Force as a Vector (Edexcel GCSE Physics)

• 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

• When there is an interaction between two objects, a force is exerted on each object which is equal in magnitude but opposite in direction
  • The pair of objects interacting are known as force pairs

• Force pairs are described by Newton's Third law
• Examples of these force pairs include:
  • The contact force of a foot on the ground, and the contact force of the ground on the foot
    • This interaction between the ground and the feet enables walking
  • The contact force on a book on the table, and the contact force of the table on the book
  • The gravitational force (weight) of the Earth on the book, and the gravitational force of the book on the Earth 

• Force pairs can be represented by arrows in vector diagrams

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

The force pairs are the Earth and the book, and the book and the table: The Earth pulls on the book and the book pulls on the Earth, The book pushes on the table and the table pushes on the book