Calculating Net Gravitational Force on Mass A in a Square Configuration

[knight4life]

Homework Statement

Each mass is 4kg find the magnitude and direction of the net gravtitational force on mass A due to the other masses. each side of the square is 10cm
http://img13.imageshack.us/img13/3815/1012447.jpg
I am having trouble with (b) the square

Homework Equations

F = Gm1m2/r^2

The Attempt at a Solution

what I did was used the formula above to find AB, AC, and then used pythagorean theorm to find radius from A to D. then I used the above equation, and added the values together getting 2.17x10^-7 the correct solution is 2.04x10^-7 What did I do wrong?

 

[husky88]

Is it possible that you used a different number of significant figures than the answer key?
The two values are very close.

Edit:
You shouldn't add the values at the end, you should find the resultant of AC with AB, and then add AD. Is this what you did?

 

[knight4life]

Is it possible that you used a different number of significant figures than the answer key?
The two values are very close.

Edit:
You shouldn't add the values at the end, you should find the resultant of AC with AB, and then add AD. Is this what you did?

yes I did do it that way, and no I am pretty sure I used the same amount of significant figures as the book did.

 

[husky88]

Well I get the same answer as the key, 2.04*10^-7.
What are some intermediate values you got?

 

[knight4life]

for AC and AB i did (6.674E-11)(4)(4)/.1^2 =1.068E-7

for AD i used (6.674E-11)(4)(4)/.5657^2 = 1.89E-9

I believe these are the correct values, now this is where I run into problems.

 

[husky88]

I used 6.67 for G, not 6.674. This will yield 2.04 E-7.
Also r for AD is 0.1414213562, not .5657. Hope you can figure out why.

 

[knight4life]

I used 6.67 for G, not 6.674. This will yield 2.04 E-7.
Also r for AD is 0.1414213562, not .5657. Hope you can figure out why.

yeah I have .1414 also, I got the .5657 from the problem I had written beneath it. I figured out what I was doing wrong. I was not taking the resultant of AC and AB like you earlier suggested. I tried it this way, and I got the correct result. Thank you for all of your help.

 

[BledCyan]

I've been trying to tackle a similar problem for longer than I would like to admit (again part b).

All sides are equal, all masses are equal, have to show that magnitude = (Gm^2/a^2)(sqrt(9/4+sqrt(2)))

the 9/4 looks like (3/2)^2, or (1+1/2); so I believe it is a creation of 60 degrees; which would make me think i need to tackle the sqrt(2) from a 30 degree standpoint.. but I don't see how I can generate sqrt(sqrt(2)) so that the first cancels out while developing magnitude.

I really didn't want to ask.. but kinda desperate to get this done.