Calc

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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 the following.
F=(GmM)/r^2
Here G is the gravitational constant and r is the distance between the bodies.
(a) Find dF/dr

(b) Suppose it is known that Earth attracts an object with a force that decreases at the rate of 2 N/km when r = 30,000 km. How fast does this force change when r = 15,000 km?

  • Calc -

    dF/dr=-2GMm/r^3=-2F/r

    b) dF/dr=-2 when r=30,000
    but the relationship is inverse, so halving the distance will double the rate.

  • Calc -

    16

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