Question

Two 10 kg spheres are placed 500mm apart. Express the gravitational attraction acting on one of the spheres as a percentage to its weight on earth.

Answer 1

To calculate the gravitational attraction between the two spheres, we can use the formula:

F = (G * m1 * m2) / r^2

where F is the force of attraction, G is the gravitational constant (6.67430 * 10^-11 N m²/kg²), m1 and m2 are the masses of the spheres (10 kg each), and r is the distance between their centers (500 mm or 0.5 m).

F = (6.67430 * 10^-11 * 10 * 10) / (0.5)^2
F ≈ 2.66972 * 10^-8 N

To calculate the weight of one sphere on Earth, we use the formula:

W = m * g

where W is the weight, m is the mass of the sphere (10 kg), and g is the acceleration due to gravity on Earth (9.81 m/s²).

W = 10 kg * 9.81 m/s²
W ≈ 98.1 N

Now, we can express the gravitational attraction as a percentage of the weight:

Percentage = (F / W) * 100
Percentage = (2.66972 * 10^-8 N / 98.1 N) * 100
Percentage ≈ 2.72087 * 10^-7 %

Therefore, the gravitational attraction acting on one of the spheres is approximately 2.72087 * 10^-7 % of its weight on Earth.