Gravitational force - point mass and circular platform

  • #1
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Homework Statement


Calculate the gravitational force between a point mass and a circular platform.

Homework Equations


G=m1*m2/r^2

The Attempt at a Solution


http://i.imgur.com/dfZf9GK.jpg

The actual solution is different. They integrated by the angle between a/r (alpha) but i do not understand the cos(alpha) at the start, check this out:

http://i.imgur.com/nwxhCEb.jpg

Can anyone explain this please? Thanks.
 

Answers and Replies

  • #2
Simon Bridge
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Force is a vector... the cosine is one of the components.
 
  • #3
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Yes, my mistake, thanks! What happens if the radius of the disc is infinite? The part I don't understand: σ(area density)=M/4πR^2, but isn't it just M/πR^2 (without "4" at the bottom)? I mean the whole mass of the disc would be M=πR^2σ, since πR^2 is the area of a cricle, with the 4 added its a sphere, but there is no sphere here just an infinite circle so where does the 4 come from?
 
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  • #4
nrqed
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Yes, my mistake, thanks! What happens if the radius of the disc is infinite? The part I don't understand: σ(area density)=M/4πR^2, but isn't it just M/πR^2 (without "4" at the bottom)? I mean the whole mass of the disc would be M=πR^2σ, since πR^2 is the area of a cricle, with the 4 added its a sphere, but there is no sphere here just an infinite circle so where does the 4 come from?
I do not know the language (what is it, by the way?) but are you sure that the expression ##\sigma = M/4 \pi R^2 ## is referring to the same question? All I see used for that question is

$$ dM = 2 \pi x \rho dx h $$ which, if you integrate over x from 0 to R gives indeed ## M = \pi R^2 h \rho## as you expected.
 
  • #5
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It is not the same question but it is related to the first one (just with x going to infinity, not to R). Anyways, I have managed to use my google-fo and found a newer edition (1996); the one I have is 1988. This part is wrong. It states that F=8πGm (force between the particle and an infinite plane. The solution states specifically that you have to limit R towards infinity BUT with σ=M/4πR^2 being a constant), but the newer one is corrected to F=2πGmσ, which is what I got as well, so this is solved, thank you. Language is Slovenian. Heres a quick snap of the newer: http://i.imgur.com/m0j9s9q.png ("neskončno velika plošča" literally means "infinitely big plate").
 
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