Geckos can walk on walls and ceilings—at least some of the adhesion is due to static electricity. Gecko feet are covered with microscopic hairs. When these hairs rub against a surface, charges separate, with the hair developing a positive charge and negative charge forming below the surface. There is an attractive force between the separated charges. This is an effective means of adhering to a surface, but it would not be without cost; two planes of charge are like two charged plates of a capacitor, which takes energy to charge. Doubling the amount of charge on each surface will increase the at- tractive force, but will also increase the energy required to separate the charge. By what factor will this energy increase?

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moya1316 moya1316 · Answer 1 · 2020-10-05T10:37:30+02:00

Answer:

U = 4 U₀

we see that the gecko must use 4 times more energy to double the force

Explanation:

For this exercise they indicate that we can approximate the situation to a charged capacitor, so the stored energy is

U = Q² / 2C

where C is the capacitance that does not change since it is the same gecko and Q is the stored charge. In the initial state

U₀ = Q₀² /2C

They tell us that the load is doubled

Q = 2Q₀

where Qo is the initial charge; the new energy is

U = (2Q₀)² / 2C

U = 4 Q₀² / 2C

U = 4 U₀

where U₀ is the initial energy

Therefore we see that the gecko must use 4 times more energy to double the force