two identical charged balls hang from the ceiling by insulated ropes equal length l=1.5m. A charged q=25*10^-6 is two identical charged balls hang from the ceiling by insulated ropes equal length l=1.5m. A charged q=25*10^-6 is applied to each ball. then the two ball hang at rest and supporting rope has an angle of 25degree respect to the vertical. what is the mass of each balls?

Question

kainui · Answer

$$F=ma$$$$F _{e}=k _{e}(\left| q _{1} \right|\left| q _{2} \right|)/r^2$$
You can set these equations equal to each other, and since the balls aren't moving, you know that the forces are in equilibrium. Using trigonometric functions separate the forces into x and y directions so that you can use substitution to solve for your unknowns. You know that there will be an acceleration downwards due to gravity and no acceleration in the x direction. You think you can solve it now?

turingtest · Answer

|dw:1329595296046:dw|In the x-direction we have$$\sum F_x=F_e-T\sin\theta=k\frac{q^2}{r^2}-T\sin\theta=0$$in the y-direction we have$$\sum F_y=F_g-T\cos\theta=mg-T\cos\theta=0$$eliminate T between these two equations and solve for m (r can be found through trig)