Two spheres of charge q 1 and q 2 that are equal in magnitude (i.e. |q 1 | = |q

Question

Two spheres of charge q1 and q2 that are equal in magnitude (i.e. |q1| = |q2|) are attached by a spring with a constant k = 1440kg/s2 and a rest length of x0 = 83.0cm. We take negative values of ?x for compression and positive ?x values for expansion. Knowing that q1 is positive and ?x = 4.40cm, what are the values of (a) q1 and (b) q2? If we know that q1 is negative and measure ?x = -3.50cm, then what are the values of (c) q1 and (d) q2? (hint for parts (c) and (d): take the magnitude of ?x under the square root sign and look at positive or negative roots for charges)

Explanation / Answer

Your first thought is (hopefully) well wait, I'm not given their distance apart(which I'll call r)! That's crap! Usually when that happens the "missing" value in question finds its way out of the problem while doing the math, which is the advantage to working out a problem symbolically, solving it, and then plugging in numbers, then you know what you REALLY need

so Fg=G*m1*m2/r^2 and Fe=C*q1*q2/r^2

What the problem tells us is they cancel out, so Fg=Fe

G*m1*m2/r^2=C*q1*q2/r^2, and sure enough multiply both sides by r^2

G*m1*m2=C*q1*q2, and q1=q2 as told in the problem, so I'll just call it q, so G*m1*m2=C*q^2

You know G, m1 and m2(they're the same as well), and C, so just solve for q

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