SOLUTION: The force of attraction, F of a body varies directly as its mass m and inversely as the square of the distance d from the body. When m = 8 kilograms and d = 5 meters, F = 100 Newto

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Question 1189966: The force of attraction, F of a body varies directly as its mass m and inversely as the square of the distance d from the body. When m = 8 kilograms and d = 5 meters, F = 100 Newtons. Find F when = 2 kilograms and d = 15 meters
please show your solution.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The mass is 1/4 as much; since the force of attraction varies directly as the mass, it goes down by a factor of 1/4.

The distance is 3 times as great; since the force varies inversely as the square of the distance, it goes down by a factor of 1/3^2 = 1/9.

ANSWER: (100)(1/4)(1/9) = 100/36 = 25/9 Newtons

Formally....

(1) Find the constant of variation using the known data

F=k%28m%2Fd%5E2%29
100=k%288%2F25%29
k=100%2825%2F8%29=2500%2F8=625%2F2

(2) Use the constant with the new data

F=%28625%2F2%29%282%2F%2815%5E2%29%29+=+%28625%2F2%29%282%2F225%29=625%2F225=25%2F9

ANSWER (the same, of course): 25/9 Newtons