Are My Gravitational Force and Field Calculations Correct?

[cvc121]

Homework Statement

I am having some trouble with gravitational force and fields and would like some confirmation if I am on the right track and approaching the questions correctly. I have attached a couple of problems that I have worked through below.

Homework Equations

The Attempt at a Solution

The questions along with my attempt at the solution has been attached below. Am I on the right track with these problems? Which questions am I doing incorrectly? Thanks. All help is very much appreciated!

 

[drvrm]

The questions along with my attempt at the solution has been attached below. Am I on the right track with these problems? Which questions am I doing incorrectly? Thanks. All help is very much appreciated!

i think you are using the correct formula for gravitational forces between the masses ;
but pl. check the calculation of distances between them as it comes as square in denominator.
regarding composition of say two forces its better to resolve them in two directions and then add them as you know the angles.
check the numbers again..

 

[cvc121]

Thanks for the reply. To which question and specific calculation are you referring to?

 

[drvrm]

Thanks for the reply. To which question and specific calculation are you referring to?

for example check the answer of question -3
its simple as G.M(3)/ R^2
= 6.67. 10^-11 . 5 . 10^30 /( 2. 1.5 . !0^11)^2
=(6.67. 5 /9) 10^-3
=(0.752 . 5 ). 10^-3 approx. comes to 3.76 x 10^-3 m/s^2
in other calculations also i will req. you not to put in values at the first instance but work with notations say m1, m2, m3 ,G and distances and put in values when you are finally calculating the numbers-the chances of error will be less.
say for
F(2-1) = G. m2. m1 / d(21) ^2
F(2-3) = G. m2. m3/ d(23) ^2 ; d(23) = Sqrt (2) d(21) so F(2-3) = Gm2.m3/ 2. d(21)^2
the above forces are making an angle of 45 degrees with each other
so you can write resultant of two forces as

R= sqrt ( F(2-1)^2 + F(2-3)^2 + 2. F(2-1). F(2-3) .Cos(45) ) then
Tan (theta) = F(2-3) sin 45/ F(2-1) where theta is the angle made by R with F(2-1)

many terms like G, m2. d(21)^2 will come out common from sqrt bracket and your calculation will be easy.