Question

A 285-kg object and a 585-kg object are separated by 4.30 m. (a) Find the magnitude of the net gravitational force exerted by these objects on a 42.0-kg object placed midway between them.

Answer 1

The magnitude of the net gravitational force exerted by these objects on a 42.0-kg object is 1.818 x 10⁻⁷ N

Step-by-step explanation:

Given;

first object with mass, m₁ = 285 kg

second object with mass, m₂ = 585 kg

distance between the two objects, r = 4.3 m

The midpoint between the two objects = r/₂ = 4.3 /2 = 2.15 m

Gravitational force between the first object and the 42 kg object;

`F = (GMm)/(r^2)`

where;

G = 6.67 x 10⁻¹¹ Nm²kg⁻²

`F = (6.67*10^(-11) *285*42)/(2.15^2) \\\\F = 1.727*10^(-7) \ N`

Gravitational force between the second object and the 42 kg object

`F = (6.67*10^(-11) *585*42)/(2.15^2) \\\\F = 3.545*10^(-7) \ N`

Magnitude of net gravitational force exerted on 42kg object;

F = 3.545x 10⁻⁷ N - 1.727 x 10⁻⁷ N

F = 1.818 x 10⁻⁷ N

Therefore, the magnitude of the net gravitational force exerted by these objects on a 42.0-kg object is 1.818 x 10⁻⁷ N