(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two identical particles, each of mass m, are located on the x axis at x = +x_{0}and x = -x_{0}.

Determine a formula for the gravitational field due to these two particles for points on the y axis; that is, write [tex]\vec{g}[/tex] as a function of y, m, x_{0}, and so on.

Express your answers in terms of the variables y, m, x_{0}, and appropriate constants. Answer in the form g_{x},g_{y}.

2. Relevant equations

[tex]\vec{g}=\frac{\vec{F}}{m}[/tex]

[tex]\vec{g}=\frac{GM}{r^2}\hat{r}[/tex]

3. The attempt at a solution

I'm really at a loss as to how to approach this problem. I would assume that, graphically, the y axis will be between the two particles and that we are trying to find the components of g in terms of the point on the y axis.

I suppose that in this frame we have a triangle with our particles on two corners and our point on the y axis at the third corner.

I'm still very unsure as to how gravitational fields work in cases like this, but here's what I attempted:

[tex]\vec{g}=\frac{\vec{F_1}}{m} + \frac{\vec{F_2}}{m}[/tex]

[tex]\vec{g}=\frac{mG}{r^2_1}\hat{r_1} + \frac{mG}{r^2_2}\hat{r_2}[/tex]

[tex]r^2_1=-x^2_0+y^2[/tex]

[tex]r^2_2=x^2_0+y^2[/tex]

[tex]\vec{g}=\frac{mG}{-x^2_0+y^2}\hat{r_1} + \frac{mG}{x^2_0+y^2}\hat{r_2}[/tex]

At this point, assuming I haven't made a mistake (I doubt that I haven't) I don't know what to do. Could someone give me a hand and some explaining, please?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Gravitational field for 2 particles

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