Objects with masses of 235 kg and a 535 kg are separated by 0.500 m. (a) Find th

Question

Objects with masses of 235 kg and a 535 kg are separated by 0.500 m.

(a) Find the net gravitational force exerted by these objects on a 65.0-kg object placed midway between them.

magnitude

b) At what position (other than infinitely remote ones) can the 65.0-kg object be placed so as to experience a net force of zero?
m from the 535-kg mass

magnitude

b) At what position (other than infinitely remote ones) can the 65.0-kg object be placed so as to experience a net force of zero?
m from the 535-kg mass

Explanation / Answer

Given that :

mass of the first objet, m1 = 535 kg

mass of the second object, m2 = 235 kg

separation distance between two object, r = 0.5 m

(a) The net gravitational force exerted by these objects on a 65 kg object placed midway between them which is given as :

using an equation,    Fnet = F1 - F2

Fnet = G m1 m / r2 - G m2 m / r2

Fnet = G m / r2 (m1 - m2)                                                                           { eq.1 }

where, r = distance midway between them = 0.25 m

G = gravitaional constant = 6.67 x 10-11 Nm2/kg2

m = mass of the other second = 65 kg

inserting the values in eq.1,

Fnet = (6.67 x 10-11 Nm2/kg2) (65 kg) / (0.25 m)2 [(535 kg) - (235 kg)]

Fnet = (433.5 x 10-11 Nm2/kg) / (0.0625 m2) [300 kg]

Fnet = (6936 x 10-11 N/kg) (300 kg)

Fnet = 2080800 x 10-11 N

Fnet = 2.08 x 10-5 N

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