Freefall (Cambridge (CIE) IGCSE Physics): Revision Note

Acceleration of free fall

• In the absence of air resistance, all objects fall with the same acceleration regardless of their mass

• This is called the acceleration of free fall

  • This is also sometimes called acceleration due to gravity

• For an object near to the surface of the Earth, the acceleration of free fall, g,

  is approximately constant and is approximately 9.8 m/s²

In the absence of air resistance, Galileo discovered that all objects (near Earth's surface) fall with an acceleration of about 9.8 m/s²

• This means that for every second an object falls, its velocity will increase by 9.8 m/s

• The symbol $g$ also stands for the gravitational field strength, and can be used to calculate the force of weight acting on an object using its mass:

$W=mg$

• Where:

  • $W$ = the force of weight acting on an object, measured in newtons (N)

  • $m$ = mass of object, measured in kilograms (kg)

  • $g$ = gravitational field strength, measured in newtons per kilogram (N/kg)

Motion of falling objects

Extended Tier Only

Falling objects 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

$W=mg$

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

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

• Where:

  • $a$ = acceleration, measured in metres per second squared (m/s²)

  • $F$ = 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 

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

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

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

• Here, the masses cancel each other out

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

• So, for objects falling in a vacuum

$a=g$

• Where $g$ = acceleration of free fall

• This theory was tested by astronauts on the Moon

  • A hammer and a feather were dropped from equal heights on the Moon, where there is no air resistance

  • The hammer and the feather fell with the same acceleration and landed at the same time

  • This proved that objects falling in a vacuum have the same acceleration regardless of their mass

• 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

 Object falling with no air resistance

In the absence of air resistance, objects fall with constant acceleration

• Objects falling through a vacuum will never reach a terminal velocity

 Falling objects with air resistance

• 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

• Air resistance increases as the speed of the object increases

• When objects fall through air, two forces are exerted on the object:

  • The force of weight

  • The force of air resistance

• When the force of air resistance becomes equal to the force of weight, then the object stops accelerating and falls at a constant speed

  • This is called terminal velocity

How does a skydiver reach terminal velocity?

The stages of a skydiver's fall until they reach terminal velocity

• When a skydiver jumps out of a plane, initially the only force acting on them is weight

  • The resultant force acts in the downward direction

  • The skydiver accelerates

• As the skydiver accelerates, their speed increases, so the force of air resistance increases

  • The resultant force acts in the downward direction with a smaller magnitude

  • The skydiver continues to accelerate but at a slower rate

• Air resistance increases until it is equal to the weight

  • The forces are balanced

  • There is no resultant force

  • Terminal velocity is reached

• The parachute is deployed, increasing the surface area of the skydiver

  • The parachute collides with many more air particles

  • Air resistance increases greatly

• The force of air resistance is now greater than the force of weight

  • The resultant force acts in the upward direction

  • The skydiver continues falling in a downward direction

  • The skydiver is decelerating

• As the skydiver decelerates, their speed decreases

  • Therefore, air resistance decreases

  • Therefore, the resultant force decreases

• Air resistance decreases until it is equal to the weight

  • The forces are balanced

  • There is no resultant force

  • A new, slower terminal velocity is reached

Graph showing the motion of the skydiver as they reach terminal velocity

The graph shows how the speed of the skydiver changes during the descent. The horizontal parts of the graph show the periods of terminal velocity

 Falling objects with liquid resistance

• When objects fall through a liquid due to the force of weight, the liquid exerts a frictional (drag) force on the object as it falls

• Drag forces oppose the motion of an object

  • They act to slow it down

• Drag increases as the speed of the object increases

• When the drag force becomes equal to the force of weight, the object stops accelerating and reaches a terminal velocity