What is the differentiation of g(mm-m^2)/r?
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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
F=F= (GmM)r2(GmM)r2
Where G is the gravitational constant and r is the distance between the bodies.
a. Find dFdrdFdr and explain what it means
b. 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?
Part a:
Derivative is dFdrdFdr = −2GmMr−3−2GmMr−3
dFdrdFdr describes how the force changes over a change of distance.
F=F= (GmM)r2(GmM)r2
Where G is the gravitational constant and r is the distance between the bodies.
a. Find dFdrdFdr and explain what it means
b. 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?
Part a:
Derivative is dFdrdFdr = −2GmMr−3−2GmMr−3
dFdrdFdr describes how the force changes over a change of distance.
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