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

"Mark Rutherford" <mark@afnetinc.com> wrote:

Because of conservation of energy laws and the restrictions, namely no
friction the car would be propelled a lot further that 40 miles on 1 cup of
fuel.  The distance it would be propelled is infinite if frictional forces
are not taken into account, Newton's law.  While if the gasoline is placed
below the  car all of the arguments Igor provided are accurate.  So a car
being propelled up in the presence of a gravitational field can not be
compared with a car moving in a straight line because no friction forces are
acting on the car.

Mark's consideration is correct for a small horizontal travel L.
However in the absence of friction the car will still not travel in a straight
line. Greatly simplified the car will feel several forces applied to it: 
1. The gravity force, vector pointing to the centre of Earth.
2. The reaction of the base vector pointed in the opposite direction.
3. The vector of centrifugal force in the same direction.
4. The linear component of rotational force applied as a tangential vector due
rotation of Earth.
5. The vector of Coriolice force. Also pointing to the centre of Earth but in a
rather complex equation.
6. The tangential vector of force propelling the car horizontally (in our case
spending the potential energy of the fuel burned). Let's call it the Propelling

Probably some more.

All except 6. are mutually compensated in our stationary sys (if we assume a
moving sys of coordinates) and according to the 1st Law of Newton do not
participate in the car's movement.

The car however will not leave the Earth' surface and will not continue to move
in a
straight line tangential to the Earth's surface. 

For simplicity let's assume that the Earth' radius is a constant R. As the
horizontal distance L increases the
vector of gravity stops being normal to the vector of Propelling force. Instead
we will have a right triangle of forces where the vector of gravity
force is a hypotenuse H of this imaginary right angle triangle ( R, L and H).
This means that the horizontal component of this gravity force
becomes tangential: Ft=Fg*sin▀, where ▀ is the angle between R  and H. This
component is applied in the same axis but with the opposite sign as the
Propelling force, effectively slowing down the vehicle.

The reality is a lot simpler, though. If the Propelling force is small, in the
absence of friction (air friction, rolling friction etc.) the car will not
travel in a straight line but rather will make infinite circles on the Earth'

However if the Propelling force is great enough once the car reaches the First
Cosmic Velocity (excuse a literal translation here, I am not sure that in
English it is called the same way) it will leave the Earth' surface and become
it's satellite.
If this force is even greater it might reach the Second Cosmic Velocity and
the Earth' gravity for good. The car needs to overcome the gravity force
which is Gamma times car's mass times Earth' mass divided by the distance
between them square, where Gamma is the gravitational constant.

Igor Kessel
'89 200TQ -- 18psi (TAP)
'98 A4TQ -- mostly stock
Philadelphia, PA