Gravitational Force of Three Identical Masses Three identical very dense masses

Question

Gravitational Force of Three Identical Masses Three identical very dense masses of 3000 kg each are placed on the x-axis. One mass is at x_1 = -120 cm, one is at the origin, and one is at x_2 = 300 cm. What is the magnitude of the net gravitational force F_grav on the mass at the origin due to the other two masses? Take the gravitational constant to be G = 6.67 times 10^-14 Nm^-2/kg^2 Express your answer in newtons to three significant figures. What is the direction of the two gravitational force on the mass at the origin due to the other two masses?

Explanation / Answer

let m1 =m2 = m3 = 3000 kg

Force due to mass at x1 = -120 cm = -1.2 m

then F1 = G*m1*m2/x1^2 = (6.67*10^-11*3000^2)/(1.2^2)= 4.16*10^-4 N

similarly F2 = G*m2*m3/x2^2 = (6.67*10^-11*3000^2)/(3^2) = 0.667*10^-4 N

Fnet = F2-F1 = (0.667-4.16)*10^-4 = -3.49*10^-4

So answer for Part A is

F = 3.49*10^-4 N

Part B)

direction is along -X-axis

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