The acceleration of gravity on the Earth's surface is [tex]9.81 m/s^2[/tex]
Explanation:
The acceleration of gravity is the rate at which every object in free fall near the Earth's surface accelerates.
Its value can be calculated as:
[tex]g=\frac{GM}{R^2}[/tex]
where
[tex]G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}[/tex] is the gravitational constant
[tex]M=5.97\cdot 10^{24}kg[/tex] is the Earth's mass
[tex]R=6.37\cdot 10^6 m[/tex] is the Earth's radius
Substituting the values, we find
[tex]g=\frac{(6.67\cdot 10^{-11})(5.98\cdot 10^{24})}{(6.37\cdot 10^6)^2}\sim 9.81 m/s^2[/tex]
It can be demonstrated that this is the acceleration of an object in free fall. In fact, according to Newton's second law:
[tex]F=ma[/tex]
where
F is the net force acting on an object
m is the mass of the object
a is its acceleration
For an object in free fall, the only force acting on it is gravity, so the net force is
[tex]F=mg[/tex]
and combining the two equations,
[tex]mg = ma \rightarrow a = g[/tex]
So, the acceleration is exactly the acceleration of gravity.
Learn more about gravity here:
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