Force as a Vector (Edexcel GCSE Physics)

Vector & Scalar Quantities

• All quantities can be one of two types:

  • A scalar

  • A vector

Scalars

• Scalars are quantities that have only a magnitude

  • For example, mass is a scalar quantity since it is a quantity that has no direction to it

Vectors

• Vectors have both a magnitude and a direction

• Velocity is a vector quantity since it is described with both a magnitude and a direction

  • When describing the velocity of a car it is necessary to mention both its speed and the direction in which it is travelling

  • For example, 60 km per hour in a Westerly direction

• Distance is a value describing only how long an object is or how far it is between two points - this means it is a scalar quantity

• Displacement on the other hand also describes the direction in which the distance is measured - this means it is a vector quantity

  • For example, 100 km in a Northern direction

Comparing Scalars & Vectors

• The table below lists some common examples of scalar and vector quantities:

Scalars & Vectors Table

• Some vectors and scalars are similar to each other

  • For example, the scalar quantity distance corresponds to the vector quantity displacement

• Corresponding vectors and their scalar counterparts are aligned in the table where applicable

Force Pairs

• When there is an interaction between two objects, the forces they exert on each other are equal in magnitude but opposite in direction

  • The pair of forces exerted by the interacting objects are known as force pairs

• Newton's third law explains the forces that enable someone to walk

  • The foot exerts a push force on the ground

  • The ground exerts a push force force on the foot

  • The forces are equal in magnitude and opposite in direction

The force pairs are the foot and the ground: The foot pushes backwards on the ground, and the ground pushes the foot forwards

• Vector diagrams can be used to represent Newton's third law

• Use the following three rules to help you identify a third law pair:

1. The two forces in a third law pair act on different objects

2. The two forces in a third law pair always are equal in size but act in opposite directions

3. The two forces are always the same type: weight, normal contact force, etc.

Scenario 1: The gravitational pull of the Earth acts on the book (weight) and the normal contact force of the table acts on the book. Scenario 2: The gravitational pull of the Earth acts on the book (weight) and the gravitational pull of the book acts on the Earth (weight)

• The diagram above shows:

  • The gravitational pull of the Earth on the book (weight) and the gravitational pull of the book on the Earth (weight)

    • Both forces are the same type (weight)

    • Both forces act on different objects (Earth on book, and book on Earth)

    • Both forces are equal and opposite

    • This is a third law pair

  • The gravitational pull of the Earth on the book (weight) and the push force of the table on the book (normal contact force)

    • These forces are not the same type (weight and normal contact force)

    • Both forces act on the same object (the book)

    • Both forces are equal and opposite

    • This is not a third law pair, this is an example of Newton's first law; the forces are balanced so there is no resultant force acting on the book