Re: Propellantless propulsion fun 3 (recirculative propelant)

"Spaceman" <spaceman@xxxxxxxxxxxxxxxxxxxxxxxxxx> wrote in message
news:7padnbhwn6puiBvVnZ2dnUVZ_szinZ2d@xxxxxxxxxxx
Greg Neill wrote:
Sorry, I don't get your point. KE is simply (1/2)*m*v^2
where m is whatever mass is involved. What is
calculating the kinetic energy going to accomplish
here?

It is going to show you that it will take more
kinetic energy to stop the larger mass then it
took to "move" the larger mass.

Since kinetic energy isn't conserved, it would not
surprise me. In fact, you could employ nearly any
amount of kinetic energy you wish to stop the
larger mass.

How? Well kinetic energy is proportional to the
mass and the square of the velocity. Say that your
mass in motion is M travelling at velocity V. You
want to bring it to a halt, but you want to use
more kinetic energy than M has to do it. So you
fire a smaller mass at it with a much higher
velocity.

Say we choose a mass m = M/10.

In order to bring the mass to a halt the smaller mass m
travelling at velocity v must be carrying exactly the
same momentum as the larger mass M. So

M*V = m*v

v = V*M/m

but m = M/10 so

v = V*10

We fire the smaller mass at ten times the velocity as the
larger mass is travelling. That gives it a kinetic energy
of

KE = (1/2)*m*v^2

= (1/2)*(M/10)*(V*10)^2

= 10*(1/2)*M*V^2

It's kinetic energy is ten times that of the mass M.



Anyways, if you want the kinetic energy of the launched
ball it's (1/2)*m*v^2. If you want the kinetic energy
of the ball and object after impact it's

(1/2)*(M + m)*v2^2
= (1/2)*(M + m)*[v*m/(M + m)]^2
= (1/2)*m^2*v^2*/(M + m)

So it's smaller than the kinetic energy of the ball alone
was by a factor of m/(M + m). Again, kinetic energy is
*not* a conserved quantity in general.

So now you think the ball getting stuck in the large mass
will violate the conservation of energy.

Nope. Kinetic energy is not conserved. It trades off
with other forms of energy to keep the sum total conserved
(liek it does with potential energy in orbits) but kinetic
energy by itslef is *not* a conserved quantity.
.

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