RE: oh well!(kaboom) - a boring excursion into physics of KinematicMotion

[four.rings@MCIONE.com]

>From the previous discussion:
>>I seem to remember reading that 1 cup of gas at the proper air/fuel ratio
>>will lift one ton 1,000 feet...people just _don't_ realize how dangerous
>>gas and gas vapor is...

Audidudi's reply:
>Actually, this sounds a bit low to me ... after all, one gallon of gas will
>propel one ton of car 40 miles or more!  ;^)
[end of previous discussion]


You wrote:

>That's not a valid comparison; one involves changing the object's potential
>energy(basically, its height*mass.)  The other is changing its velocity,
>which requires an initial change in kinetic energy(velocity*mass) and then
>countering air, rolling, and mechanical(engine/drivetrain) friction.

Mmm, wrong on several accounts.

One of the Conservation Laws states that Energy does not emerge or disappear but
rather convert from Potential into Kinetic and back.

Therefore by using your formulae we would get height*mass = velocity*mass. If we
minimise by mass we'll get: height = velocity or substituting the dimensions:
m = m/s. That's wrong.

BTW, height*mass = simply nonsence, dimensions don't agree (m*kg). Potential
Energy in a simple case of a gravitational free fall is P = m*g*h or in
dimensions it's (kg*m*m)/s^2. Since m/s is the dimension of velocity one can see
that dimension-wise it correlates with the formula for the Kinetic Energy below.

You also state that velocity*mass = Kinetic Energy. That is incorrect. In
reality velocity*mass = Impulse, whereas Kinetic Energy = 1/2*mass*velocity
square.

1. Potential Energy depends on configuration of the mechanical sys and is
measured by the amount of Work needed to bring such sys to the so-called
"zero-configuration" for which the Potential Energy could be considered zero.
2. Kinetic Energy is measured by the amount of Work which could be produced by a
moving physical body if it comes to a complete stop K = (m*v^2)/2.

Let's consider two sys of coordinates.

a). The car is standing on a cliff and is about to fall into an abyss with the
depth of h. The bottom of the abyss is zero coordinates and if the car falls
down it will produce the Work equal it's Kinetic Energy at the moment of impact
with the bottom. In this case we can talk about the Potential Energy of the car
standing on the cliff, which is equal to the above mentioned Kinetic Energy.
(for simplicity I am assuming the ideal "Torrichelli" empty space here, no air,
no friction).

b). Now the car is still standing on the same cliff but does not fall down.
In our new sys of coordinates zero would be the cliff and not the abyss' bottom.
While standing on the said cliff the car will not have any Potential Energy in
this particular sys of coordinates coz it is a zero-level.

Now some kind soul ignites a half - empty gasoline canister under it. The car
flies up in the sky. Let's assume that it will reach equilibrium at a certain
height h equal to the depth of the abyss h in the previous example where it will
gain some Potential Energy P. After that it will come down to the ground. During
it's travel the Potential Energy P will be gradually converted into it's Kinetic
Energy K so that the full energy of the car is always a momentary sum of those
two energies W=P+K. Finally it will smack into the cliff and come to rest. At
this moment all of it's Potential Energy will be converted into the Kinetic one
which is equal to the Work performed.
Where did the Work go? It produced that KABOOM! in the subject line. Got
converted into heat and was spent on heating up the Universe.

In both examples a) and b) the mass of the car and the height h were constants,
as well as the g (~9.81m/s^2) and so were the modules of their respective
Potential Energies. What's different is the sign and the value of Potential
energy in each example referenced to the sys of coordinates in another example.
On the cliff the car had some P=P* for case a) and P=0 for case b).
On the abyss' bottom it had P=0 for case a) and P=-P* for case b).
High in the sky at equilibrium it had P=2P* for case a) and P=P* for case b).

Audidudi was right when he said that the energy needed to propel the car either
forward of up is essentially the same and somebody with more free time on hands
could prove this assumption formally trough the Work performed (both useful and
parasitic i.e. friction-related heat loss etc.)

************************************************************
Igor Kessel
'89 200TQ -- 18psi (TAP)
'98 A4TQ -- mostly stock
Philadelphia, PA
USA
http://www.geocities.com/MotorCity/Garage/8949/homepage.html
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