Re: [Phys-l] What is energy? (a little long)

[John Denker <jsd@av8n.com>]

On 11/25/2007 09:50 AM, Cliff Parker wrote:
> Love the quote from your mother! 

:-)

> Just wondering something that came from 
> your website  http://www.av8n.com/physics/mass.htm#sec-car-push  why do you 
> say pour a tremendous amount of momentum into the car rather than pour a 
> tremendous amount of work into the car?  Is there a reason?

Here's the reason:

Force times time = momentum

Power times time = energy

Railroad cars are really massive.  Try pushing one sometime. :-)

Two little kids pushing on a railroad car are better modeled
as constant-force sources rather than constant-power sources
over the times and velocities of interest.  This has something
to do with how muscles work.  Specifically, the effort involved
in pushing the car is for all practical purposes independent
of velocity, given the small velocities involved.  Therefore
it seems natural to consider that the momentum grows linearly
in time (rather than energy growing linearly in time).

A similar line of thought applies to jet aircraft versus
propeller aircraft during the takeoff roll. 
 -- A propeller engine is well modeled as a constant power 
  source (except at the very lowest airspeeds) so the energy 
  grows linearly with time while the velocity grows less than 
  linearly with time. 
 -- In contrast, a pure jet is well modeled as a constant thrust
  source over quite a wide range of airspeeds, so the momentum
  grows linearly with time while the energy grows faster than
  linearly.  That is, the energy efficiency of the jet increases
  with increasing airspeed, and keeps increasing up to quite
  high airspeeds.  From this you might surmise that jets are 
  great for high-speed cruise but lousy for short-field takeoff.
  Which is true.