Resultant force, Newton's first, second and third laws, and using F = ma to relate force, mass and acceleration.

What this dot point is asking

CCEA wants you to find the resultant force on an object, state and apply Newton's three laws of motion, and use the equation force = mass times acceleration. These ideas link forces to the motion graphs and underpin terminal velocity and stopping distances.

The answer

Resultant force

For forces along one line, add forces in one direction and subtract those in the opposite direction.

Newton's first law

This explains why a car at a steady speed has a driving force exactly balancing the resistive forces.

Newton's second law

The bigger the resultant force, the bigger the acceleration; the bigger the mass, the smaller the acceleration for the same force.

Newton's third law

A third-law pair always has the same type of force (for example both gravitational, or both contact forces), the same size, and opposite directions, but acts on two different bodies. This is different from balanced forces in Newton's first law, which act on the same body and add to zero. Telling these apart is a common exam discriminator.

Worked example: a lift cable

Examples in context

Example 1. A trolley pushed across a floor

Push a $2.0\ \text{kg}$ trolley with a resultant force of $6.0\ \text{N}$ and it accelerates at $a = F/m = 6.0/2.0 = 3.0\ \text{m/s}^2$. Double the load and the same push gives half the acceleration.

Example 2. Walking

Your foot pushes backward on the ground (action); the ground pushes forward on you (reaction), and that forward reaction force drives you along, a clear Newton's third-law pair.

Example 3. A car at steady speed

When a car cruises at a constant speed the driving force from the engine exactly balances the resistive forces (friction and air resistance). The resultant force is zero, so by Newton's first law the velocity stays constant. To accelerate, the driver must increase the driving force so that it exceeds the resistance and the resultant force is no longer zero.

Try this

Q1. State Newton's first law. [1 mark]

• Cue. An object stays at rest or moves at constant velocity unless a resultant force acts on it.

Q2. A resultant force of $30\ \text{N}$ acts on a $6.0\ \text{kg}$ mass. Find the acceleration. [2 marks]

• Cue. $a = F/m = 30/6.0 = 5.0\ \text{m/s}^2$.

Q3. Forces of $50\ \text{N}$ forward and $20\ \text{N}$ backward act on a box. State the resultant force. [1 mark]

• Cue. $50 - 20 = 30\ \text{N}$ forward.