Motion, forces and energy

Learning objectives

• Use motion graphs and Newton’s laws.
• Apply conservation of momentum and energy.
• Calculate density, moments, pressure and efficiency.

The big idea

Describe motion before explaining it: graph gradients represent rates, while the area under a speed–time graph gives distance. Forces change momentum; moments describe turning effects about a pivot.

Choose a conservation model suited to the system. Momentum is conserved when external resultant force is negligible, while energy transfers must include thermal stores. Density and pressure connect everyday measurements to material behaviour.

Topics to connect

• Measurement
• Motion graphs
• Mass and weight
• Density
• Forces and moments
• Momentum
• Energy transfers and resources
• Work, power and efficiency
• Pressure

1. Measurement and motion graphs

Select instruments for the range and resolution needed, correct a known zero error and repeat readings. A distance–time gradient gives speed; the area under a speed–time graph gives distance. On a velocity–time graph, gradient is acceleration and signed area is displacement. For a bicycle going out and back, total distance can be positive while displacement is zero. Constant acceleration means equal velocity changes in equal times, not equal distances.

2. Mass, density and pressure

Mass is measured in kilograms; weight W = mg is a force in newtons. Density ρ = m/V connects mass with occupied volume. Measure an irregular sinking solid’s volume by water displacement, checking that it does not dissolve or trap air. Pressure p = F/A explains why a narrow heel exerts more pressure than a broad shoe carrying the same weight. Fluid pressure increases with vertical depth; the container’s width does not set that pressure.

3. Forces and turning effects

A resultant force changes velocity; balanced forces allow rest or steady straight-line motion. A spring’s extension is proportional to load only within its proportional range. A moment uses force multiplied by perpendicular distance from a pivot. A door handle is easier to use far from the hinge because the same force produces a greater moment. Stable equilibrium also depends on where the centre of gravity lies relative to the support base.

4. Momentum and stopping

Momentum p = mv has direction. In an isolated collision, add momenta with signs before and after; equal speeds do not imply equal momenta when masses differ. Impulse is change of momentum. A cushioning material can reduce average stopping force by extending stopping time for the same momentum change. Kinetic energy is not conserved in every collision: some can become internal energy, sound or deformation.

5. Energy, resources, work and efficiency

Mechanical work is the force component along displacement multiplied by distance. Kinetic energy is ½mv², gravitational energy change is mgΔh and power is energy transferred per second. Efficiency compares useful output with total input using matching quantities. A 100 J input giving 70 J useful output has 70% efficiency, not 30%. Compare energy resources by availability, reliability, environmental effects and energy transfers: renewable does not mean impact-free, and fossil fuels involve finite chemical stores.

A method you can reuse

1. Choose a system and sketch its motion or forces.
2. Convert mass, length, time and area to compatible units.
3. Select a graph, force, momentum or energy model that fits the question.
4. Keep direction signs for vectors and include dissipative transfers.
5. Check units, size and conservation before rounding.

Equations and relationships

Investigate and explain

Time a trolley over equal intervals or use simulation data. Plot velocity against time and estimate acceleration.

Use separate models for resultant force, moments, density and energy. A friction-free simulation is an ideal case; it does not justify ignoring friction in every real mechanism.

Open the interactive investigation

Check your understanding