Another Rate of Change

[teej047]

Newton's LAw of Gravitation says that the magnitude 'F' of the force exerted by a body of mass 'm' on a body of mass 'M' is F = GmM/r^2 where 'G' is the gravitational constant of 'r' is the distance between the bodies.

A) Fine dF/dr and explain its meaning. What does the minus sign indicate?

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

I hate being a math major and being unable to figure this stuff out.[/i]

 

[galactus]

Differentiate the function and go from there.

\(\displaystyle \L\\\frac{dF}{dr}=\frac{-2gmM}{r^{3}}\cdot\frac{dr}{dt}\)

Now use your given info to answer the other questions.