Two particles have a mass of 8 kg and 12 kg, respectfully. if they are 800mm apart, determine the force of gravity acting between them. compare this result with the weight of each particle.

Answer 1

All particles with mass exert a gravitational force on all other particles, but it is usually so small that we consider it negligible. Despite these forces being so small and imperceptible, we calculate them using the same formula that we use when determining the gravitational forces between planets and solar systems.

Newton's Law of Gravitation is given as:

F1 = F2 = G x (m1 x m2)/r^2

Where:

F is the force of gravity

G is the gravitational constant (6.67x10^-11 N*m^2/kg^2)

m1 and m2 are the masses of body or particle 1 and 2 respectively

r is the distance separating the two bodies/particles (think radius)

All forces have an equal and opposite reaction force which is why F1 = F2. The force on the moon by the earth is the same as the force on the earth by the moon and that applies for every gravitational interaction.

If we plug the given values from the problem into our equation we get:

F = 6.67x10^-11 x (8kg x 12kg)/0.8m^2

Make sure to convert distance r from mm to m so our units cancel and our answer is left in N.

We solve it through and find that F = 1.0005x10^-8 N

This is an incredibly small force compared to the weight of each particle which is the force of gravity between the particle and the earth.

We convert mass in kg to weight in N on earth by multiplying by the acceleration of gravity 9.81 m/s^2

Weight of particle 1 = 8kg x 9.81m/s^2 = 78.48N

Weight of particle 2 = 12kg x 9.81 m/s^2 = 117.72N

That is a difference of 9 and 10 orders of magnitude respectively between the force of gravity the two particles exert on each other and the force of gravity exerted by the earth, demonstrating why we typically consider these forces negligible on this scale.