- #1
diminion
- 2
- 0
Homework Statement
Hello! I signed up about week ago, in case i needed some help in physics, and today i do. I Hope someone can explain this to me a little better.
Anyways, yesterday we started the chapter on gravitation. Our professor layed out eight steps we should follow to calculate the Fgrav at a non-point mass. They were,
1. Draw a diagram
2. Pick a small chunk (dm)
3. Draw a line from dm to the 2nd mass
4. Draw a force vector starting at the 2nd mass
5. Calculate dF created between dm and the 2nd mass
6. Check symmetry
7. Calculate remaining components of dF
8. Integrate
Homework Equations
He gave us the following:
[tex]dF\ =\ G\frac{dm M_{2}}{r^{2}}[/tex]
Which he broke down into components,
[tex]dF_{x}\ =\ G\frac{dm M_{2}}{r^{2}}cos\theta[/tex]
and
[tex]F_{y}\ =\ 0[/tex] by symmetry.
The Attempt at a Solution
When i went home, i proceeded to find dFx
[tex]dm\ =\lambda dl[/tex]
[tex]\lambda\ =\frac{M}{L}[/tex]
[tex]r\ =\sqrt{(R^{2}+l^{2})}[/tex]
[tex]cos\theta\ =\frac{R}{\sqrt{(R^{2}+l^{2})}}[/tex]
[tex]dF_{x}\ =\ G\frac{\lambda dl M_{2}}{(R^{2}+l^{2})}\frac{R}{\sqrt{(R^{2}+l^{2})}}[/tex]
[tex]F_{x}\ = \int dF_{x}\ =2\int^{\frac{L}{2}}_{0} \ G\frac{\lambda dl M_{2}}{(R^{2}+l^{2})}\frac{R}{\sqrt{(R^{2}+l^{2})}}[/tex]
[tex]F_{x}\ = 2 \ G\lambda M_{2}R\int^{\frac{L}{2}}_{0}\frac{dl} {(R^{2}+l^{2})^{\frac{3}{2}}} [/tex]
Now to finish this up, it seems to me like trig substitution. Is that the correct way to proceed with he integral?
My main question that i don't understand is, What does he mean "by symmetry"? I first assumed he was going to use [tex]sin\theta[/tex] for Fy but he didnt. Why is Fy=0?
Thanks for any help you can give me about the symmetry part.
