Energy efficiency of momentum

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Is it more energy efficient to throw a large object slower than a slower object faster? For example, suppose a 100kg person out in space threw a 10 kg object away from themselves at 1 m/s. that means that the 100 kg person would move in the opposite direction at .1 m/s. And this should take (.5*10kg*1^2) equals 5 Joules to throw the 10 kg object and send the astronaut traveling at .1m/s. Now if that astronaut threw a 1kg object away from themselves at 10m/s then this would also send the astronaut traveling away at .1m/s but... the energy to throw this smaller object faster would be (.5*1kg*10^2) equal to 50 Joules. So it would seem that it would take 10 times the energy for the astronaut to travel at the same speed? Is this correct? I understand that kinetic energy isn't conserved but momentum is conserved. I am just interested in terms of e.g. fuel efficiency.
 

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Andrew Mason
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You are correct that from an energy efficiency perspective the way to maximize the change in momentum of the payload/rocket for a given amount of energy, one has to maximize the amount of mass that is ejected. But that is not practical for a rocket. With rockets, the critical issue is reducing the mass that is ejected rather than maximizing energy efficiency. Rockets are designed to give maximum thrust with a minimum of mass loss.

AM
 
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jbriggs444
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You are correct that from an energy efficiency perspective the way to maximize the change in momentum of the payload/rocket for a given amount of energy, one has to maximize the amount of mass that is ejected. But that is not practical for a rocket. With rockets, the critical issue is reducing the mass that is ejected rather than maximizing energy efficiency. Rockets are designed to give maximum thrust with a minimum of mass loss.
If you burn fuel but do not eject that fuel as reaction mass, you end up carrying dead weight. That hurts efficiency. If you eject unburnt fuel as reaction mass, you end up wasting energy. That hurts efficiency. The obvious choice is to eject burnt fuel as your reaction mass. Which is what most rockets do.

It also pays dividends to use a fuel with a high energy/mass ratio, of course. [Better to burn liquid hydrogen and liquid oxygen rather than shooting lead pellets powered by stretched rubber bands].
 
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