Force and Extension: Hooke's Law

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Enquiry questions

What is the relationship between force and extension for a spring, and at what point does the spring stop obeying Hooke's law?

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Concepts

This study delivers 1 primary concept and 4 secondary concepts.

Primary concept: Newton's Laws of Motion (PH-KS4-C008)

Type: Knowledge | Teaching weight: 3/6

Newton's first law: an object remains at rest or in uniform motion in a straight line unless acted upon by a resultant force. Newton's second law: the resultant force on an object equals its mass times its acceleration (F = ma); the acceleration is in the direction of the resultant force. Newton's third law: when object A exerts a force on object B, object B exerts an equal and opposite force on object A (action-reaction pairs).

Teaching guidance: Required Practical 20: investigate the effect of varying force and mass on acceleration. Pupils should be able to draw free body diagrams showing all forces on an object and determine the resultant force. Emphasise that Newton's third law pairs are always the same type of force (e.g., both gravitational, both contact) acting on different objects. Terminal velocity is important: as speed increases, drag increases until drag equals driving force (resultant force = 0, constant velocity). Use velocity-time graphs to analyse forces during acceleration and terminal velocity phases. Key vocabulary: resultant force, Newton's first law, Newton's second law, Newton's third law, acceleration, mass, inertia, free body diagram, terminal velocity, drag, friction, reaction force Common misconceptions: Students often state Newton's third law pairs as forces on the same object (e.g., 'weight and normal reaction are a Newton's third law pair'). These forces are equal and opposite but are NOT a Newton's third law pair because they act on the same object. Newton's third law pairs always act on different objects. Students also think that a stationary object has no forces acting on it — it has balanced forces (zero resultant).

Differentiation

Model response (Emerging): The book stays still because the forces on it are balanced. The weight (gravity pulling down) is equal to the normal contact force from the table pushing up. Since the resultant force is zero, the book remains at rest, as Newton's first law states.

Model response (Developing): Acceleration = Δv/t = (15 - 0)/10 = 1.5 m/s². Resultant force = ma = 1500 × 1.5 = 2250 N.

Model response (Secure): Initially, only weight acts downward so the skydiver accelerates at g (≈10 m/s²). As speed increases, air resistance increases (proportional to velocity²), reducing the resultant downward force and hence the acceleration. When air resistance equals weight, the resultant force is zero and the skydiver reaches terminal velocity (Newton's first law). On deploying the parachute, air resistance suddenly exceeds weight, creating an upward resultant force that decelerates the skydiver (Newton's second law). Speed decreases, reducing air resistance, until a new lower terminal velocity is reached. The v-t graph shows increasing gradient initially, then decreasing gradient to a plateau, then a sharp decrease to a lower plateau.

Model response (Mastery): Component of weight along slope = mg sin30° = 50 × 10 × 0.5 = 250 N. Normal reaction = mg cos30° = 50 × 10 × 0.866 = 433 N. Friction = μR = 0.1 × 433 = 43.3 N. Resultant force down slope = 250 - 43.3 = 206.7 N. Acceleration = F/m = 206.7/50 = 4.13 m/s². The constant friction model is a simplification. At higher speeds, air resistance becomes significant and should be included as an additional retarding force. The coefficient of friction may also vary with speed — snow compaction and meltwater lubrication change with pressure and temperature. A more complete model would include a velocity-dependent drag term.

Secondary concept: Energy Stores and Transfers (PH-KS4-C001)

Type: Knowledge | Teaching weight: 3/6

Energy is stored in physical systems in various ways: kinetic (moving objects), gravitational potential (objects above a reference level), elastic potential (deformed objects), chemical (fuels, food), thermal (hot objects), nuclear (unstable nuclei), electromagnetic (electric/magnetic fields). Energy is neither created nor destroyed (conservation of energy) but transferred between stores by mechanical work, electrical work, heating or radiation. Useful energy transfers are always accompanied by dissipation to the thermal store of the surroundings.

Differentiation

Secondary concept: Current, Potential Difference and Resistance (PH-KS4-C003)

Type: Knowledge | Teaching weight: 3/6

Electric current (I) is the rate of flow of electric charge: I = Q/t. Potential difference (V) is the work done per unit charge: V = W/Q. Resistance (R) is the ratio of potential difference to current: R = V/I (Ohm's law). For an ohmic conductor at constant temperature, resistance is constant. Resistance of a filament bulb increases with temperature; a thermistor's resistance decreases with temperature; a diode allows current in one direction only.

Differentiation

Secondary concept: Particle Model, Density and Gas Laws (PH-KS4-C005)

Type: Knowledge | Teaching weight: 3/6

The particle model describes matter as composed of tiny particles in constant motion. In solids, particles vibrate about fixed positions; in liquids, particles can flow but remain in contact; in gases, particles move rapidly and are widely separated. Density (ρ = m/V) depends on particle mass and separation. Gas pressure is caused by particles colliding with the container walls. Increasing temperature increases the kinetic energy and speed of particles, increasing the rate and force of collisions.

Differentiation

Secondary concept: Momentum and Impulse (PH-KS4-C009)

Type: Knowledge | Teaching weight: 3/6

Momentum is the product of mass and velocity: p = mv. The total momentum of a system is conserved in any interaction where no external forces act (conservation of momentum). A force acting on an object changes its momentum: F = Δp/Δt (Newton's second law in terms of momentum). Impulse (FΔt) equals the change in momentum (Δp). Applying a force over a longer time to achieve the same change in momentum reduces the peak force (the principle behind safety features such as airbags and crumple zones).

Differentiation

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Thinking lens: Cause and Effect (primary)

Key question: What caused this to happen, and how do we know? Why this lens fits: Scientific observations and enquiry serve to establish causal relationships; framing questions around 'what causes X' gives purpose to the observation work. Question stems for KS4:

Is this a necessary cause, a sufficient cause, or a contributing factor?

What confounding variables could explain this relationship?

How would you design an investigation to establish causation, not just correlation?

In this causal chain, where could an intervention have the most effect?

Secondary lens: Evidence and Argument — This cluster asks pupils to gather, record or communicate scientific findings — the core cognitive demand is evaluating what counts as valid evidence and how to present it clearly.

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Session structure: Fair Test

Fair Test

The classic scientific enquiry: formulating a testable question, making a prediction based on scientific understanding, designing a method that controls variables, collecting and recording data systematically, analysing results, and drawing a conclusion linked back to the original hypothesis.

question → hypothesis → method → data_collection → analysis → conclusion Assessment: Structured scientific report including question, hypothesis with reasoning, method with variables identified, results table/graph, and conclusion evaluating whether results support the hypothesis. Teacher note: Use the FAIR TEST template: expect pupils to derive a testable hypothesis from scientific theory and design a rigorous method with appropriate controls, precision, and sample size. Guide analysis using statistical techniques or mathematical modelling where appropriate. Demand critical evaluation of validity, reliability, accuracy, and the extent to which results support or refute the hypothesis. KS4 question stems:

How does your hypothesis follow from the underlying scientific theory?

How have you ensured sufficient precision, accuracy, and reliability in your method?

What statistical analysis supports your conclusion?

To what extent do your results support the hypothesis, and what are the limitations?

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Variables

Independent: force applied to the spring (weight of masses, F = mg) Dependent: extension of the spring (cm or mm) Controlled: same spring, same starting length, same measurement technique, masses added gently (no bouncing)

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Equipment and safety

Equipment:

spring (known spring constant, or unknown for investigation)

clamp stand, boss and clamp

ruler with mm divisions

mass hanger and slotted masses (100g increments)

pointer attached to spring

safety goggles

soft landing surface below spring

Safety notes: Wear safety goggles — springs can detach or break under excessive load. Place a soft surface (foam mat) below the apparatus to catch falling masses. Do not exceed the elastic limit of the spring. Stand to one side when loading masses in case the spring breaks. Ensure the clamp stand is stable and weighted at the base. (Hazard level: low)

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Expected outcome

Extension is directly proportional to force up to the limit of proportionality — F = ke where k is the spring constant (N/m). The graph of force vs extension is a straight line through the origin in the proportional region. Beyond the limit of proportionality, the graph curves and the spring is permanently deformed. The spring constant k equals the gradient of the straight portion. Elastic potential energy Ee = ½ke² can be calculated for any extension.

Recording format: data table of mass, force (F=mg), total length, and extension, graph of force vs extension with limit of proportionality marked, gradient calculation for spring constant, elastic PE calculation

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Enquiry type

Fair Test

A controlled investigation where one variable is deliberately changed while all others are kept the same, to determine whether the changed variable has an effect on a measured outcome. The gold-standard enquiry type for causal questions in science.

Question stems:

How does [independent variable] affect [dependent variable]?

Does changing [variable] make a difference to [outcome]?

What is the relationship between [variable A] and [variable B]?

Teacher scaffold:

What will you change? (independent variable)

What will you measure or observe? (dependent variable)

What will you keep the same? (controlled variables)

What do you predict will happen? Why?

Was your prediction correct? What does the evidence show?

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Known misconceptions

Constant force needed for constant speed

What pupils may say: An object needs a constant force to keep moving at constant speed. Correct explanation: An object moving at constant speed has balanced forces acting on it — the driving force equals the resistive forces (friction, air resistance). No net force is needed to maintain constant velocity. This is Newton's first law: an object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted on by an unbalanced force. The confusion arises because on Earth, friction is always present, so we need to push to overcome it — but the push balances friction, it does not cause the motion. Diagnostic questions:

If you push a box at constant speed across the floor, what forces are acting on it?

In space with no friction, if you give an object a push and let go, what happens?

Does a car engine create the force that makes it go, or the force that overcomes friction?

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Why this study matters

Hooke's law produces the clearest proportional relationship in GCSE physics and is the foundation for understanding elastic potential energy. The investigation naturally reveals the limit of proportionality — the point where the graph deviates from a straight line — which teaches pupils that mathematical models have domains of validity. Calculating the spring constant from the gradient connects practical measurement to mathematical analysis. The energy stored (½ke²) extends the investigation into the energy topic, making this a highly interconnected practical.

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Pitfalls to avoid

Pupils measure total length rather than extension — extension = stretched length minus natural length; set up a clear reference point

Adding masses too quickly or dropping them, causing the spring to bounce — masses must be added gently and allowed to settle before reading

Pupils assume the straight line continues forever — the limit of proportionality is a critical concept; beyond it, the spring is permanently deformed

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Vocabulary word mat

Prior knowledge (retrieval plan)

Pupils should already know the following from earlier units:

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Scaffolding and inclusion (Y10)

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Knowledge organiser

Key terms:

force

extension

Hooke's law

spring constant

limit of proportionality

elastic deformation

plastic deformation

elastic potential energy

directly proportional

Newton

Core facts (expected standard):

Newton's Laws of Motion: Applies Newton's laws to multi-force problems including friction, air resistance, and terminal velocity. Interprets velocity-time graphs to determine acceleration and resultant force. Analyses the forces during real scenarios such as skydiving and braking.

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Graph context

Node type: ScienceEnquiry | Study ID: SE-KS4-016 Concept IDs:

PH-KS4-C008: Newton's Laws of Motion (primary)

PH-KS4-C001: Energy Stores and Transfers

PH-KS4-C003: Current, Potential Difference and Resistance

PH-KS4-C005: Particle Model, Density and Gas Laws

PH-KS4-C009: Momentum and Impulse

Cypher query:

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-[:HAS_DIFFICULTY_LEVEL]->(dl)

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Generated from the UK Curriculum Knowledge Graph — zero LLM generation.