Question

You rub two 4.0-mg balloons with a wool sweater. The balloons hang from 0.50-m-long very light strings. When you attach the strings together at the top, the balloons hang away from each other each string making an angle of 37?with the vertical.

Represent the situation with the force diagram for each balloon and determine the magnitudes of the forces that the balloons exert on each other. Will the relative magnitudes change if the charge on one balloon is two times larger than on the other? How do you know?

(I know the formula k x q1q2/r^2 , but I do not know how to apply it here because no charges are given.

Answer 1

Then we apply the equilibrium condition: In the vertical: sigma F_y = 0 T cos theta - mg = 0....1 In the horizontal: sigma F_x = 0 F_e = T sin theta....2 then: F_e/mg = tan theta F_e = mg tan theta = 4 times 10^-6 * 9.8 tan 37 = 2.953 times 10^-5 N

Then we apply the equilibrium condition:

In the vertical:

$\sum F_y = 0$

. $T\cos\theta - mg = 0$ ....1

In the horizontal:

$\sum F_x = 0$

$F_e = T\sin\theta$ ....2

then:

$\frac{F_e}{mg} = \tan\theta$

$F_e = mg\tan\theta = 4\times 10^{-6}*9.8\tan 37 = 2.953\times 10^{-5} N$