Re: Potentially painful

From: Larry Brasfield (donotspam_larry_brasfield_at_hotmail.com)
Date: 03/09/05 

Date: Wed, 9 Mar 2005 12:40:20 -0800

"Robert Monsen" <rcsurname@comcast.net> wrote in
 message news:B-adnbQgnM3fx7LfRVn-rQ@comcast.com...
> Larry Brasfield wrote:
>> "John Larkin" <jjSNIPlarkin@highTHISlandPLEASEtechnology.XXX> wrote
>> in message news:sa3t2113mifbj3e38eovdn74qc546dni4i@4ax.com...
>>
>>>On Tue, 8 Mar 2005 12:44:56 -0800, "Larry Brasfield"
>>><donotspam_larry_brasfield@hotmail.com> wrote:
>>>
>>>>"Robert Monsen" <rcsurname@comcast.net> wrote in message
>>>>news:uMGdnQ0E54dKlbPfRVn-tw@comcast.com...
>>>>
>>>>>No, as I recall, kinetic energy is 1/2 * m * v^2.
>>>>
>>>>I recall seeing that claim from a high school physics teacher when
>>>>I was a smart-ass twerp. I posed the following puzzle to him:
>>>>A rocket car starts at rest, accellerating at a constant rate
>>>>because its thrust is constant. It is burning fuel at a constant
>>>>rate to produce that constant thrust. The kinetic energy of
>>>>the rocket car is allegedly M * V^2 / 2, so it is increasing
>>>>quadratically versus time. But the fuel consumed increases
>>>>only linearly with time. How can this be?
>>>>
>>>>I would be interested in your take on this. My physics teacher
>>>>could not resolve it, (but, to his credit, that bothered him).
>>>
>>>At low velocities, a rocket is a very inefficient source of
>>>propulsion; at near-zero velocity, it's using its usual amount of fuel
>>>but hardly delivering any kinetic energy to the vehicle. As velocity
>>>increases, efficiency improves (or rather becomes less terrible) and
>>>vehicle energy accumulates faster. That trend continues until you run
>>>out of fuel.
>>>
>>>In a system that goes from extremely inefficient to only rather
>>>inefficient, it's not hard to shape the efficiency curve into a
>>>quadratic. A cog railway can be nearly 100% efficient, so it will need
>>>increasing amounts of fuel if it accelerates at constant gees, but
>>>anywhere on the path it will be a lot more efficient than a rocket.
>>>
>>>That make sense?
>>
>>
>> Yes. I should have known this little puzzle would
>> not take you folks long to sort out. The key is to
>> consider that starting condition. All the energy ends
>> up in the exhaust at the limit of zero rocket speed.
>> The problem gets a little easier to see if it involves
>> chucking cannonballs from a railway car.
>
> Ok. I guess I'm feeling thick today, but it sounds like your solution is to attach a reference frame to the accelerating rocket. I
> don't know enough physics to determine if that's reasonable.

If your surmise about my choice of reference frame
was correct, I would not have had to mention "the
limit of zero rocket speed" since that speed would
be zero at all times. I don't know a lot of physics,
but I know enough to declare that accelerating
reference frames are not reasonable!

> The rate of change of kinetic energy of the rocket when the rocket isn't moving is still the time derivative of 1/2mv^2, which is
>
> F^2*t/M
>
> where M is the (assumed unchanging) mass of the rocket, and F is thrust. This is a function of t, meaning that the rate of energy
> at t=0 is 0, so all the energy goes into the fuel. That is nice, but what happens at t=1? We are still increasing our 'rate of
> change' of energy...

Gonna have to suppose some parameters and do
some math for that one. Not! (I've got enough of
that to do for pay at the moment.)

> If you were to say that, for example, the rate of change of energy of the thrust (from the point of view of a stationary observer)
> was decreasing with t, and the sum of these was constant, I'd buy that. ;)

My reason for mentioning the infinitessimal time
during which the rocket velocity is zero (for the
observer implicit in speaking of E = M V^2 / 2),
is to agree with John's explanation and elaborate
that, over some very low range of velocities, one
must realize most of the power will be imparted to
the rocket's exhaust. Only by ignoring what goes
into the exhaust can that puzzle remain a puzzle. 

-- 
--Larry Brasfield
email: donotspam_larry_brasfield@hotmail.com
Above views may belong only to me.

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