You and a friend are doing laundry when you unload the dryer and the discussion

Question

You and a friend are doing laundry when you unload the dryer and the discussion comes around to static electricity. Your friend wants to get some idea of the amount of charge that causes static cling. You immediately take two empty soda cans, which each have a mass of 120 grams, from the recycling bin. You tie the cans to the two ends of a string (one to each end) and hang the center of the string over a nail sticking out of the wall. Each can now hangs straight down 30 cm from the nail. You take your flannel shirt from the dryer and touch it to the cans, which are touching each other. The cans move apart until they hang stationary at an angle of 10 degrees from the vertical. Assuming that there are equal amounts of charge on each can, you now calculate the amount of charge transferred from your shirt.

Explanation / Answer

Hi, From given problem, the system of cans comes to rest due to repulsion between them. In this situation, there are three forces acting on each can: Weight of the can, Electrostatic repulsion between the cans and the Tension of the string. Weight of the can is acting in the downward direction (vertically downwards), Electrostatic force of repulsion acts horizontally and the Tension will be along the string, which will making an angle of 10degrees with the vertical, i.e., making an angle of 80degrees with the horizontal (from triangle laws). So, resolving the tension in the wire into mutually perpendicular directions, Weight of each can is balanced by the vertical component of the tension of string and Electrostatic force is balanced by Horizontal component of force. Step1: lets find the tension in the string. Vertical component of tension of string = T * Sin?. This will be equal to weight of string = m * g = 120 * 10^(-3) * 9.8 = 1.176 N. Hence, T = 1.176 / Sin80 = 1.1941 N. Step2: lets find the electrostatic force of repulsion between the two cans. Let q be the charge on each can. let the distance between the two cans in equilibrium condition = x. Using triangular and trigonometric equations, we can find that x/2 = horizontal distance of each can from the verticle along the point of suspension = hypotenuse * Cos80                            = 30 * Cos80 = 5.2094 cm = 0.0521m. Hence the Electrostatic force of repulsion = F = 9 * 10^9 * q^2 / (0.0521)^2 N       and this is balanced by the horizontal component of the Tension = T * Cos80.       => 9 * 10^9 * q^2 / (0.0521)^2 = 1.1941 * 0.17365       => q = 0.2501 * 10^(-6) C = 0.2501 micro coulomb
(Tried to add the diagram thrice, but it seems there is some error and its not allowing to add the diagram. I hope you can draw the diagram with the explanation given above).
Hope this helps you. (Tried to add the diagram thrice, but it seems there is some error and its not allowing to add the diagram. I hope you can draw the diagram with the explanation given above). Hope this helps you.

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