Two small metallic spheres, each of mass m = 0.186 g, are suspended as pendulums
ID: 2274092 • Letter: T
Question
Two small metallic spheres, each of mass m = 0.186 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 6.7 nC, and they come to equilibrium when each string is at an angle of ?= 4.60
Two small metallic spheres, each of mass m = 0.186 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 6.7 nC, and they come to equilibrium when each string is at an angle of ?= 4.60degree with the vertical. How long are the strings?Explanation / Answer
x direction:
T sin(theta) = k q^2/r^2
(r is the distance between tow masses)
y direction:
T cos(theta) = m g
dividing:
tan(theta) = k q^2/(m g r^2)
==> r^2 = k q^2/(m g tan(theta))
==> r^2 = 8.99e9*(6.7e-9*6.7e-9)/(0.186e-3*9.81*tan(4.60))
==> r^2 = 0.0027489
==> r = 0.05243 m
we have:
sin(theta) = (r/2)/(L)
==> L = (r/2)/sin(theta)
==> L = (0.05243/2)/sin(4.60)
==> L = 0.327 m
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