Objects with masses of 130 kg and a430 kg are separated by 0.390 m. (a) Find the

Question

Objects with masses of 130 kg and a430 kg are separated by 0.390 m. (a) Find the net gravitational force exerted bythese objects on a 39.0 kg object placedmidway between them.
1 N

(b) At what position (other than infinitely remote ones) can the39.0 kg object be placed so as toexperience a net force of zero?
2 m from the 430 kgmass (a) Find the net gravitational force exerted bythese objects on a 39.0 kg object placedmidway between them.
1 N

(b) At what position (other than infinitely remote ones) can the39.0 kg object be placed so as toexperience a net force of zero?
2 m from the 430 kgmass

Explanation / Answer

masses m = 130 kg            m'= 430 kg distance of separation r = 0.390 m (a). the net gravitational force exerted by these objects on a39.0 kg object placed midway between themis                F = (GMm / x ^ 2 ) + ( GMm ' / x ^ 2 ) where x = distanc eof the mid point from one of themasses              = r / 2= 0.195 m           G =Gravitational constant = 6.67* 10 ^ -11 N m ^ 2 / kg ^ 2           M =mass kept at center = 39 kg So, F = [ GM /x^2 ] * ( m+ m' ) (b). If the force on 39 kg due to 130 kg is equal and oppositeto the force on 39 kg due to 430 kgthen net force is zero       GMm ' / y ^ 2 = GMm /(r-y) ^ 2             m ' / m = ( [ y / ( r-y)] ^ 2 plug the values weget required distance y value

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