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Sample solution

Giancoli 7th Edition, Chapter 4, Problem 62


Recent questions and answers

Oh, and the absolute value of a number is it's positive value. What you said about taking the square root of the number squared is not technically correct, but in a practical sense it's good enough I suppose. The square root of a number technically has two answers: the positive and the negative, since squaring either gives the "radicand".

Hi Jamall, the subject you're going to want to refresh on is "factoring". A quick Google found and it seemed OK. I'll try to explain what happened in the video, putting important vocabulary words in bold, and this might make more sense after you review the basics of factoring. There are two terms here: $\dfrac{\sqrt{2}kQQ}{r_{12}^2} + \dfrac{kQQ}{2r_{12}^2}$. Terms are always separated by plus or minus signs. Each term consist of several factors. Factors are the parts within a term that multiply together, and I think it's nice to look at "multiply" in a more generic sense that includes dividing. By that I mean that dividing by "2", as in the second term in this question, is the same as multiplying by $\dfrac{1}{2}$. You can always think of dividing by a number as multiplying by it's reciprocal... The process of "factoring" is to search for all factors that are the same among all the terms. The common ones gets put outside of some brackets, and the leftovers that are not common among the terms end up within the bracket. $\sqrt{2}$ and $\dfrac{1}{2}$ are factors that are unique to the terms in which they appear, and so they are the leftovers that end up within a bracket.

All the best,
Mr. Dychko

Hi swedesanddanes, the answer to your question is in the word magnitude. That word means size. It means ignore direction, and so ignore the negative sign. magnitudes are always positive.

All the best,
Mr. Dychko

Mr. Dychko,

I think I see. So am I correct in stating that the square root of a number squared is equal to the absolute value of that number? Also, at 6:11 you begin factoring "out the common stuff, which is almost everything, which for the most part I understand. However, my problem seems to involve what is supposed to go where. By that I mean why does root 2 end up in parentheses with 1/2? And is one half just the simplification of kqq/2r?

Never mind, I took a second look at it and everything came together :)