Maximum Gravitational Force Between Bowling Ball and Billiard Ball
When it comes to the maximum gravitational force between a bowling ball and a billiard ball, it all boils down to their masses, radii, and the distance between their centers of gravity. Both the bowling ball (mass = 7.2 kg, radius = 0.10 m) and the billiard ball (mass = 0.35 kg, radius = 0.028 m) can be treated as uniform spheres.
Calculating the Maximum Gravitational Force
The maximum gravitational force is achieved when the centers of gravity are as close as they can be. Since the center of gravity for a sphere is at its center, the closest the centers of gravity of the two balls can be is the sum of their radii: bowling ball radius + billiard ball radius = 0.128 m.
The equation for the magnitude of gravitational force is Fgmax = G * (M * m) / rmin^2, where G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), M is the mass of the bowling ball (7.2 kg), m is the mass of the billiard ball (0.35 kg), and rmin is the minimum distance between their centers of gravity (0.128 m).
Plugging in the values:G = 6.67 x 10^-11 Nm^2/kg^2
M = 7.2 kg
m = 0.35 kg
rmin = 0.128 m
After solving the equation, the maximum gravitational force between the bowling ball and the billiard ball is calculated to be 1.026 x 10^-08 N.