Answer to Question #300090 in Classical Mechanics for Black

Question

Objects with masses of 200kg and 500kg are separated by 0.4m

Find

a)the net gravitational force exerted by these objects on a 50kg object placed midway between them

b) at what position can the 50kg object be placed so as to experience a net force of zero

Answer 1

a)

$F=\frac{4Gm(m_2-m_1)}{d^2}=25~\mu N,$

b)

$\frac{Gmm_1}{x^2}=\frac{Gmm_2}{(d-x)^2},$

$x=\frac d{\sqrt{\frac{m_2}{m_1}}+1}=0.15~m.$