A 0.00260-kilogram air inflated balloon is given an excess negative charge, p_1
ID: 1435684 • Letter: A
Question
A 0.00260-kilogram air inflated balloon is given an excess negative charge, p_1 = -4.00 times 10^-6 C, by rubbing it with a blanket. It is found that a charged rod can be held above the balloon at a distance of d = 0.0520 m to make the balloon float. In order for this to occur, what polarity of charge must the rod possess? How much charge, q_2, does the rod have? Assume the balloon and rod to be point charges. The Coulomb force constant is 1/(4piepsilono) = 8.99 times 10^9 N- m^2/C^2 and the acceleration due to gravity g = 9.81 m/s^2.Explanation / Answer
It has to be an attractive force, which means opposite charges, so the rod has to have a + charge.
Coulomb's law, force of attraction/repulsion = F = kQQ/r²
Q and Q are the charges in coulombs
F is force in newtons
r is separation in meters
k = 8.99e9 Nm²/C²
The electrostatic force must equal the force of gravity, which is w = mg = 0.00260 x 9.81 = 0.0255 N
0.0255 = (8.99e9)(4.0e-8)(q) / (0.052)²
q = (0.052)²(0.255) / (8.99e9)(4.0e-8)
q = 1.92e-6 C = 41.92 µC
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