Thrust vs Gravity: What's Missing?

[hal bitton]

TL;DR

Thrust at hover vs thrust at constant non zero vertical velocity.

This is a conceptual problem. Consider two identical rocket ships in a gravitational field with no atmosphere. Ship A is hovering at a fixed altitude, ship B is ascending at a constant vertical velocity. Since neither ship is accelerating vertically, the thrust required of both should be the same, namely, thrust equal to the weight of the ship. Yet ship B is gaining potential energy, and ship A is not. I realize ship B's constant vertical velocity is the result of a previous vertical acceleration, but still, at some point in time it seems that ship B will be gaining "free" energy compared to ship A. What am I missing here? Regards, Hal

 

[Ibix]

You are missing an analysis of the energy of the rocket exhaust. It will be different in the two cases, the exhaust being slightly slower for the rising rocket.

 

[russ_watters]

...but still, at some point in time it seems that ship B will be gaining "free" energy compared to ship A. What am I missing here?

You're saying it backwards: ship A is wasting all of its energy.

 

[A.T.]

This is a conceptual problem.

This might help:
https://en.wikipedia.org/wiki/Gravity_drag

 

[Dale]

at some point in time it seems that ship B will be gaining "free" energy compared to ship A.

Since B is burning rocket fuel the energy is not free, regardless of what you compare it to.

Rocket engines are very inefficient at low speed, with 0% efficiency at 0 speed. So the difference is simply that rocket B has slightly greater efficiency than rocket A. Maybe 0.001% efficiency instead of 0%.

 

[DaveE]

It seems like this talk of rocket engines might be missing a fundamental part of your question. Let's switch from "rocket engine" to some generic magic force in it's place. Yes, in both cases the lifting force can be the same, but one does work and the other doesn't. Force and work (or energy) just aren't the same things. It is as simple as that, almost a definition instead of an explanation. The magnet stuck to your refrigerator isn't doing any work to stay there, but there is a force generated. From this point you can dig deeper into how the forces are created or applied, as in the previous answers.

 

[hutchphd]

Summary:: Thrust at hover vs thrust at constant non zero vertical velocity.

I realize ship B's constant vertical velocity is the result of a previous vertical acceleration, but still, at some point in time it seems that ship B will be gaining "free" energy compared to ship A. What am I missing here?

The energy that B gains is not free. The fuel in the moving rocket contains more energy (the kinetic energy in the Earth frame of reference associated with its upward motion). As the fuel is burned this extra energy is what seems to be free, but really it is already paid for and the ledger is in fact perfectly balanced.

 

[Lnewqban]

Summary:: Thrust at hover vs thrust at constant non zero vertical velocity.

... What am I missing here? Regards, Hal

I believe that the non-zero velocity, which means kinetic energy, which means work done on the rocket is what you are missing, Hal.

This problem could be compared to a crane statically suspending first and then lifting a load at constant speed: mechanical energy coming from its engine does the lifting work.
Crane's drum brake and tension in the cable are what keep the load suspended at zero vertical velocity.

Copied from:
https://en.m.wikipedia.org/wiki/Work_(physics)

"Work is closely related to energy. The work-energy principle states that an increase in the kinetic energy of a rigid body is caused by an equal amount of positive work done on the body by the resultant force acting on that body. Conversely, a decrease in kinetic energy is caused by an equal amount of negative work done by the resultant force. Thus, if the net work is positive, then the particle’s kinetic energy increases by the amount of the work. If the net work done is negative, then the particle’s kinetic energy decreases by the amount of the work."