Determine the force of attraction of two contacting iron balls with a density of 8 x 10 ^ 3 and a diameter of 20 cm each.

Given:

ro = 8 * 10 ^ 3 kg / m ^ 3 – density of iron balls;

R = 20 centimeters = 0.2 meters – the radius of the iron balls;

G = 6.67 * 10 ^ -11 m ^ 3 / kg * s ^ 2 – gravitational constant.

It is required to find the force of attraction between two balls F (Newton).

Let’s find the volume of the iron ball:

V = 4 * pi * R ^ 3/3 = 4 * 3.14 * 0.2 ^ 3/3 = 0.03 m ^ 3.

Let’s find the mass of the ball:

m = V * ro = 0.03 * 8 * 10 ^ 3 = 240 kilograms.

According to the condition of the problem, the balls are in contact, that is, the distance between their centers of gravity will be equal to two radii.

Then the force of attraction between the two balls will be equal to:

F = G * m * m / (2 * R) ^ 2 = 6.67 * 10 ^ -11 * 240 * 240 / (4 * 0.2 * 0.2) =

= 384192 * 10 ^ -11 / 0.16 = 2401200 * 10 ^ -11 = 2.4 * 10 ^ -6 Newton = 2.4 μN.

Answer: the force of attraction of the balls is 2.4 μN.