Two helium-filled, spherical balloons, each with charge q, are tied to a 9.00-g

Question

Two helium-filled, spherical balloons, each with charge q, are tied to a 9.00-g mass with strings of negligible mass, and the system floats in equilibrium as shown in the figure below. The distance between the balloons is L_1 = 55.0 cm, and the strings are L_2 = 120.0 cm long. Ignore the weight of the balloon material, and assume that the density of air is 1.29 kg/m^3 and the density of helium inside the balloons is 0.200 kg/m^3. (a) Find the magnitude of the charge q on the each balloon. Assume that the charge on each balloon acts as if it were concentrated at its center. (b) Find the volume of each balloon.

Explanation / Answer

(a)

Apply Coulomb's law,

F = k q1 q2/ r2

Considering given figure

cos = sqrt ( 1.2)2 - ( 0.275)2 = 1.168

sin = 0.275/1.2 = 0.229

2T x cos = mg

T = mg/ 2 cos = 0.009 x 9.8/2.34 = 0.038N

Coulomb force = tension force

k q2/ r2 = T sin

9 x 109 x q2 /0.552 = 0.038 x 0.229

q= 0.54 micro C

(b)

U = m'g + T cos

V P( air) g = V P (ballon)g + 0.009g/2

V ( 1.29) g = V 0.2g + 0.0045 g

V (1.29-0.2) = 0.0045

V = 4.128 x 10-3 m3

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