In article ,
Wim Dekker wrote:
I don't understand why kinetic energy increases quadratically
with speed while the energy it costs to increase speed itself
seams to be directly proportional to the speed.

Assuming that that last phrase should have been "to the speed increase",
no, it's not. The energy cost is what you'd expect from the quadratic
increase in total energy with speed -- the energy increment required for a
speed increment rises with the absolute speed as well as with the size of
the speed increment.

You have to be very careful to do your bookkeeping consistently, and to
use the same frame of reference throughout. You cannot measure total
energy with respect to the ground, and energy increment with respect to
the vehicle!

The rate of energy consumption of a rocket engine looks constant only when
measured with respect to the vehicle. When all measurements are done with
respect to the ground, much of the energy invested in accelerating the
vehicle early on -- when its tanks are nearly full -- goes into making the
fuel more energetic, providing the rocket engine with much higher energy
later in flight.

For a rocket, it is usually much more useful to think in terms of momentum
than in terms of energy.
--
MOST launched 1015 EDT 30 June, separated 1046, | Henry Spencer
first ground-station pass 1651, all nominal! |