Where Should the Third Mass Be Placed to Experience No Net Gravitational Force?

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To determine where a third mass (16.0 kg) experiences no net gravitational force between two other masses (43.0 kg at the origin and 11.8 kg at x = 52.8 m), the gravitational forces exerted by M1 and M2 must balance. The gravitational force formula F = G(m1 * m2) / r^2 is applied, where G is the gravitational constant. The user attempts to calculate the forces acting on the third mass and considers its position on the x-axis between 0 and 52.8 m. They seek guidance on whether their approach to solving for the position x is correct. The discussion focuses on the calculations necessary to find the equilibrium point for the third mass.
sheri1987
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Homework Statement



M1 is a spherical mass (43.0 kg) at the origin. M2 is also a spherical mass (11.8 kg) and is located on the x-axis at x = 52.8 m. At what value of x would a third mass with a 16.0 kg mass experience no net gravitational force due to M1 and M2?


Homework Equations



F= G(m1 * m2)
r^2


The Attempt at a Solution



G = 6.67*10-11, m1 = 43, m2= 11.8 and r^2 = 52.8 ...I plugged all of this into solve for F, then I think I have to use this equation again and multiply the top by a m3 and solve for x using the F I found previous...is this right, if not could you help me out? Thanks
 
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suppose m3 is located at some value x that is between 0 and 52.8m.

What is the force m1 exerts on m3? What is the force m2 exerts on m3? Take right to be positive... left to be negative.
 

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