Kinetic Energy - Change Calculation

[tardis]

Is the energy required to accelerate mass m 1 meter/sec2 for 1 second, the same whether that mass is:
a) currently traveling at 3 meters per sec or
b) 300 meters per sec?

 

[Hootenanny]

I suggest you put some numbers in and find out.

~H

 

[KingNothing]

No. Since kinetic energy is proportional to $$v^2$$, a change of +1 m/s at 300 m/s will result in a 300.5J KE increase, whereas at 3 m/s it will only result in a 3.5J increase.

 

[tardis]

Thanks that is consistent with the calculations. I'm having trouble understanding work and impulse. Specifically, consider a mass with a rocket on it - the rocket burns for 1 second regardless of how fast the mass is currently moving, and the total chemical potential energy in the rocket doesn't change when it's moving.

Is the force the rocket applies to the mass the same when the mass is stationary and when it's moving? If so, isn't it applying the same force over a larger distance and thus doing more work with the same amount of energy (clearly a contradiction)? If not, does that mean there is some "absolute" reference frame relative to which the mass's motion is measured?

 

[Pengwuino]

The rocket can't be creating thrust (thus, no force) if its not using some of the chemical potential energy.

 

[Farsight]

Tardis:

Work is Force x Distance, which you can translate into "Kinetic Energy". It's a way of thinking about "stopping distance". A rocket going twice as fast takes twice as much fuel to stop, and while it's stopping, it goes four times as far.

Impulse is Force x Time, which you can translate into Momentum. It's a way of thinking about "stopping time". A rocket going twice as fast takes twice as much fuel to stop, and stops in twice the time.

Both are just different ways of looking at a moving object. Think about the situation where the rocket kicks out its exhaust at 300m/s. At the start of the burn an outside observer sees the exhaust moving at 300m/s, and the rocket hardly moving at all. Hence most of the "work" is going into the exhaust. Later when the rocket reaches 300m/s, none of the "work" goes into the exhaust, because the observer notes that the exhaust is now moving at 0m/s. But inside the rocket you see a constant fuel consumption, acceleration, and "work" rate.

The observer is treating work as stopping distance. You're thinking of work as stopping time. And the bottom line is that work and energy here are just concepts to do with relative motion, and aren't real.

 

[tardis]

Thank you Farsight. That is very helpful.