Gravitational Force: between 3 objects ?

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To calculate the gravitational force on a 5kg object placed between two 75kg masses, the forces from each mass must be determined separately using the formula F=G(m1)(m2)/r^2. The calculated gravitational force from the closer mass (0.25m away) is approximately 4.00356e-7 N, while the force from the farther mass (0.75m away) is about 4.4484e-8 N. Since the forces act in opposite directions, the net gravitational force on the 5kg object is found by subtracting the smaller force from the larger one, resulting in approximately 3.5587e-7 N. Understanding the inverse relationship of gravitational force with distance is crucial for these calculations. This approach effectively resolves the problem.
littlejim
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Homework Statement


Two 75kg masses are separated by a distance of 1 meter. a 5kg object is placed .25 meters from one of the masses, .75 meters from the other along the line joining the masses. What is the gravitational force on the object?


Homework Equations



F=G(m1)(m2)/r^2

The Attempt at a Solution


So for this I have started by calculating the force between each 75kg mass and the 5kg mass separately. I get 4.00356e-7 for the .25m distance, and 4.4484e-8 for the .75m distance.

Im not quite sure where to go from here to answer the question; i remember that as distance increases between two objects, the force of gravity between them is an inverse relationship. So I think that means here that the force with the .75m distance is like 1/9 of the other...or something like that. I have confused myself at this point. I just don't know how to proceed with this. :/
 
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Hi littlejim, welcome to PF.
Forces due to two masses on the object are in the opposite direction. So, to find the net force, find the difference between them.
 
So just
(4.00356e^-7)-(4.4484e^-8)= 3.5587e^-7

Well that explains it. Thanks
 

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