Question 915039

(b) Suppose it is known that the earth attracts an object with a force that decreases at the rate of 4 N/km when r = 30,000 km. 
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{{{dF/(dr) = (-2GmM)/r^3}}}

Substitute -4 for {{{dF/(dr)}}} and 30000 for r

{{{-4 = -2GmM/30000^3}}}

{{{-4*30000^3 = -2GmM}}}

{{{-1.08*10^13 = -2GmM}}}

Substitute {{{-1.08*10^13}}} for {{{-2GmM}}} in

{{{dF/(dr) = (-2GmM)/r^3}}}

{{{dF/(dr) = (-1.08*10^13)/r^3}}}

How fast does this force change when r = 15,000 km?

Just substitute 15000 for r in

{{{dF/(dr) = (-1.08*10^13)/r^3}}}

{{{dF/(dr) = (-1.08*10^13)/15000^3}}}

{{{dF/(dr) = -32}}}{{{N/km}}}

Edwin</pre>