the problem already shown doesn\'t help much Objects with masses of 135 kg anda

Question

the problem already shown doesn't help much Objects with masses of 135 kg anda 435 kg are separated by 0.430 m. (a) Find the net gravitational force exerted bythese objects on a 51.0 kg objectplaced midway between them. (b) At what position (other than infinitely remote ones) canthe 51.0 kg object be placed so as toexperience a net force of zero?
the problem already shown doesn't help much Objects with masses of 135 kg anda 435 kg are separated by 0.430 m. (a) Find the net gravitational force exerted bythese objects on a 51.0 kg objectplaced midway between them. (a) Find the net gravitational force exerted bythese objects on a 51.0 kg objectplaced midway between them. (b) At what position (other than infinitely remote ones) canthe 51.0 kg object be placed so as toexperience a net force of zero?

Explanation / Answer

Given masses m = 135 kg                     m ' = 435 kg                    m " = 51 kg distance of the separation r = 0.43 m (a). distance of the mid point from one of the mass x =r / 2 = 0.225 m the net gravitational force exerted by these objects on a51.0 kg object placed midway betweenthem     F = [ Gm m " / x ^ 2 ] - [ Gm' m " / x^ 2 ]       = Gm" / x ^ 2 * ( m - m ')      = ( 6.67 * 10 ^ -11 ) (51 ) (435-135) / 0.225 ^ 2      = 2.015 * 10 ^ -5 N (b). Let the required distance is at a distance X from the mass m then net gravitational force F ' = Gm m " / X ^ 2+ Gm' m " / ( r-X ) ^ 2 given F ' = 0 Gmm" / X ^ 2 = Gm'm " / ( r -X ) ^ 2     m / X ^ 2 = m ' / ( r-X)^2 ( r-X) / X = [m ' / m ]                  = 1.795            r-X = 1.795 X              X = r / 2.795                  = 0.1538 m

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