Direct and inverse proportions

Question

The force of attraction between two magnets is inversely proportional to the square of the distance between them. When the magnets are rcm apart, the force of attraction between them is F newtons (N). If the distance between the magnets is increased by 400%, the force of attraction between them becomes cF N. Find the value of c.

Answer 1

Hi Jerry, I can take a stab at this one.

We can express the force between two magnets as: F = k/r^2, where r is the distance between both magnets.

So if the distance between the magnets is increased by 400%, the new distance would become 5*r, since 100% + 400% = 500%.

Our equation for the new force of attraction is c*F = k/(5r)^2, or c*F = k/25*r^2

Now compare this two our generalized equation for the force between two magnets: F = k/r^2.

To find c, notice that our equation for the force between both magnets gets multiplied by 1/25 when we increase the distance between magnets by 400%. Hence, our c is 1/25, or approximately 0.04.