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I was thinking about this problem:

How much work is required to hold an object stationary in a gravitational field?

or:

How much energy is required to keep an object stationary in a gravitational field, i.e. how many J/s are required?

and I realized I could not come up with a satisfactory answer.

Let's setup an example to limit our scope: First of all let's consider an mini-copter of mass m=10 kg on earth which uses its' rotor blades to reach altitude of h=1 meter. The work required to get it there is roughly: mgh = 9.82 m/s * 10 kg * 1 m.

Which means we spent 98.2 Joules of energy getting it there. So if this work was done under the time t= 2s the effect of the mini-copter engine would be roughly $mgh/t$ ~ 98.2 Joules / 5s ~ 19.64 watt.

Now, obviously the engine would have to keep on running to keep the quadrocopter at the height of 1m, roughly how much effect would be required?

So this is kind of a high-school level question but I can't seem to wrap my head around it.

Jimmy Pettersson
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1 Answers1

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You do not need to spend any energy to keep an object stationary in a gravitational field, but you do need a force that is opposite to gravity, so that the object can be at rest.

For instance, you can put the object on a table, or "hang" it, and the object will stay there without any energy requirement. So the answer is zero, you do not need to do any work. The fact that you might need to spend energy to generate the force does not change that.

bobie
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