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Given $\frac {dF}{dr} = -2GmMr^{-3}$

Suppose that it is known that the Earth attracts an object with a force that decreases at the rate of $2 N/km$ when $r = 20,000km$. How fast does this force change when $r = 10,000km$?

In this problem, do I just plug in the values for $r$?

2 Answers 2

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The problem is analogous to finding points on a line. You have a given value which will determine the equation for you. From the information given, we know that $\frac{dF}{dr} = -2$ when $r = 20000$. This gives you $-2 = -2GmM(20000)^{-3}\implies (20000)^3 = GmM$ From the given information, what can you say when $r=10000$?

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    Ok, I get it, sorry lol2012-10-22
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You're going to need your given information to determine the value of the constant $GmM$. (Note that you are not given the mass of the other object, so even if you look up the value of $G$ and the mass of the earth, you still need to use the given piece of information.) Then you are correct that you can then plug in $r = 10,000$ to get the desired value of $dF/dr$.

(It's also possible to think of this problem in terms of proportions: $dF / dr$ is inversely proportional to the cube of $r$.)

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    So if I were to plug in $10,000$ and $20,000$, I would get: $\frac {-2GmM}{(20,000)^3}$ and $\frac {-2GmM}{(10,000)^3}$ correct?2012-10-22