Why Does a Rocket's Momentum Remain Unchanged but Its Kinetic Energy Increases?

[liquidblot]

hi guys!~ i was going through my test papers and found a question that i don't understand >_<

when a rocket is shot upwards and at the point where it stops in the air, it explodes...

so why does its momentum remain unchanged but the kinetic energy is increased??

~by the way, the answer that i came up wif was that its momentum and kinetic energy increases, because the formula for momentum and kinetic energy both has mass and velocity in it, so what i tot was that both would have to increase together or remain unchanged together ==''

 

[azatkgz]

I think the rocket's energy and momentum increases ,when some small part of it turns to heat and gives impulse.

 

[LURCH]

In your imagination, try to trace the path fo the rocket's center og gravity wen it is exploding. That might yield some useful insight.

 

[liquidblot]

its weird, because the answer i got from my teacher was that the total momentum was unchanged while the total kinetic energy had increased.

i can see how the total kinetic energy increased, but why does the total momentum remain unchanged? or is my teacher actually saying the wrong answer :( ?

@LURCH
the center of gravity would be in the middle wouldn't it? and then the explosion would cause all the pieces to fly in every degree of a sphere, am i right?

 

[azatkgz]

It's fundamental law of nature.Total momentum of rocket when it stops is zero.If it explodes,all the pieces fly in a such direction that total momentum remains zero.Momentum depends on direction,because it's vector quantity.

 

[HallsofIvy]

I think the rocket's energy and momentum increases ,when some small part of it turns to heat and gives impulse.

its weird, because the answer i got from my teacher was that the total momentum was unchanged while the total kinetic energy had increased.

i can see how the total kinetic energy increased, but why does the total momentum remain unchanged? or is my teacher actually saying the wrong answer :( ?

@LURCH
the center of gravity would be in the middle wouldn't it? and then the explosion would cause all the pieces to fly in every degree of a sphere, am i right?

Your teacher is assuming no air resistance while azatkgz's "some small part of it turns to heat" is assuming air resistance. Because the explosion is "internal" (in the sense of not a force imposed from outside), total momentum of the rocket (or parts of the rocket!) is conserved. Total kinetic energy is not conserved because chemical energy is changed to kinetic energy.

 

[LURCH]

@LURCH
the center of gravity would be in the middle wouldn't it? and then the explosion would cause all the pieces to fly in every degree of a sphere, am i right?

Exactly; the pieces fly (kinetic energy), but they fly in every direction equally, so the center of mass remains statinary, so net momentum of the total system = 0.

 

[liquidblot]

ohh~ thanks a lot for helping~ i learned a lot =D