How Does a Rocket Engine Maintain Constant Thrust While Power Increases?

[npena29]

ok here's the problem. i really need on this. its not a calculation but more of an explanation.

Consider a rocket engine. It delivers a constant thrust, which is the force exerted on the rocket by the expanding exhaust gases from the burning fuel.This typically is true in real life:both the thrust and the rate at which fuel is burned are constant. However, the instantaneous power is given by P=F x v. Since the force is constant, the rocket is accelerating, therefore v is increasing, therefore P is icreasing. However, the fuel is burning at a constant rate; therefore it is producing energy at a constant ratem therefore the power due to the burning fuel is constant. Is there a contradiction here? Explain what's happening, in gory detail.

ok, what i got is the velocity is increasing due to less mass..so less mass the velocity gets faster...what else is needed?

 

[jbsteele]

No, there is no contradiction here. The thrust of a rocket engine is the force exerted on the rocket by the expanding exhaust gases from the burning fuel, and this thrust is constant. This means that the rate of acceleration of the rocket is constant, as it is being pushed with a constant force by the exhaust gases. However, since the velocity of the rocket is increasing due to the constant acceleration, the instantaneous power of the rocket is increasing. This is because the power is given by P=F x v, and since F (the force) is constant and v (the velocity) is increasing, the power must also increase. At the same time, the fuel is burning at a constant rate, meaning that the energy produced by the burning fuel is also constant. This is because the energy produced by the burning fuel is proportional to the rate at which the fuel is burned. Since the fuel is being burned at a constant rate, the energy produced by the burning fuel is also constant. So, the power of the rocket is increasing due to the increasing velocity, but the power due to the burning fuel is constant due to the constant rate of fuel burning. There is no contradiction, as the power of the rocket is increasing due to the increasing velocity, and the power due to the burning fuel is constant due to the constant rate of fuel burning.