MYP integrated science

PS2.1 — Introduction to Mechanical Energy

In Unit 1 you investigated how waves transfer energy without moving matter. This unit focuses on mechanical energy — the energy of moving objects and stored energy due to position or deformation. Today you’ll explore different forms of mechanical energy and see how energy is conserved and transferred between them.

Objectives

Identify the main forms of mechanical energy: kinetic, gravitational potential, and elastic potential.
Describe energy transfer and the principle of conservation of energy.
Give everyday examples of energy transformation between different forms.

Key Ideas & Example

Mechanical energy includes kinetic energy (moving objects), gravitational potential energy (raised objects), and elastic potential energy (stretched or compressed materials).

Principle of conservation: Energy cannot be created or destroyed; it can only change from one form to another.

Example: A roller coaster at the top of a hill has maximum GPE. As it descends, GPE is converted into KE. At the bottom, KE is maximum, but total energy (GPE + KE) stays the same.

Activity — Mechanical energy circus

Apparatus and materials

Toy car + ramp (KE and GPE).
Spring or rubber band (EPE).
Weights and pulley (GPE → KE).
Simple pendulum.
Worksheet for recording observations.

Procedure (30-minute working window)

Divide class into small groups. Set up 3–4 quick “stations” demonstrating KE, GPE and EPE.
At each station, perform the activity once and record: (1) energy at start, (2) energy at end, (3) how energy was transferred.
Rotate every 7–8 minutes until all stations have been observed.
As a group, complete a simple concept map linking the three forms of mechanical energy with arrows showing transfers.

Safety

Check ramps and weights are stable before use.
Ensure no one is in the way of moving toy cars or pendulums.
Keep elastic bands/springs under control to avoid snapping hazards.

Discussion prompts

Where did the energy “go” in each demo? Was it lost or just transformed?
Which examples showed energy stored and then released?
How do these simple systems demonstrate the principle of conservation of energy?

Summary

Mechanical energy includes KE, GPE, and EPE.
Energy is conserved: total energy stays the same though forms change.
Everyday systems show transformations between mechanical energy types.

Check your understanding

1) A stretched rubber band is released. Which type of energy is converted into which?

2) Why is the total energy of a roller coaster (ignoring friction) the same at the top and bottom of a hill?

3) Name one example of KE being transformed into GPE in everyday life.

PS2.2 — Mechanical energy formulae

Last lesson you saw examples of mechanical energy and how it is conserved. Today we link these ideas to mathematics by introducing the formulae for kinetic, gravitational potential and elastic potential energy, and using a simulation to visualise energy transfers.

Objectives

Recall and use the formulae for kinetic energy (KE), gravitational potential energy (GPE), and elastic potential energy (EPE).
Perform simple calculations involving KE, GPE, and EPE.
Use a simulation to visualise energy transfers and conservation.

Key Formulae

KE = ½mv² (m = mass in kg, v = velocity in m·s^-1)

GPE = mgh (m = mass in kg, g = 9.8 m·s^-2, h = height in m)

EPE = ½kx² (k = spring constant in N·m^-1, x = extension in m)

Example: A 2.0 kg mass lifted 1.5 m gains GPE = 2.0 × 9.8 × 1.5 = 29.4 J.

Activity — Energy calculations and PhET simulation

Apparatus and materials

Worksheet with KE, GPE, and EPE calculation problems.
Calculators.
Computers/tablets with PhET Energy Skate Park.

Procedure (30-minute working window)

Start with 2–3 worked examples as a class (KE, GPE, EPE).
In pairs, complete worksheet problems (increasing difficulty).
Open PhET Energy Skate Park. Observe energy bar charts for a skater at different positions on a track.
Record one example where GPE is high, one where KE is high, and one where energies are balanced.
Extension: Explore effect of friction toggle on energy conservation (energy transfer to heat).

Safety

No physical hazards (calculation and simulation activity).

Discussion prompts

How do the formulae for KE, GPE, and EPE link to the situations you saw last lesson?
What does the Energy Skate Park simulation show about conservation of energy?
How does friction change the energy bar charts?

Summary

Kinetic, gravitational potential, and elastic potential energy have simple formulae.
Total energy in a system is conserved, but may transform between KE, GPE, and EPE.
Simulations help visualise abstract energy transfers and conservation.

Check your understanding

1) A 1.5 kg ball is moving at 4.0 m·s^-1. What is its KE?

2) A 3.0 kg object is lifted 2.0 m. How much GPE does it gain?

3) A spring has k = 20 N·m^-1 and extension 0.10 m. Calculate its EPE.

PS2.3 — Work done basics

Last lesson you used formulae for KE, GPE and EPE to calculate energy values and saw how energy is conserved. Today we turn to the concept of work done — how forces transfer energy when they act through a distance.

Objectives

Define work done as force × distance moved in the direction of the force.
State and use the formula W = Fd.
Recognise that work is measured in joules (J) and connects to energy transfer.

Key Ideas & Example

Work done: When a force moves an object through a distance, energy is transferred.

Formula: W = F × d (F in newtons, d in metres, W in joules).

Example: A student pushes a box with 25 N force over 2.0 m. Work done = 25 × 2.0 = 50 J.

Activity — Measuring work done

Apparatus and materials

Masses or weights (2–5 kg).
Spring balance or force sensor.
Trolley and ramp (optional).
Metre sticks or tape measures.
Worksheet for data table.

Procedure (30-minute working window)

Attach spring balance to a weight. Lift it vertically by 0.5 m, record the force (≈ weight) and distance.
Calculate work done (W = Fd). Compare with increase in GPE (mgh).
Repeat using trolley pulled along a flat surface for 1–2 m. Record force and distance, calculate W.
Optional: Compare with ramp — less force but more distance → same work overall.
Groups complete at least two examples, then answer: How is work done related to energy transfer?

Safety

Lift weights safely, bending knees if necessary.
Keep ramp stable; prevent trolley from rolling freely into people.

Discussion prompts

Why is work measured in joules — the same as energy?
How does lifting a weight illustrate both work done and increase in potential energy?
What is the difference between applying a force and actually doing work?

Summary

Work done = force × distance in the direction of the force.
Work is measured in joules and equals energy transferred.
Lifting, pulling, or pushing examples show clear links between work and changes in energy.

Check your understanding

1) How much work is done when a 20 N force moves an object 3.0 m?

2) A student lifts a 5.0 kg mass through 0.40 m. How much work is done (take g = 9.8 m·s^-2)?

3) Why is no work done if you push hard on a wall that does not move?

PS2.4 — Work done in real life

In the last lesson you defined work done as force × distance and measured it in simple cases. Today we apply this idea to real-life scenarios, including motion with and without friction, and compare the effect of resistive forces on energy transfer.

Objectives

Apply the formula W = Fd to different real-life contexts.
Describe the effect of resistive forces (like friction) on work done and energy transfer.
Explain how work done by friction converts useful energy into heat.

Key Ideas & Example

When friction is absent, all work done contributes to useful energy (e.g., lifting = GPE gained). With friction, some work is dissipated as heat.

Example: A box is pushed 3.0 m across a smooth surface with a 50 N force. Work done = 150 J, all stored as KE. On a rough surface with 40 N friction opposing, net force = 10 N, so KE gained = 30 J. The missing 120 J is work done against friction → heat.

Activity — Comparing work with and without friction

Apparatus and materials

Trolley or block with hook for pulling.
Spring balance (to measure pulling force).
Flat surface (smooth and rough, e.g., table + sandpaper strip).
Metre stick, worksheet.

Procedure (30-minute working window)

Use spring balance to pull trolley 1.0 m across a smooth surface at steady speed. Record force and distance, calculate W.
Repeat across rough surface. Record larger force needed, calculate W.
Compare results: where did the extra work go?
Optional: Push trolley up a ramp at steady speed. Work against gravity = GPE gained; additional work may be lost to friction.

Safety

Ensure surfaces are stable; avoid pulling too hard or jerking the trolley.
Keep walkway clear of obstacles.

Discussion prompts

Why is the work done greater on the rough surface compared to the smooth surface?
What forms of energy are produced by friction?
How do engineers reduce unwanted work done by resistive forces?

Summary

Work done is calculated the same way in all cases: W = Fd.
In real life, resistive forces like friction mean more work must be done for the same motion.
Work done against friction converts energy into heat and sometimes sound.

Check your understanding

1) Why is more work required to push a box across a carpet than a smooth floor?

2) A 60 N force pulls a trolley 2.0 m at steady speed on a rough surface. Work done = ?

3) Where does this work go if the trolley’s speed is constant?

PS2.5 — Energy conservation down a ramp (data collection)

In the last lesson you applied work done to real-life examples with and without friction. Today you will measure how gravitational potential energy (GPE) at the top of a ramp changes into kinetic energy (KE) at the bottom, and use the results to estimate the work done against friction.

Objectives

Measure the GPE of an object at the top of a ramp and its KE at the bottom.
Compare GPE and KE values to estimate energy lost to friction.
Apply the principle of conservation of energy in a practical context.

Key Ideas & Example

Conservation of energy: In an ideal ramp (no friction), GPE lost = KE gained.

With friction: Some energy is transferred to heat/sound → KE gained is less than GPE lost.

Example: A 0.50 kg block is raised 0.40 m (GPE = 0.50 × 9.8 × 0.40 = 2.0 J). At the bottom its KE = 1.6 J. The missing 0.4 J was work done against friction.

Activity — Block of ice down a ramp

Apparatus and materials

Small block of ice (or alternative sliding object).
Wooden ramp with protractor to measure angle.
Mass balance to measure mass of block.
Metre stick or ruler to measure height of ramp.
Stopwatch or light gates to measure speed at bottom.
Towels/tray to catch ice and avoid slipping hazard.

Procedure (30-minute working window)

Measure the mass of the block (m) and the vertical height of the ramp (h).
Calculate GPE at top: mgh.
Release block from rest at top. Measure time over final 0.5 m, calculate velocity at bottom (v = d/t).
Calculate KE at bottom: ½mv².
Compare GPE lost and KE gained. Record difference as energy lost to friction.
Repeat 2–3 trials and average results.

Safety

Ice blocks are slippery: catch them in a tray at the ramp base.
Wipe up meltwater immediately to prevent slips.

Data table (example)

Mass (kg): ____
Height (m): ____ → GPE (J) = mgh
Time (s): ____ → v (m·s^-1) = d/t
KE (J) = ½mv²
Energy lost to friction (J) = GPE – KE

Summary

On a ramp, GPE converts mainly into KE, but friction reduces the amount observed.
Energy “lost” is actually transferred to heat/sound by friction.
Conservation of energy allows us to calculate energy changes even with friction present.

Check your understanding

1) A 1.0 kg block slides down a 0.50 m ramp. GPE lost = ?

2) At the bottom, speed = 2.0 m·s^-1. KE = ?

3) How much energy was lost to friction in this case?

PS2.6 — Energy conservation down a ramp (presentation & simulation)

Last lesson you measured GPE at the top of a ramp and KE at the bottom, and calculated energy lost to friction. Today you will present your results to the class, compare trends between groups, and then use a simulation to explore energy transfers in an idealised system.

Objectives

Present and compare experimental results on energy conservation down a ramp.
Identify how friction affects the relationship between GPE lost and KE gained.
Use a simulation to visualise energy conservation in frictionless and resistive systems.

Key Ideas

Conservation of energy: Without friction, GPE lost = KE gained exactly. With friction, KE gained < GPE lost; the difference is energy transferred to heat/sound.

Simulations: Energy bar charts make conservation clear — as one store decreases, another increases, with total energy remaining constant.

Activity — Results presentation and simulation

Apparatus and materials

Student worksheets and data tables from Lesson 5.
Whiteboard/flipchart or projector for group reporting.
Computers/tablets with PhET Energy Skate Park.

Procedure (30-minute working window)

Each group shares one set of results (GPE, KE, energy lost to friction).
As a class, compare results: did all groups see GPE > KE? How consistent were the losses?
Teacher highlights common trends and sources of error (timing, measurement accuracy).
Students then explore PhET Energy Skate Park in pairs. Use “Bar Chart” view to observe energy transfers.
Toggle friction on/off. Record differences in how energy bars change.

Safety

No physical hazards — computer-based work after presentations.

Discussion prompts

How close was your measured KE to the calculated GPE?
What do the PhET energy bars show when friction is set to zero?
How does the simulation confirm the principle of conservation of energy?

Summary

Real ramps show friction losses: KE gained is less than GPE lost.
Simulations confirm energy is conserved — total remains constant even if distributed differently.
Comparing experiment and simulation deepens understanding of energy conservation.

Check your understanding

1) Why did your experimental KE values differ from your GPE values?

2) In the PhET simulation with no friction, what happens to the total energy?

3) What forms of energy increase when friction is turned on in the simulation?

PS2.7 — Elastic potential energy

In the last lesson you compared experimental results with a simulation to confirm the principle of energy conservation. Today you will focus on elastic potential energy (EPE) — energy stored in a stretched or compressed spring. You’ll test Hooke’s law, plot a force–extension graph, and calculate the energy stored.

Objectives

State Hooke’s law: extension is proportional to force until the elastic limit.
Plot and interpret a force–extension graph for a spring or elastic band.
Calculate EPE using EPE = ½kx².

Key Ideas & Example

Hooke’s law: F = kx, where F = force in newtons, x = extension in metres, k = spring constant in N·m^-1.

Elastic potential energy: EPE = ½kx².

Example: A spring with k = 40 N·m^-1 is stretched 0.10 m. EPE = ½ × 40 × (0.10)² = 0.20 J.

Activity — Stretching a spring

Apparatus and materials

Clamp stand, spring, and pointer/ruler.
Slotted masses (50 g–200 g).
Metre stick or ruler to measure extension.
Graph paper (or spreadsheet if available).

Procedure (30-minute working window)

Set up spring vertically with pointer aligned at zero on ruler.
Hang 50 g mass, measure extension. Add masses in 50 g steps up to ~200–300 g, record force (F = mg) and extension (x).
Plot F vs x. Draw best-fit straight line through proportional region.
Calculate spring constant k from gradient (F/x).
Pick one extension value, calculate EPE = ½kx². Compare with area under F–x graph triangle.

Safety

Ensure clamp stand is stable and cannot topple.
Do not overload spring beyond elastic limit; stop if spring is permanently deformed.

Discussion prompts

Does your graph show proportionality (straight line through origin)?
How can you tell when Hooke’s law no longer applies?
Why is EPE proportional to the square of extension?

Summary

Hooke’s law: F ∝ x, valid up to the elastic limit.
Spring constant k = gradient of F–x graph.
Elastic potential energy = ½kx², equal to area under the F–x graph.

Check your understanding

1) What does Hooke’s law state?

2) A spring extends 0.08 m when loaded with 4.0 N. What is its spring constant?

3) How much EPE is stored in this spring at 0.08 m extension?

PS2.8 — Conservation of mechanical energy in catapults (design)

Last lesson you measured elastic potential energy in springs and rubber bands. Today you will apply that knowledge by designing and beginning to build a simple catapult. The aim is to show how elastic potential energy is converted into kinetic energy and gravitational potential energy, and to consider efficiency.

Objectives

Design and build a simple catapult using everyday materials.
Explain how elastic potential energy is transformed into kinetic and gravitational potential energy.
Consider energy efficiency in practical systems.

Key Ideas & Example

Catapults: Store elastic energy in a stretched or bent material (rubber band, stick, spoon). On release, EPE → KE of projectile + GPE if it rises.

Efficiency: Not all stored energy becomes useful KE. Some is lost as heat, sound, and deformation.

Example: A rubber band catapult stores 0.50 J of EPE. Projectile KE = 0.35 J, so efficiency = (0.35 / 0.50) × 100 = 70%.

Activity — Catapult design & build

Apparatus and materials

Craft sticks, plastic spoons, elastic bands, tape, glue, cardboard, small projectiles (marshmallows, paper balls).
Rulers, protractors, measuring tape.
Worksheet for design sketch and notes.

Procedure (30-minute working window)

In groups, sketch a simple catapult design (lever arm, elastic storage, projectile holder).
Gather materials and begin construction.
Record where elastic energy is stored and how it is released.
Prepare a short explanation: Which energy transfers will occur when launching?
By end of lesson: design sketch, partly-built catapult, and notes on energy transfers.

Safety

Only use soft, safe projectiles (no sharp/hard objects).
Wear goggles if elastic bands are tightly stretched.
Keep workspaces clear and catapults pointed away from people.

Planning prompts

Where is elastic potential energy stored in your design?
How will you measure or estimate the energy transfers?
What design choices might improve efficiency?

Summary

Catapults demonstrate conversion of elastic potential energy into kinetic and gravitational potential energy.
Efficiency depends on how much stored energy is transferred usefully.
Design stage focuses on planning, safe construction, and energy transfer explanation.

Check your understanding

1) Which form of energy is stored in the stretched rubber band of a catapult?

2) Name two forms of energy that reduce efficiency in real catapults.

3) How can you make your catapult more efficient?

PS2.9 — Conservation of mechanical energy in catapults (presentation & testing)

In the last lesson you designed and started building a catapult to demonstrate energy conservation. Today you will finish construction, test your design, and present results showing how elastic potential energy was converted into kinetic and gravitational potential energy.

Objectives

Complete and test a working catapult model.
Measure performance (distance, height, or speed of projectile).
Explain energy transfers and evaluate efficiency.

Key Ideas

Catapults show energy conservation in action: elastic potential energy → kinetic energy + gravitational potential energy.

Efficiency can be estimated by comparing useful output (projectile KE + GPE) with input (elastic energy stored).

Example: Rubber band stores 1.0 J of EPE. Projectile KE + GPE = 0.7 J → efficiency = 70%.

Activity — Catapult testing and presentations

Apparatus and materials

Catapults built in Lesson 8.
Soft projectiles (marshmallows, paper balls).
Measuring tape, metre sticks, stopwatch (optional).
Worksheets/log sheets for results.

Procedure (30-minute working window)

Finish any last construction adjustments.
Test-launch projectiles. Record distance travelled, maximum height, or time of flight.
Estimate KE or GPE at peak if data allow (optional with advanced groups).
Groups prepare a short 2-minute presentation: describe design, show results, explain energy transfers, and discuss efficiency.
Present to class. Audience notes one strength of each design.

Safety

Only use soft projectiles; never aim at people.
Wear goggles if high-tension bands used.
Maintain safe distances during launches.

Discussion prompts

Which designs travelled furthest/most accurately? Why?
Where was energy lost in your catapult?
How might efficiency be improved?

Summary

Catapults convert stored elastic energy into projectile motion.
Testing provides evidence of energy transfers and system efficiency.
Presentations show how different designs balance distance, height, and control.

Check your understanding

1) What forms of energy did your catapult convert?

2) How did you know some energy was lost as heat or sound?

3) Suggest one design change to improve your catapult’s efficiency.

PS2.10 — Review and assessment

Last lesson you completed and tested catapults, presenting how elastic energy transformed into kinetic and gravitational energy. Today you will consolidate the whole unit: reviewing key concepts, completing a short quiz, and reflecting on misconceptions.

Objectives

Review the main formulae for KE, GPE, EPE and work done.
Apply the principle of conservation of energy to problem-solving.
Reflect on personal understanding and identify areas to improve.

Key Ideas

KE = ½mv², GPE = mgh, EPE = ½kx², W = Fd.

Conservation of energy: Total energy remains constant, though forms may change.

Efficiency = useful output ÷ total input × 100.

Activity — Quiz and reflection

Apparatus and materials

Printed quiz sheets (10–12 short questions: mix of conceptual and calculation).
Whiteboards or notebooks for quick review tasks.
Reflection sheets (“one thing I understand well, one thing to work on”).

Procedure (30-minute working window)

Quick recap: ask 2–3 oral questions (energy forms, formulae, conservation).
Students complete end-of-unit quiz individually (~15 minutes).
Self-mark or peer-mark with class discussion of answers.
Complete reflection sheet to record confidence and next steps.
Optional: Kahoot or online quiz for interactive review.

Safety

No safety hazards (paper-based activity).

Discussion prompts

Which calculation did you find easiest? Which most difficult?
How does the principle of conservation of energy apply in real life?
What concept would you like more practice with?

Summary

The unit covered KE, GPE, EPE, work done, and conservation of energy.
Experiments and projects showed how these energies transfer in real systems.
The principle of energy conservation underpins all these ideas.

Check your understanding

1) State the formulae for KE, GPE, and EPE.

2) What does conservation of energy mean in your own words?

3) Give one everyday example of energy efficiency less than 100%.

Now test yourself

Click on the button below to access the self-tests for MYP9 and MYP10.

MYP Self-test

Physical Science Enhancement - Physics 2 - Mechanical energy

Introduction

Content