v Question Completion Status: Two small metallic spheres of mass 0.2g are suspen

Question

v Question Completion Status: Two small metallic spheres of mass 0.2g are suspended as pendulums by light strings of length L. The spheres are given the same electric charge so they repel each other. They come to equilibrium when each string is at an angle of 5 degrees from vertical. There are three forces: tension, weight, and electric force. Find the electric force required for equilibrium. Do this like a Physics 251 problem. QUESTION 2 1 points save Now that you know the electric force, find the distance between the spheres if each is charged to 7.2nc QUESTION 3 1 points Now use trig to find the length of the string Save All Answers Save and S Click Save and Submit to save and submit. Click Save All Answers to save all answers

Explanation / Answer

Given,

m = 0.2 g ; theta = 5 deg

We need to find the electric force.

For the force in x direction:

Fx = T sin(theta) - Fe = 0

Fe = T sin(theta)

In y direction:

mg = T cos(theta)

Fe/mg = tan(theta)

Fe = m g tan(theta)

Fe = 0.2 x 10^-3 x 9.81 x tan5 = 1.72 x 10^-4 N

Hence, Fe = 1.72 x 10^-4 N

We know that,

Fe = k q1 q2/r^2 = k q^2/r^2

r = q sqrt (k/F)

r = 7.2 x 10^-9 sqrt (9 x 10^9/(1.72 x 10^-4)) = 0.0521 m

Hence, r = 0.0521 m

Using trig,

(r/2)/L = sin(theta)

L = (r/2)/sin(theta) = (0.0521/2)/sin5 = 0.2988 m

Hence, L = 0.298 m ( = 0.3 m)

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