Exploring the Relationship between Impulse and Work in Rocket Dynamics

[Persson]

Homework Statement

I have a hipotetic rocket that have a power of 3000 watt, however its position don't change because the effect of a gravity of 10m/s^2 do the rocket remains like it would be resting. I need to determine the mass of the rocket. In a similar problem I have a rocket also in an unchangeable altitude by the effect of the gravity with a mass of 400kg and I need to determine the power of the rocket engine.
I would like to know if I could consider in this case impulse and work as synonymous or if there's another way to solve the problem. Since there's a spend of energy by the rockets .

Homework Equations

It's not used the rocket equation, it is just a hypothetical situation to calculate the energy spend to remain a static position

The Attempt at a Solution

 

[CWatters]

Homework Statement

I have a hipotetic rocket that have a power of 3000 watt, however its position don't change because the effect of a gravity of 10m/s^2 do the rocket remains like it would be resting. I need to determine the mass of the rocket.

In a similar problem I have a rocket also in an unchangeable altitude by the effect of the gravity with a mass of 400kg and I need to determine the power of the rocket engine.
I would like to know if I could consider in this case impulse and work as synonymous or if there's another way to solve the problem. Since there's a spend of energy by the rockets .

You cannot solve either. You need more information. Do you know the mass flow rate from the rocket engine? The exit velocity?

The work done on a rocket is the thrust * velocity. When the rocket is hovering the velocity is zero. So the work done on the rocket is zero. This means the efficiency is zero. All of the work done by the rocket (or helicopter rotor) is wasted. The power required to hover depends on the efficincy of the engine.

 

[Persson]

Thank you so much