Question 951584: The repulsive force f between the north poles of two magnets is inversely proportional to the square of the distance d between them. If the repulsive force is 29 lb when the distance is 25 in., find the repulsive force when the distance is 5 in.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula for inverse variation between force and distance is:
f = k / d^2
when f = 29 and d = 25, the formula becomes:
29 = k / 25^2
solve for k to get k = 29 * 25^2 = 18125.
k always stays the same which is why it's called the constant of variation.
when d = 5, the formula of y = k / d^2 becomes y = 18125 / 5^2.
solve for y to get y = 725.
when the distance between the objects is 5, the repulsive force is equal to 725 pounds.
when the distance became 1/5 as much, the repulsive force became 25 times as high.
29 = 18125 / 25^2
725 = 18125 / 5^2
when you solve for k in the formula of f = k / d^2, you get k = f*d^2.
f * d^2 will always be equal to k which will always be equal to 18125, based on the fact that, when f = 29, d was equal to 25.
29 * 25^2 = 29 * 625 = 18125.
725 * 5^2 = 725 * 25 = 18125.
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