- #1
Darkwolf312
- 1
- 0
1. Two small, identical spheres of mass m each are attached to thin light threads of length L each and hung from the same point. When charges q1 and q2 are placed on upon the spheres(with both charges having the same sign), the two spheres repel each other and, upon reaching equilibrium, hang at angles \theta and \theta' from the vertical.
a) If q1= 3q2, what is \theta' in terms of \theta? (Hint: Consider Newton's Third Law)
b) Draw a free-body diagram for either sphere, and hence find the distance x between the spheres in terms of q1, q2, L, m, and any necessary physical constants. Assume that \theta is small such that \theta \approx Sin\theta \approxTan\theta
F= kq1q2/d2
In my first attempt at the problem, I assumed the forces caused by the charges were perpendicular to the vertical and thus got the answer Sin\theta/Sin\theta' = 1. I think this answer is incorrect, but I got it by equating the two forces caused by the charges, and hence equating the x-component of the two tension forces.
I guess the correct way to do it would be to take the electrostatic forces as being in line with the distance, but I can't seem to figure out the angle between the force and the horizontal. I am also unsure as to whether I should use the statement given in part b as how small \theta is. Any help would be greatly appreciated.
a) If q1= 3q2, what is \theta' in terms of \theta? (Hint: Consider Newton's Third Law)
b) Draw a free-body diagram for either sphere, and hence find the distance x between the spheres in terms of q1, q2, L, m, and any necessary physical constants. Assume that \theta is small such that \theta \approx Sin\theta \approxTan\theta
Homework Equations
F= kq1q2/d2
The Attempt at a Solution
In my first attempt at the problem, I assumed the forces caused by the charges were perpendicular to the vertical and thus got the answer Sin\theta/Sin\theta' = 1. I think this answer is incorrect, but I got it by equating the two forces caused by the charges, and hence equating the x-component of the two tension forces.
I guess the correct way to do it would be to take the electrostatic forces as being in line with the distance, but I can't seem to figure out the angle between the force and the horizontal. I am also unsure as to whether I should use the statement given in part b as how small \theta is. Any help would be greatly appreciated.
Last edited:
)
when it talks about θ being small! 
