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Math Help - Rates of Change - Newton's Law

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    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.
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    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.
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