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:
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[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
Application of 2nd law
Choose the system to be the body only - the second law:
- the force law:
- the equation of motion:
- the second law:
- The solution: already established in Key Point 1.4.
- Application of 3rd law
- choose the two systems: body, B and earth, E
- the third law:
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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.[C] Inertial and gravitational mass
- In Newton’s 2nd Law
m is strictly the inertial mass.
In the gravitational force equation
m is strictly the gravitational mass.- The claim that these masses are the same leads to the prediction that all bodies have the same free fall acceleration.
- This claim is one expression of the Principle of Equivalence
- Forward reference: S2.13