Question

How far from a very small 160 kg ball would a particle have to be placed so that the ball pulled on the particle just as hard as the earth does? Is it reasonable that you could actually set up this as an experiment? Why? I arrived at the correct answer of 3.30 * 10^-5 but is it reasonable to set up this as an experiment? For full credit and thumbs up, please fully explain your answer..

Answer 1

Mass of the ball, M = 160 kg

Mass of earth, Me = 6 x 10²⁴ kg

Radius of earth, R = 6400 km

Mass of the particle = m

Let x be the distance between the ball and particle such that the force between ball and particle is same as the force between the particle and earth.

Using Newton’s law of gravitation,

GMe m/R² = GMm/x²

Me/R² = M/x²

X² = M R²/Me = 160 x 6400 x 6400/(6 x 10²⁴ )= 10.92 x 10^-16

X = 3.30 x 10^-8 km = 3.3 x 10^-5 m

Distance of the particle from the ball, x = 3.3 x 10^-5 m

This is not reasonable to set up as an experiment.

The separation x = 33 micrometre is extremely small and much less than the diameter of a ball of mass 160 kg.

Suppose the ball is made of steel which has a density nearly 8000 kg/m³. The radius of such a steel ball of mass 160 kg is few centimetres while the separation   is few micrometre thus, the distance 3.3 x 10^-5 m can not be realised in practice.