Acceleration Due to Gravity (College Board AP® Physics 1: Algebra-Based)

Study Guide

Written by: Ann Howell

Reviewed by: Caroline Carroll

If the gravitational force is the only force exerted on an object, the observed acceleration of the object in $m / s^{2}$ is numerically equal to the magnitude of the gravitational field strength in $N / kg$ at that location
- When expressed in $m / s^{2}$ this is called the acceleration due to gravity
Near the surface of Earth
- the strength of the gravitational field is $g = 10 N / kg$
- the acceleration due to gravity is $g = 10 m / s^{2}$

A vacuum is a space that contains no matter, so there are no particles to exert frictional forces on a falling object
- When objects fall in a vacuum, there is no air resistance or liquid resistance so the only force acting on them is the force of weight

$Weight = m g$

$a = \frac{F}{m}$

Where:
- $a$ = acceleration, measured in $m / s^{2}$
- $F$ = force exerted on object, measured in newtons $N$
- $m$ = mass of object, measured in kilograms $kg$

Since the only force acting on a falling object in a vacuum is weight, the equation can be expressed as

$a = \frac{Weight}{m}$

Weight is the product of mass and gravitational field strength, so the equation can be expressed as

$a = \frac{m g}{m}$

$a = \frac{m g}{m}$

$a = g$

Where:
- $g$ = acceleration due to free fall, measured in $m / s^{2}$
This also applies when air resistance is so small that it can be disregarded
- When air resistance is described as negligible, it can be approximated to an object falling in a vacuum
On Earth when air resistance is considered negligible all objects in free fall will accelerate towards the Earth's center of mass at $g = 10 m / s^{2}$ regardless of their mass

When objects fall through a fluid (liquid or gas), the fluid exerts a frictional force on the object as it falls
When an object falls through air, it experiences air resistance
- Air resistance is a frictional force produced by collisions with air particles as the object moves through the air
Objects of different surface area and mass will travel at different speeds through a fluid due to the air resistance

Last updated: 10 September 2024

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