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

Acceleration due to gravity

• If the gravitational force is the only force exerted on an object, the observed acceleration of the object in is numerically equal to the magnitude of the gravitational field strength in at that location

  • When expressed in this is called the acceleration due to gravity

• Near the surface of Earth

  • the strength of the gravitational field is

  • the acceleration due to gravity is

Objects in free fall without air resistance

• 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

• Newton's second law of motion describes acceleration as:

• Where:

  • = acceleration, measured in

  • = force exerted on object, measured in newtons

  • = mass of object, measured in kilograms

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

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

• Here, the masses cancel each other out

• So, for objects falling in a vacuum

• Where: 

  • = acceleration due to free fall, measured in

• 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 regardless of their mass
  

Objects in free fall with air resistance

• 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

Acceleration due to free fall in air resistance