that acceleration is the change in velocity per unit time, or

a = (v2 - v1) / t

You can solve this formula for time and get

t = (v2 -v1) / a

If you plug this value of t back into the "x" formula, you're going to get
velocity-squared terms. If you solve for "a" and plug this into the F = ma
formula you'll get

Fx = 1/2 mv^2 which is = E, or kinetic energy.

The units still work out. If velocity is in m/s then the square of this is
m^2 / s^2. Multiply this by mass in kg and you get

kg-m^2 / s^2, or "kilogram meters squared per second squared".

You get the same thing with work = Fx. Force is in newtons and displacement
is in meters...but newtons are a derived unit. A newton is the force it
takes to accelerate one kilogram to one meter per second squared, so

N = kg-m^2 / s^2, or one newton equals one kilogram meter per second
squared. Multiply this by x in meters and you get..."kilogram meters
squared per second squared". The same thing.

Now, how the speed of light figures into relativistic equations is another,
more complicated story, but I think you just wanted to know how "squared
velocity" relates to energy and it doesn't take relativity to explain it.

Don
Kansas City



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