Where did all the energy dissaper?

Question

Cannon fired a ball of mass M = 1 kg with muzzle velocity
v = 500 m/s in due west direction on the equator.
Kinetic energy of the ball is K = mv²/2 = 125kJ.
This energy came from burning 1 kg of gunpowder.

But if we look at this from the North pole, the picture is different:
Initial velocity of the ball is equal to speed of earth rotation:
v = 500 m/s. Final velocity is 500-500 = 0.
Thus cannon ball lost all its initial kinetic energy 125kJ,
and the gunpowder is now gone too.

Answer 1

I believe that energy is used up increasing the rotation of the earth slightly. You have to look at all parts of the system, not just the cannonball.

Answer 2

Nicknamr is abosolutely right. Suppose you were flying due West at 500m/s in reference to someone on the ground, and just as you fly over the cannon, it is shot. You will see the cannon ball flying next to you (V=0), but you will notice the speed of the Earth's rotation increasing. If you were to measure the increase of the Earth's speed, and find the energy required to do that, you will find it's equal to the energy from the Gunpowder.

Answer 3

You are worried about 125kJ ? From the viewpoint of an observer on the cannon ball, the whole cannon, in fact the entire earth (as far as said observer can see) , just accelerated to 500m/s , now where did that energy come from?

Answer 4

The picture it not different from any angle. The work done of moving the mass relative to its original position on earth plus the sound waves produced from the explosion are the same.

This is because the original position on earth and the final position have both moved by the same amount. You could say there is a very small change but not so you would see it.

The same could be said about how much work is required to move from the front seat of a car to the back if the car is traveling at 100mph or stopped, its the same.

Answer 5

NASA fires there rockets from west to east to get the same energy or about 1000 mph.

Answer 6

Your setup is fundamentally wrong and shows a poor understanding of relative frames and earth rotation. I would suggest standing in front of that cannon at the north pole and seeing what happens.

Answer 7

The energy didn't disappear. The recoil gave the earth a little extra extra kick.

Answer 8

from that reference point the cannon ball has negative energy before it was fired, or energy in the oposite direction.