Answer to Question #101322 in Physics for Will

Question

Three identical small Styrofoam balls (m = 1.94g) are suspended from a fixed point by three nonconducting threads, each with a length of 54.7cm and with negligible mass. At equilibrium the three balls form an equilateral triangle with sides of 29.9cm. What is the common charge q carried by each ball?

Answer 1

For the equilibrium on the y-axis:

$$T\cos \gamma=mg$$

For the equilibrium on the x-axis:

$$T\sin \gamma=2F\cos {\frac{\alpha}{2}}=2\frac{kq^2}{a^2}\cos 30$$

$$\tan\gamma=2\frac{kq^2}{mga^2}\cos 30$$

$$\cos \gamma=\frac{b}{L}=\frac{\sqrt{3}a}{4L}=\frac{\sqrt{3}(0.299)}{4(0.547)}$$

$$\gamma=76.31\degree$$

$$\tan(76.31\degree)=2\frac{(8.99\cdot 10^9)q^2}{(0.00194)(9.8)(0.299)^2}\cos 30$$

$$q=1.59\cdot 10^{-6}C$$