Question

A bowling ball (mass = 7.2 kg, radius = 0.15 m) and a billiard ball (mass = 0.31 kg, radius = 0.028 m) may each be treated as uniform spheres. what is the magnitude of the maximum gravitational force that each can exert on the other?

Answer 1

4.7x10^-9 newtons Since both the billiard ball and the bowling ball are uniform spheres, you can simplify the math by assuming that both are gravitational point sources centered within each sphere. And since the gravitational attraction increases as the bodies move closer together, you want to place them as close as possible to each other which would be touching. So when touching, the distance between the two point sources of gravity would be the sum of their radiuses. 0.15m + 0.028m = 0.178m The formula for gravitational attraction is F = G(m1m2)/(r^2) G = 6.67x10^-11 m^3/(s^2 kg) m1, m2 = masses r = radius. So substituting the known values gives F = 6.67x10^-11 m^3/(s^2 kg) (7.2 kg * 0.31 kg) / (0.178 m^2) F = 6.67x10^-11 m^3/(s^2 kg) (2.232 kg^2) / (0.031684 m^2) F = 6.67x10^-11 m/(s^2) (2.232 kg) / (0.031684) F = 6.67x10^-11 m/(s^2) 70.44565 kg F = 4.69872x10^-9 kg m/s^2 F = 4.69872x10^-9 newtons Since the number of significant figures provided is only 2, the result should be rounded to 2 significant digits giving a result of 4.7x10^-9 newtons