Total Energy Dilemma: Cruiser vs Battleship

[Mephisto]

I was presented with a very simple physics problem today which unfortunately stumped me for some reason:
you have two spaceships: a cruiser weighing a ton, and a battleship weighing 100 tons. Now let's say the cruiser is moving towards the battleship at constant speed. From battleships point of view, the cruiser is coming towards it, so energy in the system is just 1/2 m_cruiser v^2. But from cruisers point of view, the energy in the system is 1/2 m_battleship v^2, which is MUCH greater since m_battleship >> m_cruiser.
So the energy in the two systems is different, and yet isn't that exactly the same physical problem? This is such a noob question i almost feel bad asking it.

 

[miknsk]

What's the problem? Energy conservation laws are applicable in any inertial system, but you can not "jump" from one system to another so easily. Energy is not a constant value which does not depend on choice of system.

 

[tiny-tim]

Hi Mephisto!

If m(a² - b²) + M(c² - d²) = 0,

then m((a-v)² - (b-v)²) + M((c-v)² - (d-v)²) = 2m(bv - av) + 2M(dv - cv);
which is zero, from conservation of momentum.

 

[Doc Al]

KE is frame dependent

So the energy in the two systems is different, and yet isn't that exactly the same physical problem?

The speed and thus kinetic energy of an object depends on the frame doing the measurement. But that doesn't change any physics. (Conservation laws will work the same from any inertial frame's viewpoint.)

 

[Mephisto]

The speed and thus kinetic energy of an object depends on the frame doing the measurement. But that doesn't change any physics. (Conservation laws will work the same from any inertial frame's viewpoint.)

omg, that makes perfect sense. even when you calculate the potential energy of an object due to gravity you take an arbitrary reference point. I should have remembered that. All that matters is that the conservation laws work. Stupid me :) thanks