# Basic question about work and gravity

Hi!

Work is defined as

$$dW = F\cdot dr$$

so there is no work required to keep things spatially fixed in a gravitational potential. However, consider a hovering helicopter. Even though it is not moving in the gravitational field, it will eventually run out of fuel. Ofcourse there are dissipative losses but obviously it takes energy to keep the chopper from falling down.

Or when I'm flying my jetpack, I can't stay put at 100 ft indefinitely, it costs energy to keep hovering - still no work is being done.

Where does the energy go?

Doc Al
Mentor
In those cases no work is being done against gravity, but energy is required to create the thrust to oppose gravity.

Supporting the helicopter can be done by placing it on the ground. No energy required. But if you want to support the helicopter in the air, you need to turn the blades and push air down--that takes energy.

So one could basically say that there IS work done because as the blades cut through the air there's a vertical component to the force exerted on the air molecules which for a brief period of time pushes them downward?

Doc Al
Mentor
Sure, work is being done to move those blades through the air. But it's not work against gravity.

it iz spent in supplying the necessary centripetal force.

Doc Al
Mentor
it iz spent in supplying the necessary centripetal force.

Ok, so suppose that the helicopter is instead placed upon a rigid body. The distances between molecules in the supporting body are slightly compressed and thereby act as a bunch of tiny springs (if we assume that intermolecular forces can be modeled as derived from a harmonic potential). The compression thus causes a force that balances the gravitational one and an equilibrium state is reached in which no energy consumption is needed.
How is this situation different from the first? Why do we need a constant supply of power to keep an object still in the air, but no power to keep it still on the ground?

Doc Al
Mentor
How is this situation different from the first? Why do we need a constant supply of power to keep an object still in the air, but no power to keep it still on the ground?
You need a constant supply of energy to keep the blades moving, which is required to produce the force needed to support the helicopter in mid air. If you just rest the helicopter on the ground (or hang it from a hook), you won't need to do that. Up to you.

In any case, you're not doing any work against gravity.

You need a constant supply of energy to keep the blades moving, which is required to produce the force needed to support the helicopter in mid air. If you just rest the helicopter on the ground (or hang it from a hook), you won't need to do that. Up to you.

In any case, you're not doing any work against gravity.

Fair enough.

But am I doing work against anything else?

Doc Al
Mentor
But am I doing work against anything else?
Of course. You are doing work against the resistance of the air (as the blades turn). (Not to mention overcoming any friction within the mechanism.)

Ok, I think I follow you now. Thanks a lot!