Three identical very dense masses of 6800 kg each are placed on the x axis. One

Question

Three identical very dense masses of 6800 kg each are placed on the x axis. One mass is at x1 = -150 cm , one is at the origin, and one is at x2 = 400 cm.

What is the magnitude of the net gravitational force Fgrav on the mass at the origin due to the other two masses?

Take the gravitational constant to be G = 6.67×1011 Nm2/kg2 .

I'm stuck on this one, I believe the net grav force G_net would be: G_1 + G_2 where G can be found with: G*M*m/r^2

The M,m = 6800kg, r = -1.5m, 4m.   But when I solve, the answer is coming back as wrong. Any help appreciated!

Explanation / Answer

G = 6.67×1011 Nm2/kg2

m1=m2=m3 =6800 kg

x1=-150 cm , x2 = 400 cm

F21 = - Gm1m2/x1^2 = -(6.67x10-11x6800x6800)/(1.5x1.5)

F21 = - 1.371x10-3 N along negative x-direction

F23 = Gm3m2/x2^2 = (6.67x10-11x6800x6800)/(4x4)

F23 = 0.1928x10-3 N along positive x-direction

F2 =F21 +F23 = - 1.371x10-3 + 0.1928x10-3 N

F2 = 1.1782x10-3 N

Magnitude of the net gravitational force Fgrav on the mass at the origin due to the other two masses is

1.1782x10-3 N

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