# Math Help - Rates of Change - Newton's Law

1. ## Rates of Change - Newton's Law

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 and r is the distance between the bodies.

(a) Find dF/dr and explain its meaning. What does the minus sign indicate?
(b) Suppose it is known that the 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?

-im sorry for giving you the whole problem. i am trying to work some of it out but i am very bad with word problems. any help with either parts of a or b would be greatly appreciated, thanks.

2. $F = \frac{GMm}{r^2}$

(a) Find dF/dr and explain its meaning. What does the minus sign indicate?
$\frac{dF}{dr} = -\frac{2GMm}{r^3}$

the negative sign indicates that the magnitude of the gravitational force decreases with respect to r.

(b) Suppose it is known that the 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?
cutting r in half will increase F by a factor of 8.