Question

A 165-kg object and a 465-kg object are separated by 4.30 m.

(a) Find the magnitude of the net gravitational force exerted by these objects on a 41.0-kg object placed midway between them.

Answer: 1.77*10^-7, Got this , Can't find B

(b)At what position (other than an infinitely remote one) can the 41.0-kg object be placed so as to experience a net force of zero from the other two objects?

Answer? ______

Answer 1

Part (b)

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

Mass of object 1 = m₁ = 165 kg

Mass of object 2 = m₂ = 465 kg

Mass of object 3 = m₃ = 41 kg

Distance between object 1 and object 2 = D = 4.3m

Let the object 3 be at a distance 'd' from object 2 such that it experiences zero net force.

Distance of object 3 from object 1 = D-d

Distance of object 3 from object 2 = d

Gravitational force on object 3 due to object 1 = F₁

Gravitational force on object 3 due to object 2 = F₂

The net force on object 3 is zero.

F₁ = F₂

d = 7.215 - 1.678d

2.678d = 7.215

d = 2.694 m

The 41 kg object needs to placed at a distance of 2.694m from the 465 kg object so that the 41 kg object will experience a zero net force due to the other two objects.