beth12345
  • beth12345
The force of gravity on an approaching asteroid is 200000 Newtons at a certain distance from the Earth. Calculate the force of gravity on the asteroid when it reaches a point one-ninth of this distance from the centre of the Earth.
Physics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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beth12345
  • beth12345
is \[F= G \times \left[\begin{matrix}m _{1} \times m _{2} \div\\ r ^{2}\end{matrix}\right]\]the equation I should use?
anonymous
  • anonymous
Yes, except instead of \(r\) you have \(\frac{r}{9}\).
beth12345
  • beth12345
what is the little symbol under the r?

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anonymous
  • anonymous
9
beth12345
  • beth12345
oh ok, where would I plug in the 200000N
anonymous
  • anonymous
Well, the force of gravity \(F\) is modified at a distance \(r_{new}=\frac{1}{9}r_{old}\), and you square \(r\)...
anonymous
  • anonymous
Alright, take for instance, I had a variable \(a\) that earlier was measured to be \(a=10\). If \(F=a^2=100\), then if I double \(a\) I get \(F=\left(2a\right)^2\).
beth12345
  • beth12345
k, I got \[F= 6.67 \times 10^{-11}\left[\begin{matrix}5.98 \times 10^{24} \div\\ (1/9 \times r )^{2}\end{matrix}\right]\]
beth12345
  • beth12345
is r the radius of the earth? and I don't really understand about what I should do with the 200000N
anonymous
  • anonymous
200000 N is the force of gravity as stated in the question
beth12345
  • beth12345
I don't really know where I would put it though, like in the equation
anonymous
  • anonymous
F is the force of Gravity or just vist these site http://en.wikipedia.org/wiki/Gravity_of_Earth
anonymous
  • anonymous
you should substitute the value in F of equation
beth12345
  • beth12345
oh, and like get the r and then put the 1/9 in to get the 1/9 of that distance?
beth12345
  • beth12345
as in\[200000N= 6.67 \times 10^{-11} \left[\begin{matrix}5.98 \times 10^{24} \div \\ r ^{2}\end{matrix}\right]\]and then find the r that way, and use it to plug into the r times the 1/9?
anonymous
  • anonymous
wait ... @badreferences can you please explain what is 1/9
beth12345
  • beth12345
I'm pretty sure it's the one ninth distance away from the Earth, but I might be wrong
anonymous
  • anonymous
sorry i did not read the question as whole i got it
anonymous
  • anonymous
now calculate the radius and then find out the force of gravity when it is just 1/9 from the radius of the earth you can divide the radius of the earth by 9 6400/9=711 then put these value in the formula
beth12345
  • beth12345
ok
beth12345
  • beth12345
I got \[6.44 \times 10^{-33}\] would that be right? I don't know if I was supposed to square the 1/9 part too with the r, or not
beth12345
  • beth12345
like \[r ^{2} \div9\] or\[(r \div9)^{2}\]
beth12345
  • beth12345
actually ya, I see that I have it in brackets up higher so that should be it, thank you so much for helping and having patients with me :)
anonymous
  • anonymous
its ok dude but you should do like these \[r ^{2}\div9\]

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