Question

Objects with masses of 140 kg and a 440 kg are separated by 0.500 m.

(a) Find the net gravitational force exerted by these objects on a 43.0-kg object placed midway between them.

Magnitude:

(b) At what position (other than infinitely remote ones) can the 43.0-kg object be placed so as to experience a net force of zero?
   m from the 440-kg mass

Answer 1

Gravitational constant = G = 6.674 x 10^-11 m³kg^-1s^-2

Mass of object 1 = M₁ = 440 kg

Mass of object 2 = M₂ = 140 kg

Mass of object 3 = M₃ = 43 kg

Distance between object 1 and object 2 = D = 0.5 m

Part A :

The 43 kg object is placed midway between object 1 and object 2.

Distance of object 1 from object 3 = d₁ = 0.25 m

Distance of object 2 from object 3 = d₂ = 0.25 m

Gravitational force of object 1 on object 3 = F₁

Gravitational force of object 2 on object 3 = F₂

Net force on object 3 = F

F = 1.377 x 10^-5 N

Part B :

The 43 kg object is placed such that it experiences zero net force.

Distance of object 1 from object 3 = d

Distance of object 2 from object 3 = D - d = 0.5 - d

Gravitational force of object 1 on object 3 = F₃

Gravitational force of object 2 on object 3 = F₄

No net force is acting on the 43 kg object.

F₃ = F₄

d = 0.319 m

The 43 kg object has to be placed 0.319m from the 440 kg object so that it experiences zero net force.