Gravitational force among 4 spheres

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Homework Help Overview

The problem involves calculating the gravitational force exerted on one of four spheres, each with a mass of 7.5 kg, positioned at the corners of a square with a side length of 0.70 m. The original poster attempts to derive the total gravitational force acting on a specific sphere due to the other three spheres.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the equation proposed by the original poster and question its correctness. There is an exploration of the forces involved, particularly the distinction between the forces acting at different angles. Some participants seek clarification on the definitions of the forces used in the equation.

Discussion Status

The discussion is ongoing, with participants providing feedback on the original poster's approach and encouraging further elaboration on the calculations. There is an indication that some participants are attempting to guide the original poster toward a clearer understanding of the problem without reaching a consensus on the solution.

Contextual Notes

Participants note the need for specific values in the calculations and express uncertainty about the original poster's substitutions and the final answer. There is a suggestion that the original poster may have made errors in their calculations.

gillyr2
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Homework Statement


Four 7.5kg spheres are located at the corners of a square of side 0.70 m.
Calculate the magnitude of the gravitational force exerted on one sphere which is in left and down corner of the square by the other three.


Homework Equations



F_tot = F_2 + sqrt(2) * F1

The Attempt at a Solution



came up with that equation, but it says i am wrong.
can anyone help/
 
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It'll be better if you explain your equation (or your solution).
 
well since they are in a square and have equal masses F_1 = F_3 in magnitude. and for our triangle we have 1/sqrt2 are the sides and 1 is the hypotenuse. i got that. but i don't think its right
 
am i way offf? can anybody help
 
gillyr2 said:

Homework Equations



F_tot = F_2 + sqrt(2) * F1
If I understand what you're saying here, this is correct. But it's not the final answer.

What are F_2 and F_1?
 
F1 and F3 are the 90 degree forces and F2 is the 45 degree force. what do i still need to do?
 
Still your solution solution looks bit wrong. Show the substitution process (the values for F1 ..) and and calculation, so that I can help you better.
 
gillyr2 said:
F1 and F3 are the 90 degree forces and F2 is the 45 degree force. what do i still need to do?
That's just the schematic of the answer. Now you have to figure out F1 & F2 and plug in the numbers. I assume they want an actual answer for the force in Newtons.
 
F1 = ((6.67 * 10 ^-11)* 7.5 *7.5 )/ .70^2 = 7.66 * 10^-9

length of hypotnuse
sqrt(.70^2 +.70^2); = .99

F2 = ((6.67 * 10 ^-11)* 7.5 *7.5 )/ .99^2 = 3.83*10^-9

F_tot = 3.83*10^-9 + sqrt(2) * 7.66*10^-9 =

1.46 * 10^-8

PROBLEM SOLVED. I MUST HAVE JUST PLUGGED IN SOME WRONG NUMBERS. THANKS ANYWAY
 

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