Forces As Vectors (AQA GCSE Combined Science: Synergy: Physical Sciences): Revision Note

Forces as Vectors

• A scalar quantity is described by magnitude only

  • For example, speed or mass

• A vector quantity is described by both magnitude and direction

  • For example, force or velocity

• Forces are therefore vector quantities

• The magnitude of a force is measured in newtons

• The direction of a force can be described as left, right, up or down

A free body diagram of an object with two forces acting on it

• Vector quantities are represented by an arrow

  • The length of the arrow represents the magnitude of the force

  • The direction of the arrow represents the direction of the force

• The direction of a force can be imagined using a number line

  • Numbers to the left of zero are negative as are forces pointing left

  • Numbers to the right of zero are positive as are forces pointing right

Vectors represented as positive or negative vectors depending on their direction

• Not all forces are directed perfectly horizontally or vertically and thus need to have an angle described

  • It is useful to describe an angle with respect to the vertical or the horizontal

A force of magnitude 100 N directed 40° to the horizontal

Force Pairs

• When there is an interaction between two objects, a force is exerted on each object by the other

  • This is known as a force pair

• Examples of these force pairs include:

  • A laptop resting on a desk

    • The laptop exerts a downward force on the desk

    • The desk exerts an upward force on the laptop

  • A basketball player throwing a basketball

    • The basketball player exerts a push force on the ball

    • The ball exerts a push force on the basketball player

  • A person standing on the Earth

    • The Earth exerts a gravitational pull force on the person

    • The person exerts a gravitational pull force on the Earth

• Force pairs can be represented by arrows in vector diagrams

The force pairs present with respect to a rock being pushed by a person

• The person pushes on the rock, and the rock pushes on the person

• The rock pushes on the ground, and the ground pushes on the rock

• The person pushes on the ground, and the ground pushes on the person

Contact & Non-Contact Forces

• A force is defined as:

A push or a pull that acts on an object due to the interaction with another object

• Forces can have an effect on bodies in several different ways, such as by:

  • changing their speed

  • changing their direction

  • changing their shape

• Some examples of these changes are:

  • An engine can increase the speed of a vehicle due to a force called thrust

  • A comet’s direction can be affected by gravitational attraction

  • A spring can have its shape changed by the force from a heavy load

Diagram showing the effects of forces on different objects

• Important forces to be familiar with:

  • Weight – the name given to the force of gravity on a mass

  • Electrostatic force – the force between two charged objects

  • Thrust – the force causing an object to move (such as the force from a rocket engine)

  • Air resistance (or drag) – the friction of the air on a moving object

  • Upthrust – the force of a fluid (such as water) pushing an object upwards (making it float)

  • Compression – forces that act inward on an object, squeezing it

  • Tension – force transmitted through a cable or a string when pulled on by forces acting on its opposite ends

  • Reaction force – a force due to contact between two objects

Diagram showing several different types of forces acting on objects

• All forces can be categorised into one of two types:

  • Contact forces

  • Non-contact forces

What is a contact force?

A contact force is defined as:

A force which acts between objects that are physically touching

Contact force examples

• Examples of contact forces include:

  • Friction

  • Air resistance

  • Tension

  • Reaction force

• Friction:

  • is a force that opposes motion

  • occurs when objects rub against each other

• Air resistance:

  • is a type of friction

  • occurs when an object moves through air

• Tension:

  • is a force that pulls two objects connected by a length, such as a string or rope

  • occurs when a force is applied to the length

• Reaction force:

  • is a force that pushes touching objects apart

  • occurs when objects are supported by a surface

Examples of contact forces

What is a non-contact force?

• A non-contact force is defined as:

A force which acts at a distance, without any contact between bodies, due to the action of a field

Non-contact force examples

• Examples of non-contact forces include:

  • Gravitational force

  • Electrostatic force

  • Magnetic force

• Gravitational attraction:

  • The attractive force experienced by two objects with mass

  • For example, the force between a planet and a comet

• Electrostatic force:

  • A force experienced by charged objects which can be attractive or repulsive

  • For example, the attraction between a proton and an electron

• Magnetic force:

  • A force experienced between magnetic poles that can be attractive or repulsive

  • For example, the attraction between the North and South poles of magnets

Examples of non-contact forces