National 5PhysicsSQARevision NotesDynamicsNewton’s LawsFree-Fall & Terminal Velocity

Free-Fall & Terminal Velocity (SQA National 5 Physics): Revision Note

Exam code: X857 75

Katie M

Written by: Katie M

Reviewed by: Caroline Carroll

Updated on

Free-fall & terminal velocity

  • 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

acceleration space of space freefall space equals space straight g space equals space 9.8 space straight m space straight s to the power of negative 2 end exponent

  • This means that, when an object falls under gravity, its velocity will increase by 9.8 m s-1 every second

leaning-tower-of-pisa, IGCSE & GCSE Chemistry revision notes

In the absence of air resistance, Galileo discovered that all objects (near Earth's surface) fall with an acceleration of about 9.8 m s-2

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

W space equals space m g

  • 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)

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 an object falls in a vacuum, there is no air resistance, so the only force acting on it is its weight

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

a space equals space fraction numerator space F over denominator m end fraction

  • Where:

    • a = acceleration, measured in metres per second squared (m s-2)

    • F = unbalanced force exerted on object, measured in newtons (N)

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

  • The weight provides the unbalanced force, so the equation can be expressed as: 

a space equals space W over m

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

a space equals space fraction numerator m g over denominator m end fraction

  • Here, the masses cancel each other out

a space equals fraction numerator space up diagonal strike m g over denominator up diagonal strike m end fraction

  • So, for objects falling in a vacuum

a space equals space 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

Freefall graph, IGCSE & GCSE Physics revision notes

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 objects fall through a fluid, the fluid exerts a frictional force on the object as it falls

    • Fluids are liquids or gases

  • Frictional forces oppose the motion of an object

    • They act to slow it down

  • 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?

Diagram showing the phases of a parachute jump for IGCSE & GCSE revision notes

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 their 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

Velocity-time graph of a skydiver

Velocity-time graph of a skydiver's jump. The gradient is initially very steep as the person accelerates. The line then curves toward the horizontal as the air resistance increases to the point at which it is equal to weight. The line dramatically curves downwards when the parachute is opened and the person decelerates. Then the line curves toward the horizontal as a new slower terminal velocity is reached.
The graph shows how the velocity of the skydiver changes during the descent. The horizontal parts of the graph show the periods of terminal velocity

Worked Example

A small object falls out of an aircraft. Choose words from the list to complete the sentences below:

air resistance       gravitational field strength       air pressure

accelerates       falls at a steady speed       slows down

 

(a) The weight of an object is the product of the object's mass and the __________.

(b) When an object falls, initially it ____________.

(c) As the object falls faster, the force of ______________ acting upon the object increases.

(d) Eventually the object ______________ when the force of friction equals the force of weight acting on it.

Answer:

Part (a)

The weight of an object is the product of the object's mass and the gravitational field strength.

  • The weight force is due to the Earth's gravitational pull on the object's mass as it falls through a uniform gravitational field

Part (b)

When an object falls, initially it accelerates.

  • The resultant force on the object is very large initially, so it accelerates

  • This is because there is a large unbalanced force downwards (its weight) - the upward force of air resistance is very small to begin with

Part (c)

As the object falls faster, the force of air resistance acting on the object increases.

  • The force of air resistance is due to friction between the object's motion and collisions with air particles

  • Collisions with air particles slow the object down, so air itself produces a frictional force, called air resistance (sometimes called drag)

Part (d)

Eventually, the object falls at a steady speed when the force of friction equals the force of weight acting on it.

  • When the upward acting air resistance increases enough to balance the downward weight force, the resultant force on the object is zero

  • This means the object is no longer accelerating; it is moving at a steady speed called terminal velocity

Examiner Tips and Tricks

Don't confuse 'air resistance' with 'air pressure' - these are two different concepts!

Exam questions about terminal velocity tend to involve the motion of skydivers as they fall

A common misconception is that skydivers move upwards when their parachutes are deployed; however, this is not the case, they are in fact decelerating to a lower terminal velocity

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    Author
    Reviewer
    Katie M

    Author: Katie M

    Expertise: Physics Content Creator

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.

    Caroline Carroll

    Reviewer: Caroline Carroll

    Expertise: Physics & Chemistry Subject Lead

    Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.