Calculate Magnitude of Gravitational Force on One Sphere

[sugarntwiligh]

Homework Statement

Four 9.5 kg spheres are located at the corners of a square of side 0.60 m. Calculate the magnitude of the total gravitational force exerted on one sphere by the other three.

Homework Equations

F=G(mass of #1)(mass of #2)/r^2
F=G(mass of #1)(mass of #3)/r^2
F=G(mass of #1)(mass of #2)/r^2
For #3 take Fsin(45)=x value
For #3 x value=y value

x and y components added
F=squareroot(x^2+y^2)

The Attempt at a Solution

r=0.6m
m=9.5kg
F#2x=1.625e-8
F#2y=0
F#3x=0
F#3y=-1.672e-8
F#4x=1.182e-8
F#4y=-1.182e-8
FTotal= 4.037e-8

Correct answer in book for FTotal: 3.2e-8

 

[hage567]

Can you show how you got

F#2x=1.625e-8
F#4x=1.182e-8
F#4y=-1.182e-8

 

[sugarntwiligh]

RE:
Can you show how you got

F#2x=1.625e-8
F#4x=1.182e-8
F#4y=-1.182e-8

Begin Reply:
F#2x=(G)(9.5)(9.5)/(0.6^2)
=1.672e-8
Which was a typo, thanks for pointing that out.
F=#4x=[(G)(9.5)(9.5)/(0.6^2)]sin(45)=
=1.182e-8
F=#4y=[(G)(9.5)(9.5)/(0.6^2)]cos(45)=
=1.182e-8

 

[hage567]

The distance between the two masses diagonally across from each other will NOT be 0.6 m. 0.6 m is the length of the sides of the square.

 

[sugarntwiligh]

Wow thank you so much! I can't believe I missed that. I plugged in my values again and I got 3.13e-8, which I attribute to rounding. Thanks again!

 

[hage567]

You're welcome.