Two small metallic spheres, each of mass m = 0.214 g, are suspended as pendulums

Question

Two small metallic spheres, each of mass m = 0.214 g, are suspended as pendulums by light strings of length L as shown in the figure below. The spheres are given the same electric charge of 7.1 nC, and they come to equilibrium when each string is at an angle of ? = 5.50

Two small metallic spheres, each of mass m = 0.214 g, are suspended as pendulums by light strings of length L as shown in the figure below. The spheres are given the same electric charge of 7.1 nC, and they come to equilibrium when each string is at an angle of ? = 5.50 degree with the vertical. How long are the strings?

Explanation / Answer

sum forces in the y for a sphere

T cos theta - mg = 0
T = m g/cos theta

sumforces in the x

k q^2/r^2 - T sin theta = 0

k q^2/r^2 - m g tan theta = 0

but r = 2 L sin theta
so
9.0E9*7.1E-9^2/(2*L*sin(5.5 degrees))^2 - 0.214E-3*9.81*tan(5.5 degrees)=0
solve for L
L=0.247 m

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