Question

8. Rubbing a plastic bag and a balloon with a cloth gives both objects a net negative charge. The balloon's
charge is -1x10^-10 C and the bag's charge is -1x10^-5 C, and each object has a mass of 0.02 grams.
Wearing insulating gloves, you hold the bag above the balloon and let go. How far above the center of the
balloon will the bag 'levitate'?

Answer 1

Answer:

0.214 m

Explanation:

In order for the bag to levitate and not fall down, the electrostatic force between the bag and the balloon must balance the weight of the bag.

Therefore, we can write:

$k\frac{q_1 q_2}{r^2}=mg$

where

k is the Coulomb constant

$q_1=-1\cdot 10^{-10}C$ is the charge on the balloon

$q_2=-1\cdot 10^{-5} C$ is the charge on the bag

r is the separation betwen the bag and the balloon

$m=0.02 g=2\cdot 10^{-5} kg$ is the mass of the bag

$g=9.8 m/s^2$ is the acceleration due to gravity

Solving for r, we find the distance at which the bag must be held:

$r=\sqrt{\frac{kq_1 q_2}{mg}}=\sqrt{\frac{(9\cdot 10^9)(-1\cdot 10^{-10})(-1\cdot 10^{-5})}{(2\cdot 10^{-5})(9.8)}}=0.214 m$