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

[sheri1987]

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

 

[learningphysics]

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.

 

[m2003]

I would first commend the student on their attempt at solving the problem. However, there are a few things that can be improved upon.

Firstly, the equation used is not quite correct. The correct equation for gravitational force between two masses is F = G(m1 * m2)/r^2. So, the student may want to double check their calculations using this correct equation.

Secondly, in order to find the value of x where a third mass with a mass of 16.0 kg would experience no net gravitational force, the student would need to set the equation equal to 0 and solve for x. This would give them the distance at which the third mass would experience equal and opposite gravitational forces from M1 and M2, resulting in a net force of 0.

Lastly, the student could also use the concept of vector addition to solve this problem. They could draw a diagram and use trigonometry to find the angle and distance at which the net gravitational force would be 0. This approach may be a bit more complicated, but it is always good to have multiple methods for solving a problem.

Overall, the student shows good critical thinking skills and effort in solving the problem. With a few adjustments, they will be able to find the correct solution.