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Gravitational Acceleration near the Surface of the Earth

In the absence of air friction, objects near the surface of the Earth accelerate downward with an acceleration known as the gravitational acceleration.

The magnitude of the gravitational acceleration, indicated with gg, depends on the distance of the object from the Earth's center.

This means that the magnitude of the gravitational acceleration changes with location and with altitude.

So, objects on the poles experience a slightly larger acceleration than objects on the equator because they are slightly closer to the center of the Earth (remember, the Earth is not a sphere).

However, as long as an object remains close to the Earth's surface, the changes in the gravitational acceleration are quite small.

Therefore, when we don't need to be super precise, it is fine to consider the gravitational acceleration to be constant for objects near the surface of the Earth.

But what should be the constant value that we give to gg?

Generally speaking, we should measure the gravitational acceleration near the surface at the location that we're interested in and have that as the constant value.

However, when knowing the exact value of gg is not important, a conventional value of 9.80665 m/s2\pu{9.80665 m/s^2} is assumed.

In problems where we deal with gravitational acceleration, we often write gg to three significant figures:

g=9.81 m/s2g = \pu{9.81 m/s^2}

As you may have noticed, we did not say anything about the specific characteristics of an object.

This is because countless experiments have shown us that all objects, regardless of size, shape, mass, or any other characteristic, experience the same gravitational acceleration as long as they are in the same location.

For example, when an apple and a feather are left falling from the same height in a vacuum, their motions are identical:

Apple and feather in a vacuum.

This goes against our intuition because in our daily lives we're used to seeing heavy objects fall faster than light objects.

Once again, this is because of air resistance which is felt more by light objects.

However, once we eliminate air resistance, all objects experience only the gravitational acceleration, which is the same as long as they are in the same location.

In problems with falling objects, we often assume that there is no air resistance.

Since a dense object, such as a small heavy stone, experiences negligible air friction, the results that we arrive at in such problems are still good approximations for dense objects.

Therefore, in problems, such as the ones where we have an object that is left falling from some height, or that is thrown vertically upward, we assume that the object moves with constant acceleration along a straight line, i.e., its motions is a uniformly accelerated linear motion.

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