I need help finding net gravitational force for the figures below. I know : G=6.

Question

I need help finding net gravitational force for the figures below.

I know : G=6.67*10^-11         F=GMm/R^2

              M=3.0kg                   R=10cm=.1m

              m=3.0kg

When I put F=(6.67*10^-11*3*3)/(.1^2), it tells me I have the wrong answer, the answer I got was 6.003*10^-8

Is it wrong because the balls are in a triangle/square or is it wrong because I am supposed to use grams instead of kilograms for the mass making M=3000g and m=3000g.

Please work out the problem and tell me where I when wrong here is the problem below

THE PROBLEM BELOW

QUESTIONS ASKED: PLEASE HELP ON THESE

Find the magnitude of the net gravitational force on mass A due to the other masses in point (a).

Find the magnitude of the net gravitational force on mass A due to the other masses in point (b).

THANK YOU SO MUCH!!!!

Explanation / Answer

what you are doing is calculating Force because of one ball

in first case

there are total three balls

so forfce on A is due to B and C

remember they will be in diffrent directions..so you just cant sum them up and make ans = 2*F since there are two balls..

what you have to do is vector sum of those two forces

Ans = sqrt( F^2 + F^2 + 2F^2cos(60)) = sqrt(3)F

F is what you have calculated

in second case ...

there are three force acting

two force perpendicular and force due to D is along diagonal

resultant of first two will be along diagonal>

this force and force due to D are in same direction

magnitude of Force due to D is slightly different because its distance from A is different

d = sqrt(2) * .1 m

Fd = F/2

FInal Ans for second part =sqrt(3)F + F/2 = F(.5 +sqrt(3)) = 13.39 x 10^-8

update

dont put in the the value of F in the beginning..work out with F .. which gives sqrt(3)F . means multiply F value with sqrt(3) . The F value you have calculated is correct . Units were taken rightly.
sqrt(3)F = 10.4 x 10^-8

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