Static Electricity Legacy Problem #8 Guided Solution

An effective problem solver has a sequence of steps that they typically progress through in the solution to a problem. The beginning steps always involve the careful reading of the problem, the picturing of what's going on, as well as the extraction of numerical information from the problem statement. The effective problem solver then identifies the unknown quantity and begins to plot out a strategy by which to take the known information and physics knowledge in order to solve for the unknown quantity. Applied to this problem, what we have are two objects with some sort of charge. The amount of charge is identical. That means the quantity of charge on one of the objects, q1, is equal to the quantity of charge on the other object, q2. What we know is that q1 equals q2. We also know the separation distance between the objects. That's a d of 52 centimeters, a unit which I'm not particularly fond of, so I'm going to convert that to meters, such that d equals 52 centimeters, or 0.52 meters. I know the force of repulsion between these like-charged objects. It's 2.74 e to the negative 3 newtons. What I'm asked to calculate is the quantity of charge on each of the balloons. I wish to find q1 and q2, which will be equal amounts of charge. Now I need to think of a strategy. The strategy is obviously going to include the use of the Coulomb's Law equation, f equal k times q1 times q2 divided by d squared. What I wish to solve for is the q's. So I would rearrange my equation to take this form, q1 times q2 equal f times d squared divided by k. Now I wish to solve for either one of the q's. The fact that q1 is equal to q2 means that q1 times q2 is equal to q squared. So my equation now becomes q squared equal f times d squared divided by k. My value of d needs to be used in units of meters because my value of k is a constant value of 8.99 times 10 to the 9th newtons times meters squared per Coulomb squared. Now I can take my known quantities and substitute them into my equation and solve for q squared. And when I do that I get 8.2413 times 10 to the negative 14th. That's the value for q squared and what I want to know is the value of q. Take the square root of each side and I'll get the value of q. It comes out to be about 2.8708 times 10 to the negative 7th units of Coulombs and I can round that to two significant digits.