Masses in a Triangle - Gravitational Force

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Homework Help Overview

The problem involves three uniform spheres positioned at the corners of an equilateral triangle, with two spheres having known masses and the third sphere's mass being unknown. The objective is to determine the initial acceleration of the third sphere due to gravitational forces exerted by the other two spheres.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the application of the superposition principle for gravitational forces and question the assumptions regarding the mass of the third sphere. There are attempts to calculate the gravitational force between the spheres and explore the relationship between force, mass, and acceleration.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations of the problem. Some guidance has been offered regarding the calculation of forces and the relationship between force and mass, but there is no explicit consensus on how to proceed with finding the mass of the third sphere or its initial acceleration.

Contextual Notes

There is a lack of information regarding the mass of the third sphere, which is central to solving the problem. Participants are navigating the implications of this missing information while discussing gravitational interactions.

Student3.41
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Homework Statement



Three uniform spheres are located at the corners of an equilateral triangle. Each side of the triangle has a length of 1.23 m. Two of the spheres have a mass of 2.84 kg each. The third sphere (mass unknown) is released from rest. Considering only the gravitational forces that the spheres exert on each other, what is the magnitude of the initial acceleration of the third sphere

Homework Equations



F=Gm1m2/f^2


The Attempt at a Solution



Not sure what to do here.
 
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Try out superposition.
 
Student3.41 said:
Bump

erm :redface: … we're waiting for you to start :frown:
 
Ok well, mass 1 is on the top corner, mass 2 and 3 are on the bottom corners of the triangle.

F_12 = (6.67x10^-11)(2.84)(2.84)/(1.23)^2 = 3.56x10^-11N

I assumed the acceleration is going to be the same for each mass.

a = 3.56x10^-11/2.84 = 1.25x10^-11
 
(try using the X2 icon just above the Reply box :smile:)

But the question is asking for the (initial) acceleration of the third sphere. :redface:

(and btw, what was the point of multiplying by 2.84 and then dividing by it again? :wink:)
 
I have no idea.

There is no information given for [m][3], I am assuming I would have to find the mass of sphere 3 to the inital acceleration. I know F=ma so, m=F/a I am not sure if I would let x = [m][3] and solve for x, then once I have the mass I can easily get acceleration? or am I completely off
 
Student3.41 said:
There is no information given for [m][3], I am assuming I would have to find the mass of sphere 3 to the inital acceleration. I know F=ma so, m=F/a I am not sure if I would let x = [m][3] and solve for x, then once I have the mass I can easily get acceleration? or am I completely off

Call the mass m, find the force, then divide by m …

what do you get? :smile:
 
tiny-tim said:
Call the mass m, find the force, then divide by m …

what do you get? :smile:

You will get the inital acceleration of the mass, but I am unsure how to get the mass and the Force on M3
 
Student3.41 said:
You will get the inital acceleration of the mass, but I am unsure how to get the mass and the Force on M3

Call the mass m, and find the force.
 

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