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

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SUMMARY

The discussion focuses on determining the position of a third mass (16.0 kg) along the x-axis where it experiences no net gravitational force from two other masses: M1 (43.0 kg) at the origin and M2 (11.8 kg) at x = 52.8 m. The gravitational force is calculated using Newton's law of universal gravitation, F = G(m1 * m2) / r^2, where G is the gravitational constant (6.67 x 10^-11 N(m/kg)^2). The user attempts to find the equilibrium position by calculating the forces exerted by M1 and M2 on the third mass and setting them equal to each other.

PREREQUISITES
  • Understanding of Newton's law of universal gravitation
  • Knowledge of gravitational constant (G = 6.67 x 10^-11 N(m/kg)^2)
  • Ability to solve equations involving forces and distances
  • Familiarity with basic algebra and solving for variables
NEXT STEPS
  • Calculate the gravitational force between two masses using F = G(m1 * m2) / r^2
  • Learn how to set up equations for equilibrium in gravitational systems
  • Explore the concept of gravitational fields and their effects on mass placement
  • Investigate the implications of mass distribution on gravitational forces
USEFUL FOR

Students studying physics, particularly those focusing on gravitational forces and equilibrium, as well as educators seeking to enhance their understanding of gravitational interactions in a multi-body system.

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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