SOLUTION: The force of attraction (F) between two opposite electric charges varies inversely as the square of the distance (d) between them. If F = 30 newtons when d = 5 meters, find F when
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Question 1172668: The force of attraction (F) between two opposite electric charges varies inversely as the square of the distance (d) between them. If F = 30 newtons when d = 5 meters, find F when d = 12 meters.
You can put this solution on YOUR website! The force of attraction (F) between two opposite electric charges varies inversely as the square of the distance (d) between them.
Let's pause here.
For all proportion problems, start with this:
Varying "directly" or product of "jointlys" or 1 if none
quantity = k ∙ ----------------------------------------------------------
inversely variable or product of "inverselys" or 1 if none
In this problem the varying quantity is F. There are no "directly" or "jointly"
variable. So the numerator is the number 1. We have one inversely, d2. So we
have F on the left, 1 on the top of the fraction and d2 on the bottom:
-----------------------
If F = 30 newtons when d = 5 meters,
Let's pause again here.
Let's substitute 30 for F in , and 5 for d2>/sub>, and solve for k:
Put 1 under 30 and write 52 as 25:
Cross-multiply:
Now we substitute 750 for k in
find F when d = 12 meters.
newtons.
Edwin
Be wary of any advice that says "for all problems like this, THE way to start is ...."
A very formal solution like the one provided by the other tutor is fine, if a very formal solution is required.
If not, the problem can be solved far more quickly using a basic understanding of variation and some simple arithmetic.
The force varies inversely as the square of the distances; so when the distance changes from 5m to 12m, the force gets multiplied by (5/12)^2 = 25/144.
