Re: vector quantities and energy

[Doug Craigen <dcc@CYBERSPC.MB.CA>]

GARY HEMMINGER wrote:
> Since we study momentum before energy I've had kids ask me the
> question - why isn't energy (particulary kinetic energy)  a vector?
> It strikes me that this is a great question because it can be
> addressed at so many levels.  Feynman would no doubt say something
> rather different to his colleagues than I would to my weakest 10th
> graders and so on.     How would you answer this?

First of all, a good diagnosis of their difficulty would be helpful.  My
guess is that they have been given a description like what I was given
in high school physics: a vector is something with magnitude and
direction. You've just been covering momentum which necessarily is a
vector - it has both.  Now you go on to kinetic energy.  The same moving
object, moving in some direction, also has some magnitude of kinetic
energy.  It has magnitude, it has direction, why isn't this a vector?

The thing here is that even though the object is moving in some
direction, you don't change the energy by changing the direction -
unlike momentum, there is nothing about kinetic energy that requires you
to know the direction of the motion.  So whereas momentum requires more
than one number to describe it: magnitude plus angles wrt some
coordinate system, or magnitudes of its components along a base set of
axis  -  kinetic energy is described entirely by one number.  If you
change the direction of motion of an object you change its momentum, but
you don't change its kinetic energy.


()-()-()-()-()-()-()-()-()-()-()-()-()-()-()-()

Doug Craigen
          Latest Project - the Physics E-source
          http://www.dctech.com/physics/