The gravitational force between two spheres 5 meters apart from each other is 48 Newtons. How many Newtons of force will result when the distance between the two spheres changed from its original distance of 5 meters apart to 25 meters apart?

Question

whpalmer4 · Answer

This can be done a bit more simply by realizing from the equation given that the force varies inversely with the square of the distance between them, so $$F = \frac{k}{r^2}$$We know that when $r = 5$, $F = 48$, so $$48 = \frac{k}{(5)^2}$$or$$k = 48*25$$Now we want $F$ when $r = 25$, so
$$F = \frac{48*25}{(25)^2} = \frac{48}{25} = 1.92$$

Or another route, $$F = \frac{k}{r^2}$$We are increasing $r$ by a factor of $5$, so replace $r$ by $5r$:
$$F_{new} = \frac{k}{(5r)^2} = \frac{k}{25r^2}$$and it should be evident upon comparison that that is $1/25$ of the original force, or $0.04 * 48 \text{ N} = 1.92 \text{ N}$