QCE Physics - Unit 2 - Linear motion and force

Newton's laws, forces and free-body diagrams

Learn forces and motion for QCE Physics Unit 2 with worked reasoning, equations, original diagrams and checked practice.

Part of the free QCE Physics notes library for Unit 2: Linear motion and force.

Updated 2026-08-09 - 7 min read

Construct free-body diagrams and apply Newton's laws to one-dimensional resultants. This note is designed for active learning: predict the physical outcome before calculating, state the system and assumptions, and then use an equation or diagram to make the reasoning testable. Physics becomes reliable when words, signs, graphs, units and energy or momentum ledgers all tell the same story.

The physical model

A force is an interaction, and acceleration follows the vector sum of all external forces. Newton's third-law pairs act on different objects, so they never cancel on one object's free-body diagram.

A useful physics model deliberately leaves some features out. Before using it, name the system boundary, the time interval and the conditions that make the relationship appropriate. For a thermal problem this may mean negligible energy loss; for a circuit it may mean ideal wires and meters; for motion it may mean one dimension or constant acceleration; for a wave it may mean a uniform medium. An assumption is not a weakness when it is visible and justified. It becomes a problem only when the conclusion is extended beyond the model's conditions.

Physics explanations should form a causal chain: identify the interaction or energy transfer, state the relevant change, connect it to the mathematical relationship, then describe the observable consequence. Avoid replacing that chain with a label such as "because of inertia", "because heat rises" or "because waves bend". The label names the topic; the chain explains it.

Governing relationships

$ \sum F=F_{\mathrm{net}}=ma $

$ F_g=mg $

Write the relationship before substituting numbers. Define the sign convention and translate every value into SI units unless the equation or data book clearly permits another unit. A negative answer can represent direction or a decrease; it is not automatically an arithmetic error. A positive magnitude without a stated direction can still be incomplete.

Check dimensions before accepting an answer. Joules, watts, volts, newtons and pascals are compact descriptions of base-unit relationships, not decorative labels. If the units do not reduce to the requested quantity, the calculation cannot be correct even when the calculator work is flawless.

Build the concept connections

1. Interpret the model

Newton's first law describes zero resultant force: velocity remains constant, which includes rest. The second law links non-zero resultant to acceleration. The third law links equal and opposite forces between interacting objects.

2. Connect the evidence

A free-body diagram isolates one object and draws only forces acting on it: weight, normal force, tension, friction, drag or an applied interaction as relevant.

3. Protect the boundary conditions

Normal force is a contact response perpendicular to a surface and is not automatically equal to weight. Its value follows from the force balance for the actual motion.

The diagram above is a reasoning tool rather than decoration. Recreate it from memory and annotate the invariant quantities, the quantities that change and the boundary conditions. If the context changes, ask which arrows, graph regions or force labels must change. That comparison is often the fastest route through an unfamiliar question.

A repeatable method

1. Choose one object as the system and sketch it as a point or simple box.
2. Identify each external interaction and draw a labelled force arrow from the object.
3. Choose a positive axis and convert arrows into signed force components.
4. Apply $\sum F=ma$ and interpret the sign of acceleration physically.

This sequence is a scaffold, not a sentence template. A short numerical response may compress several decisions into one line, while an investigation or explanation must keep the evidence visible. Do not substitute until the system, direction and model have been chosen. Preserve unrounded intermediate values and round only the final result to precision supported by the supplied data.

Worked example

Cover the steps and reproduce the solution from the problem statement. Then change one condition: reverse a direction, double a quantity, introduce a loss, change the boundary or swap a series connection for a parallel one. Predict the effect before recalculating. This counterfactual check exposes whether the method is understood or merely copied.

Experimental and graphical reasoning

Physics data are measurements with uncertainty, not exact copies of equations. Start by reading both axes, units and scale. Decide whether the useful information is a point value, intercept, gradient, area or curve shape. Quote processed evidence when it supports a claim, but always explain the physical meaning of that evidence.

A gradient should be found from well-separated points on a best-fit line rather than two convenient raw points. Where minimum and maximum plausible lines are available, compare their gradients to estimate uncertainty. An area must include the graph's units and sign. A straight line through the origin can support proportionality only when the uncertainty and physical model make a non-zero intercept implausible.

Repeated trials reveal random variation and allow averaging, but they do not remove a systematic offset, energy leak, miscalibrated sensor or consistently wrong zero. Improve validity by changing the method so the dependent variable genuinely measures the stated construct and the relevant confounding variables are controlled. Improve reliability through repeatable procedures and sufficient measurements.

When evaluating evidence, separate the observed pattern from the inference. State a limitation by explaining its likely direction and consequence: for example, energy transferred to the surroundings makes an ideal calorimetry value too low, or uncorrected background count makes a decay reading too high. "Human error" is rarely specific enough to guide an improvement.

Common mistake and repair

The repair matters because an answer can contain a familiar formula and still use the wrong physical model. Before moving on, audit direction, conservation, units and limiting behaviour. Ask what should happen if a key quantity becomes zero, doubles or grows very large. A result that violates that prediction needs investigation.

Practice and verification

Now attempt the second check without returning to the worked example:

• A $4.0,\mathrm{kg}$ object has net force $-12,\mathrm N$. What is its acceleration?

Then attempt this unfamiliar transfer:

• A skydiver moves downward at constant terminal velocity. Which force statement is correct?

For each answer, add one verification sentence. Suitable checks include a reverse substitution, a conservation ledger, graph-area units, an independent equation, a limiting case or a qualitative prediction of direction and scale.

Assessment transfer

In lift, towing or terminal-speed contexts, decide whether velocity or acceleration is constant before declaring the net force.

In a QCAA-style response, match the cognitive verb. Describe the relevant features accurately. Explain the causal relationship. Analyse patterns, relationships and uncertainty in supplied evidence. Evaluate a claim or process against explicit criteria and evidence. Solve with a visible model choice, substitutions, units, appropriate precision and a physical interpretation.

Use diagrams deliberately. Force arrows should begin on the isolated object and name real interactions. Ray angles should be measured from a normal. Circuit diagrams should use standard symbols and unambiguous nodes. Graphs should label variables and units. A clear figure can earn its place by preventing an assumption from remaining hidden.

Before submitting, use this checklist:

• The system and positive direction are stated where relevant.
• The equation's conditions match the context.
• Every substituted value has compatible units.
• Conservation of charge, energy or momentum has been checked where applicable.
• The final result includes direction, sign and appropriate precision.
• The conclusion distinguishes measured evidence from inference.
• A limitation explains how confidence or the result is affected.

Sources

• QCAA Physics subject page
• QCAA Physics 2025 v1.3 syllabus
• QCAA Physics formula and data book
• OpenStax University Physics

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