Re: vector quantities and energy

[Bob Sciamanda <trebor@VELOCITY.NET>]

How about E = (1/2)m*V^2*[v] , where [v] = a unit vector in the direction of
the velocity.
This can be reduced to
E = (1/2)m*V*( V_x*[i] + V_y*[j] + V_z*[k] )

Bob Sciamanda
Physics, Edinboro Univ of PA (ret)
trebor@velocity.net
http://www.velocity.net/~trebor

-----Original Message-----
From: Doug Craigen <dcc@CYBERSPC.MB.CA>
To: PHYS-L@LISTS.NAU.EDU <PHYS-L@LISTS.NAU.EDU>
Date: Friday, January 22, 1999 12:08 PM
Subject: Re: vector quantities and energy


> Since conservation of energy has come up a few times:
>
> Suppose we break the KE down into components, just like the momentum.
> KEx = Px^2/2m
> KEy = Py^2/2m
> KE = P^2/2m  =  Px^2/2m + Py^2/2m  = KEx + KEy
> so far this looks like it works - the components of kinetic energy in
> the x and y directions add up to the total energy, as energy
> conservation tells us to expect.
>
> BUT - if KE is a vector, then its relation to KEx and KEy must be
>         KE = +/- SQRT(KEx^2 + KEy^2)
> which can only match the equation above if KEx=0 or KEy=0, in which case
> KE is a scalar not a vector
>
> So, we do not have a consistent format for dealing with KE having vector
> components.
>
> *****************
>
> One more thing while I'm at it, if anybody does dig up references to KE
> as a component of any vector this presents an opporunity to make sure
> they understand the difference between a vector and its scalar
> components.
>
> ()-()-()-()-()-()-()-()-()-()-()-()-()-()-()-()
>
> Doug Craigen
>          Latest Project - the Physics E-source
>          http://www.dctech.com/physics/