Forces and their interactions

Key content

A force is a push or pull that acts on an object because of its interaction with another object.

Scalar and vector quantities

• Scalar quantities have magnitude only – for example distance, speed, mass, energy, time and temperature.
• Vector quantities have magnitude and direction – for example displacement, velocity, force, acceleration and momentum.

A vector can be shown as an arrow: the length of the arrow represents the magnitude, and the direction of the arrow shows the direction.

Contact and non-contact forces

Force is a vector quantity. Forces are either:

• Contact forces – the objects are physically touching: friction, air resistance, tension, normal contact force.
• Non-contact forces – the objects are physically separated: gravitational force, electrostatic force, magnetic force.

When two objects interact, each one exerts a force on the other. For example, the Earth pulls a book down (its weight) and the book pulls the Earth up; the book pushes down on a table and the table pushes up on the book (the normal contact force). Each force is a vector, drawn as an arrow on the object it acts on.

Gravity

• Weight is the force acting on an object due to gravity. The force of gravity close to the Earth is due to the gravitational field around the Earth.
• The weight of an object depends on the gravitational field strength at the point where the object is.
• Weight can be considered to act at a single point called the object's centre of mass.
• Weight and mass are directly proportional ($W \propto m$).
• Weight is measured using a calibrated spring-balance (a newtonmeter).

On Earth, $g = 9.8$ N/kg. Your mass (in kg) is the same everywhere; your weight (in N) depends on $g$.

Resultant forces

A number of forces acting on an object may be replaced by a single force that has the same effect. This single force is called the resultant force.

• Forces in the same direction add; forces in opposite directions subtract.
• In the diagram, the resultant is $12 - 5 = 7$ N to the right. The vertical forces are balanced.

Higher tier only

Higher tier: a free body diagram shows the magnitude and direction of all the forces acting on an isolated object. Use scale vector diagrams to find the resultant of two forces at an angle to each other, and to resolve a single force into two components at right angles (the two components together have the same effect as the single force). If the resultant is zero, the forces are in equilibrium, and a vector diagram of them forms a closed shape.

Equations

Worked examples

Common misconceptions