SOLUTION: The force F with which a magnet attracts a steel ball is inversely proportional to the square of the distance d of the ball from the magnet. If the steel ball is now 8 cm from the

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Question 644068: The force F with which a magnet attracts a steel ball is inversely proportional to the square of the distance d of the ball from the magnet. If the steel ball is now 8 cm from the magnet, how far from the magnet should it be placed to attain an attracting force 4 times as great as its present attracting force?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The force F with which a magnet attracts a steel ball is inversely proportional to the square of the distance d of the ball from the magnet.
That means we can write F as a function of d as
F%28d%29=K%2Fd%5E2 , with K being some constant.
If the steel ball is now 8 cm from the magnet, d=8, and the force would be
F%288%29=K%2F8%5E2=K%2F64
We want to attain an attracting force 4 times as great as its present attracting force, meaning a force of 4%2A%28k%2F64%29=K%2F16 , so we need to find d so that
F%28d%29=K%2Fd%5E2=K%2F16 <--> d%5E2=16 <--> highlight%28d=4%29