Kinetic Energy Changes at fast speeds

Originally posted by wolfgang59
Consider a very fast (non-relativisic) space-ship travelling at 1,000,000 m/s.

An astronaut inside of mass 100 kg walks towards the front at 1m/s.

a) What was his KE standing still?
b) What is his KE walking?
c) What is the increse in his Kinetic Energy and where does it come from?

Momentum is conserved in a sealed system. By my working, using conservation of momentum, when the man is walking (if we can assume his velocity w.r.t. the ship is then 1 m.s) it can be shown that the kinetic energy of the man+ship combination has increased by exactly 50 joules over when he was at rest, exactly the same as if he had gone from rest to walking on earth, and which is the useful energy provided by the man's muscles. The man and ship have to be considered together because the ship slows down a bit when the man speeds up.

Originally posted by iamatiger
Momentum is conserved in a sealed system. By my working, using conservation of momentum, when the man is walking (if we can assume his velocity [b]w.r.t. the ship is then 1 m.s) it can be shown that the kinetic energy of the man+ship combination has increased by exactly 50 joules over when he was at rest, exactly the same as if he had gone from rest to ...[text shortened]... d ship have to be considered together because the ship slows down a bit when the man speeds up.[/b]

Sorry, I should have said almost exactly 50 joules, it is very slightly less.

Originally posted by iamatiger
Momentum is conserved in a sealed system. By my working, using conservation of momentum, when the man is walking (if we can assume his velocity [b]w.r.t. the ship is then 1 m.s) it can be shown that the kinetic energy of the man+ship combination has increased by exactly 50 joules over when he was at rest, exactly the same as if he had gone from rest to ...[text shortened]... d ship have to be considered together because the ship slows down a bit when the man speeds up.[/b]

You have not answered question a, b or c.

Originally posted by sonhouse
Yes that is totally true but like an open door in front or back of the craft where mass can be ejected rocket-like is the only case where actual matter leaves the craft. In the case of heat, it is eventually like an open door to the outside, heat loss cannot be avoided, no matter what kind of technology you put in place to conserve heat, some of it will eve ...[text shortened]... ly be radiated, thus slowing down the craft if that continued. There is no way around that fact.

But if you "move an object back and forth" you need to exert energy to move it against friction (e.g. chemical potential energy). THAT is the energy that becomes heat, not the KE of the spacecraft.

I didn't answer a, b and c mainly because mtthw answered them correctly. Of course the increse in total k.e. of the system of about 50 joules is because the astronaut's muscles have done some useful work. I think the exact increase depends intuitively on the spaceship's mass because:

If the spaceship is as light as a feather, the astranaut finds it very hard to accelerate himself and it ends up going backwards very fast.

Of the spaceship is very heavy the astranout can accelerate himself more easily by pushing against it.