Gravity Problem two shells, one inside other on particle

[Jediknight]

Homework Statement

wow if this picture posts like this i don't have to explain much, cool. particle is at x=3.0R, answer in terms of G . m(inner) m(particle) r(inner)

Homework Equations

F(1on 2)=Gm(1)m(2)/[r(1-2)]^2

The Attempt at a Solution

The way we prooved gravity can be treated as coming from the center mass of a sphere was based on shells, so I figured I could just treat it as such an add forces
Gm(particle)[(m(inner)/(2.2R)^2+3.0m(inner)/(3.0R)^2]

whats wrong with my thinking here?

(this might be an advanced question idk its engineering physics 2 with calculus, so its not what my school would call introductory physics, but its not fluid dynamics or anything either

 

[Nathanael]

How do you know it's wrong? I would've done the same thing. The force of gravity is additive (that is, the resultant force is the vector sum of the individual forces) so I don't see why it wouldn't work.

 

[BvU]

Without a problem statement it is a bit difficult to find out why the answer is wrong -- if it's wrong.
My telepathic capabilities are very limited. What is the question ?

 

[Jediknight]

sorry BvU, thought picture was explanitory but I guess I'm in these sections right now so maybe its more obvious to me. I'm finding the sum of the gorces of gravity exerted by the two shells described on a particle placed at x=3

Mastering Physics said I was wrong, I have heard of them being wrong before. but of course every time in the past I've been so frustrated to think that was the case its always an error on my part

thanks for replies! i just found this forum and it seems awsome

 

[haruspex]

Your posted answer is fine as far as it goes, but obviously can be simplified. What final form did you submit as answer?

 

[Jediknight]

Your posted answer is fine as far as it goes, but obviously can be simplified. What final form did you submit as answer?

I am about to try to simplify after a few problems that I think will help me learn more, it seems like I'm getting this one. mastering physics doesn't usually care too much unless I can cancell out a variable but maybe this time they do

thanks for confirming I am getting the idea, ill pop back to this thread and let you know if I get it "right" and what I enter when I try.

so far I just entered the same thing I put in the first post (Gm(particle)(m(inner)/(2.2R)^2+3m(inner)/(3R)^2) i didn't even square the cooeficients on the R's or combine anything. All I did was pull out G and m(particle) so I didn't have to type them twice. so your probably right