How can a moving frame transmit energy (a fighter plane shoots a bullet)?

Question

This question shows that a bullet shot from a flying plane receives a large amount of energy from the plane, even much more than the energy from the propellant of the bullet.

But I wonder how can the plane transfer additional energy to the bullet? For example, the propellant gas expands and creates the pressure that pushes the bullet forward, this energy is limited by the propellant itself. While the plane only recoils backward, how can the plane transfer force, or energy to the bullet, in what method since it even does not touching the bullet? If the barrel is a part of the plane, the plane even pulls the bullet backward by friction.

The frame does not transmit energy. Energy is not a frame invariant. — ACuriousMind, Feb 14 '15 at 03:51
@user2174870 I'm legitimately curious why you think that comment will in any way improve the situation you're in? — Jim, Feb 18 '15 at 16:46
The situation I am in is a dead end, why I need a better comment than that? — user2174870, Feb 18 '15 at 16:49
Tell me if anything I can do to get the better thing out of this situation? — user2174870, Feb 18 '15 at 16:57
Perhaps you could try modifying your question to explain why it's not a duplicate of that question? — Kyle Kanos, Feb 18 '15 at 17:09
At very least, you could avoid rude and/or offensive language. That will do much more to make people want to help you all they can. — Jim, Feb 18 '15 at 17:35

score 1 · Answer 1 · answered Feb 14 '15 at 09:05

It appears that the confusion both in your question and in the question linked stem from a confusion of reference frames, leading to an apparent difference in outcomes across multiple tests of the "same" process. The original question regards a cannon that fires a 2kg shell at 1km/s muzzle velocity, i.e. imparts 1MJ energy to the projectile. The question then points out that the same cannon mounted on an airplane flying at 1km/s will result in the projectile having a velocity of 2km/s when fired, and thus a kinetic energy of 4MJ (since energy scales with the square of velocity).

Note that the above velocities are both in relation to the ground. Obviously if you consider from the frame of reference of the cannon, the projectile has the same muzzle velocity in each case - since the same amount of the same propellant is used and thus the same chemical energy is released - and thus there's no difference between being on the ground or mounted to a plane. In the frame of reference of the projectile, it gains no kinetic energy whatsoever and instead the rest of the universe accelerates past it with an enormous collective kinetic energy difference. Of course this violates conservation of momentum because we are ignoring the acceleration of the reference frame itself.

That said, the logical reference frame to use for these calculations is the center of mass of each system - of the Earth-projectile system for a cannon fixed on the ground, and the plane-projectile system for a cannon fixed into an airplane. In each case, when the propellant is ignited, an equal momentum is transferred to each "side" of the system, and the total absolute momentum is a function of the released chemical energy of the propellant.

How can a moving frame transmit energy (a fighter plane shoots a bullet)?

1 Answers1

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