A bowling ball (mass = 7.2 kg, radius = 0.14 m) and a billiard ball (mass = 0.40 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?
since the minimum distance between their centers of mass is .14m + .028m = .168m,
plug that into the usual formula.
BTW, who ever heard of a 2.8cm, 400g billiard ball? The standard size and weight are around 5.7cm and 160g.
Maybe a golf ball is 2.8cm. Dunno.
To calculate the magnitude of the maximum gravitational force between the bowling ball and the billiard ball, you can use the equation for gravitational force between two objects:
F = (G * m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2), m1 and m2 are the masses of the two objects, and r is the distance between their centers.
In this case, the distance between the centers of the two balls is the sum of their radii:
r = radius1 + radius2
First, let's calculate the distance:
r = 0.14 m + 0.028 m
r = 0.168 m
Now we can calculate the gravitational force between the two balls:
F = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (7.2 kg) * (0.40 kg) / (0.168 m)^2
Calculating this equation gives us:
F = 1.407 × 10^-6 N
Therefore, the magnitude of the maximum gravitational force that the bowling ball and the billiard ball can exert on each other is approximately 1.407 × 10^-6 Newtons.