Question about past discussion of acceleration:

One of the biggest mis-understandings in my own journey into physics was the post about acceleration, I was unaware that undergoing acceleration by a constant power source would have some limit, that is to say, the acceleration would get less and less as time goes by.

My question that never got answered is this:
How does an object going at some non-relativistic velocity know it is at some velocity and the power supply giving said acceleration, say a 200 megawatt source powering the Vasimir rocket, we calculated it would have around 0.04 G's or thereabouts, thus making a trip to Mars in around 40 days (accel halfway, then decel)

So the gist of the constant power source is the accel is not linear, that is to say the G force when it starts out may be 0.04 G's but when it gets time to reverse the motors, it may have gone down to some lesser #, say 0.03 G's or something.

I still have problems knowing how the spacecraft knows it is not a relative zero velocity vs what the velocity is down the line. Any explanation for that?

Originally posted by sonhouse
One of the biggest mis-understandings in my own journey into physics was the post about acceleration, I was unaware that undergoing acceleration by a constant power source would have some limit, that is to say, the acceleration would get less and less as time goes by.

My question that never got answered is this:
How does an object going at some non-rel ot a relative zero velocity vs what the velocity is down the line. Any explanation for that?

I think anyone would have trouble explaining to you ( or to themselves) how the spacecraft "knows" its absolute velocity. Your statement implies that the spacecraft is conciousiosly changing its acceleration based on its velocity continuously. Newtonian mechanics just uses second order equations as the basis( ie the starting point of the general models of motion), but becuase of continuity there are nth order changes in different rates of things, accelerations of accelerations, of accelerations ect... Just remember that equations are logically simplified "models" that help us to understand our perception of the physical ( or illusory ) world, and in this world we have a simplified model for force:

F = ma
Power: P = Fv

such that

P = m*a*v

a = (P/m)(1/v)

so if both power and mass are constant (by assumption) then velocity is inversely porportional to acceleration (in this very specific scenario).

hope this helps
Eric

This is where I've recorded my own exploration of this topic:

http://athousandyoung.blogspot.com/2010/01/power-and-velocity.html

There is a little robotic space probe floating out in space that is not accelerating. We can take it's inertial frame of reference as v=0.

The engine, when on, provides 1 watt of power which is converted to kinetic energy. The probe has a mass of 2 kg. After one second, the probe has 1 J of kinetic energy, and it's velocity is

1 J = (2 kg)(v^2)/2
1 J/kg = v^2
1 (m/s)^2 = v^2
1 m/s = v

OK, so after one watt is used to accelerate the probe, it is now moving at 1 m/s with respect to the orginal frame of reference.

Now, I want to present two chains of reasoning:

A) If I run the engine for three more seconds, the probe will move at a speed of 2 m/s with respect to the original frame of reference as calculated by K=mv^2/2.

B) According to classical relativity, all inertial frames of reference are equivalent in terms of how the laws of physics acts within them. Thus, after the first second, we can choose a new inertial frame of reference that moves with the ship. Now the ship has v=0 and K=0 with respect to the new frame of reference.

We let the engine run for 1 s. Now the ship has a velocity of 1 m/s with respect to the new frame of reference. If we reset the frame of reference every second, this process will continue each second.

After four seconds, the probe is moving at 1 m/s with respect to the fourth frame of reference. The fourth frame of reference is moving at 1 m/s with respect to the third frame of reference, so the probe is mobing at 2 m/s with respect to the third frame...and 3 m/s with respect to the second frame...and the probe has a velocity of 4 m/s with respect to the probe's original velocity four seconds ago.

Why am I getting different answers?

2/9/10 A person whom I shall call BrotherGeeWhiz commented on my confusion:

I think the issue would be resolved if you took into account the acceleration, which is the quantity I like to think about in classical mechanics. It's proportional to force and invariant to changes in inertial reference frames. If one proposes some continuous form for the acceleration, then the velocities should add along different reference frames (as long as v < < c).

Also (tiny point), for an isolated mass in space to move, it has to propel some "fuel" in the opposite direction to conserve momentum. This changes the mass, but since the fuel can move arbitrarily fast, the change in mass can be made arbitrarily small.

http://athousandyoung.blogspot.com/2010/01/power-and-velocity.html

Originally posted by AThousandYoung
This is where I've recorded my own exploration of this topic:

http://athousandyoung.blogspot.com/2010/01/power-and-velocity.html

There is a little robotic space probe floating out in space that is not accelerating. We can take it's inertial frame of reference as v=0.

The engine, when on, provides 1 watt of power which is converted to kine ...[text shortened]... trarily small.

http://athousandyoung.blogspot.com/2010/01/power-and-velocity.html

This has me bollixed also. One of the dudes here showed a different formula that used constant energy turned to kinetic energy and supposedly showed the same acceleration cannot be constant, it will go down with time.