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S2.5 Gravitational force near the earth`s surface

[A] About the force

The gravitational force on a body of mass m within a small enough region near the earth’s surface is:

\[ \vec{F}_G = -mg \hat{y} \]
where
Graphic - No title - localvertical

[B] Example problem

Determine the motion of a body of mass m experiencing only a uniform gravitational force, and consider the implications of the 3rd law.

Solution

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So the earth experiences the same magnitude of force due to the body as the body does due to the earth. The reason we tend to think about the latter and forget about the former is that the acceleration that the earth exhibits as a result is so much smaller than the acceleration of the body. The ratio of the two accelerations is just the inverse of the ratio of the masses, as we saw in S2.2.
 

ALose (...and gain) weight easily....

[C] Inertial and gravitational mass