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From: Timo Nieminen on 27 May 2010 06:48
On May 27, 6:55 pm, boltar2...(a)boltar.world wrote:
> Timo Nieminen <t...(a)physics.uq.edu.au> wrote:
> >The rate at which the kinetic energy of the rocket is increasing is Fv,
> >where F is the thrust and v is the current speed of the rocket, as per the
> >usual power P = Fv. Meanwhile, if the exhaust speed relative to the rocket
> >is V, then the speed of the exhaust, relative to whatever we measure the
> >rocker to be moving at v, is V-v. As v increases, the rocket gains a
> >larger part of the total energy output, and the exhaust a smaller part.
>
> >If the mass lost per second in the exhaust is m, the force is F = mV. If v
> >is much smaller than V, the KE put into the exhaust per second is then
>
> >KE_e = (1/2) m(V-v)^2 = approx (1/2) mV^2 - mVv
>
> >and the KE put into the rocket per second is
>
> >KE_r = P = Fv = mVv.
>
> >The total power output, KE_e + KE_r, is constant.
>
> Ok , that makes sense. But what happens when you get to the point where v
> is as close to zero as makes no difference and so the rocket is getting most
> of the energy being created? Would the rocket continue accelerating at the
> same rate?

Still works pretty much the same way. Rather than a rocket firing
continuously, it's easier to do the calculation for something like a
spring pushing 2 masses apart (which you can then turn into the rocket
calculation by repetition; make the mass of the "exhaust" mass much
smaller).

Even if the rocket is moving faster than the exhaust speed, it still
works. In this case, the rocket gains more KE than the motor is
providing, but the exhaust is losing energy, not gaining energy, since
it ends up moving slower than it started.

> Or I suppose a better example would be if there was no exhaust and the
> spaceship was simply reacting against a magnetic field using a constant
> power electromagnet. What happens once the power being supplied to the
> electromagnet is less than the gain in kinetic energy required to continue
> accelerating at the current rate?

This one is trickier. To get a force, you need a gradient in the
external magnetic field. If the electromagnet-"rocket" is in a uniform
field, there is no force (but might be a torque). As the electromagnet
moves through the magnetic field, the magnetic field changes (because
there's a gradient in the field), and there'll be an induced potential
in the electromagnet. To maintain the same current (and thus the same
field, and the same force), you'll need a higher voltage, and use more
power.

Doesn't help to use a permanent magnet instead; the energy you get out
of moving in the external field is just what was used to move the
magnet to the starting position.
From: boltar2003 on 27 May 2010 07:26
On Thu, 27 May 2010 03:48:06 -0700 (PDT)
Timo Nieminen <timo(a)physics.uq.edu.au> wrote:
>Even if the rocket is moving faster than the exhaust speed, it still
>works. In this case, the rocket gains more KE than the motor is
>providing, but the exhaust is losing energy, not gaining energy, since
>it ends up moving slower than it started.

That doesn't make sense. The KE can only come from the energy the motor
is providing. It can't come out of nowhere.

B2003


From: Timo Nieminen on 27 May 2010 07:40
On May 27, 9:26 pm, boltar2...(a)boltar.world wrote:
> On Thu, 27 May 2010 03:48:06 -0700 (PDT)
>
> Timo Nieminen <t...(a)physics.uq.edu.au> wrote:
> >Even if the rocket is moving faster than the exhaust speed, it still
> >works. In this case, the rocket gains more KE than the motor is
> >providing, but the exhaust is losing energy, not gaining energy, since
> >it ends up moving slower than it started.
>
> That doesn't make sense. The KE can only come from the energy the motor
> is providing. It can't come out of nowhere.

All it is is (energy provided by motor) = (change in KE) = (change in
KE of rocket) + (change in KE of exhaust). If (change in KE of
exhaust) is negative - that is, the exhaust is losing energy - then
(change in KE of rocket) can be more than (energy provided by motor).
Energy provided = energy gained, no energy from nothing.
From: boltar2003 on 27 May 2010 07:54
On Thu, 27 May 2010 04:40:25 -0700 (PDT)
Timo Nieminen <timo(a)physics.uq.edu.au> wrote:
>On May 27, 9:26=A0pm, boltar2...(a)boltar.world wrote:
>> On Thu, 27 May 2010 03:48:06 -0700 (PDT)
>>
>> Timo Nieminen <t...(a)physics.uq.edu.au> wrote:
>> >Even if the rocket is moving faster than the exhaust speed, it still
>> >works. In this case, the rocket gains more KE than the motor is
>> >providing, but the exhaust is losing energy, not gaining energy, since
>> >it ends up moving slower than it started.
>>
>> That doesn't make sense. The KE can only come from the energy the motor
>> is providing. It can't come out of nowhere.
>
>All it is is (energy provided by motor) =3D (change in KE) =3D (change in
>KE of rocket) + (change in KE of exhaust). If (change in KE of
>exhaust) is negative - that is, the exhaust is losing energy - then
>(change in KE of rocket) can be more than (energy provided by motor).
>Energy provided =3D energy gained, no energy from nothing.

In that scenario the rocket will at some point start taking all the KE from
the exhaust which will then have a speed of zero (ignoring relativity) so
then what? The rocket according to F = MA will still have to accelerate but
theres not enough power from the motor to provide the extra KE it needs in the
time required.

B2003

From: Puppet_Sock on 27 May 2010 08:41
On May 26, 10:16 am, boltar2...(a)boltar.world wrote:
[snips]

Been beaten to death numerous times.
http://groups.google.com/group/sci.physics/browse_frm/thread/4e6a2b2775b57d4d/fd7463ef5b0ae14
Socks
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