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handin01 - Physics 212 Classical and Modern Physics Spring...

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Physics 212 Classical and Modern Physics Spring 2008 Solutions for Hand-In Set #1 Problem A3 — Attractive balloons Each balloon has three forces on it: gravity, tension, and the electric attraction. Here’s the free body dia- gram for the balloon on the left F e T mg θ x y We are trying to get an expression for q in terms of m and θ , so we’ll need to find the tension in terms of these quantities. Consider the y -component of the net force: F y = T cos θ - mg = ma y = 0 T = mg/ cos θ Now we consider the horizontal components. The mag- nitude of the electric force is F e = k | q 1 || q 2 | r 2 = kq 2 x 2 Newton’s 2nd law gives F x = F e - T sin θ = ma x = 0 Now solve for q : F e = T sin θ kq 2 x 2 = mg cos θ sin θ q 2 = x 2 mg tan θ k q = x mg tan θ k Wolfson Chapter 20-10 + + + + + + + + + + + + + + The positive charges on the balloon all mutually repel. This works against the elastic force, so it makes the bal- loon expand. If we used negative charges instead, they would still mutually repel and expand the balloon.
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