Question

You and a friend are doing the 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.

Answer 1

Q_total = 2 10⁻⁶ C

Step-by-step explanation:

Let's apply the conditions of static equilibrium to this case, in the adjoint we can see a diagram of the forces.

X axis

Tₓ - Fe = 0

Tₓ = Fe

Y axis

`T_(y)` - W = 0

T_{y} = W

Let's use trigonometry to find the stress components, the angle is measured with respect to the vertical

sin 10 = Tₓ / T

cos 10 = T_{y} / T

Tₓ = T sin 10

T_{y} = T cos 10

we substitute

T sin 10 = Fe

T cos 10 = W

T = mg / cos10

T = 0.120 9.8 / cos 10

T = 1,194 N

Fe = 1,194 sin 10

Fe = 0.2073 N

the electric force is

F = k q₁q₂ / r²

in this case, as the cans touch, they have the same charge and the distance r is searched for by trigonometry

sin 10 = y / L

y = L sin 10

y = 0.30 sin 10

y = 0.052 m

this is the distance from the vertical to one can the distance between the two cans is

y_total = 2y

y_totlal = 2 0.052 = 0.104 m

Fe = F = k q² / r²

q = √ (F r² / k)

q = √ (0.2073 0.104²/9 10⁹) = √ (24.913 10⁻¹⁴)

q = 4.99 10⁻⁷ C

This is the charge of a can, as the transfer is carried out by contact, the flannel transfers half of its charge to the cans and these when separating face one keeps half of the transferred charge, therefore the total charge of the flannel is

Q_total = 4 q

Q_total = 19.97 10⁻⁷ C

Q_total = 2 10⁻⁶ C