You have a pair of cannon balls, each 100kg in mass, and a ‘charge shuttling’ de

Question

You have a pair of cannon balls, each 100kg in mass, and a ‘charge shuttling’ device which can be used to remove electrons from one object and place them on another. One of the cannon balls is suspended from the ceiling with an insulating cord. You want to use electrostatic attraction to cause the other to hang in space beneath it, just by removing electrons from the upper cannon ball, and placing them on the lower one. How many electrons must you “shuttle” in order to get the lower cannon ball to hover 2.0m below the upper one? Give your answer in moles.

Explanation / Answer

Each cannon ball has a weight of mg = 100 x 9.8 = 980N

When the lower cannon ball (ball 1) is hanging 2.0m below the upper ball (ball 2), the resultant force on ball 1 is zero

so the upwards electrostatic attraction on ball 1 is 980N.

If N electrons are transferred from ball 2 to the ball 1, the charges on the balls will be +Ne on ball 2 and -Ne on ball 1

(where e = 1.6x10¹ C).

Since |F| = k|q1||q2|/d^2

980 = [(9 x 10^9) x (N x 1.6 x 10^-19) x (N x 1.6 x 10^-19)] / 2^2

980 = (23.04 x 10^-29 x N^2) / 4

980 = 5.76 x 10^-29 x N^2

N^2 = 170 x 10^-29

N^2 = 17 x 10^-28

N = 4.123 x 10^-14 C

one mole of electrons is the same as 96500 coulombs

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