Gravitational Force of Three Identical Masses Problem

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SUMMARY

The problem involves calculating the net gravitational force on a mass located at the origin due to two other identical masses of 8000 kg positioned at x1 = -140 cm and x2 = 440 cm. The gravitational constant used is G = 6.67×10-11 N⋅m2/kg2. The gravitational force formula F = G(m1m2/r2) is applied, taking into account that the distances from the origin to the two masses differ, resulting in a nonzero net force. Proper vector addition is crucial for accurate calculations.

PREREQUISITES
  • Understanding of gravitational force calculations using Newton's law of gravitation.
  • Familiarity with vector addition and its application in physics.
  • Knowledge of the gravitational constant and its significance in force calculations.
  • Ability to perform dimensional analysis to ensure results are in the correct units.
NEXT STEPS
  • Review the principles of Newton's law of gravitation and its applications.
  • Learn about vector addition techniques in physics, particularly in gravitational contexts.
  • Study dimensional analysis to verify the correctness of physical equations.
  • Explore examples of gravitational force problems involving multiple masses and their configurations.
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Students studying physics, particularly those focusing on gravitational forces, as well as educators looking for examples of gravitational force calculations involving multiple masses.

KWalker015
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Homework Statement


Three identical very dense masses of 8000kg each are placed on the x axis. One mass is at x1 = -140cm , one is at the origin, and one is at x2 = 440cm . 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 = 6.67×10−11N⋅m2/kg2 .



Homework Equations


F=G(m1m2/r^2)


The Attempt at a Solution


I have tried everything, but Mastering Physics still gives me this message: Although the two masses not at the origin are identical, they are not the same distance from the origin, so there will be a nonzero net force on the mass at the origin. Am I adding the vectors wrong? I got 2.1*10^-3
 
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i think it would be better if you show how you get this number. But I think you are on the right direction when you mention vector addition and the right formula you refer to.
 
Force has dimension. As long as your answer is dimensionless it is going to be wrong.

Assuming the intended unit is Newton, it seems to be in the right ballpark. Did you round your results during computation? It would be much easier to judge if you had posted your work.
 

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