Objects with masses of 175 kg and a475 kg are separated by 0.390 m. (a) Find the

Question

Objects with masses of 175 kg and a475 kg are separated by 0.390 m. (a) Find the net gravitational force exerted by these objectson a 44.0 kg object placed midway betweenthem. This equals 2.315 x 10^-5. I know this is correct. Here is where i get stuck. (b) At what position (other than infinitely remote ones)can the 44.0 kg object be placed so as toexperience a net force of zero? (m from the 475 kg mass)
Objects with masses of 175 kg and a475 kg are separated by 0.390 m. (a) Find the net gravitational force exerted by these objectson a 44.0 kg object placed midway betweenthem. This equals 2.315 x 10^-5. I know this is correct. Here is where i get stuck. (b) At what position (other than infinitely remote ones)can the 44.0 kg object be placed so as toexperience a net force of zero? (m from the 475 kg mass)

Explanation / Answer

Given m = 175 kg          m ' = 475kg distance r= 0.39 m Let at a distance x from the mass m ' the net force F =0 then the distance of the point from mass m is r -x If the gravitational force on point due to mass m isequal and opposite to the force on point due to mass m ' i.e., GMm / ( r-x)^2 = GMm ' / x ^ 2           [x/(r-x)]^2 = m ' / m            x/( 0.39-x) = [ m ' / m ]                             = 1.6475                           x = 0.6425 - 1.6475 x               2.6475x = 0.6425                          x = 0.243 m

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