In simple terms
A friendly intro before the formal notes — no formulas yet.
Gravitational potential energy and kinetic energy
Cambridge 9702 Paper 2 - Gravitational potential energy and kinetic energy (5.2). Senpai Corner diagram-backed pilot with premium structure and live visuals.
- 1
GPE depends on mass, gravity, and vertical height.
- 2
The reference point for 'h' is arbitrary; it defines where GPE is zero.
- 3
Work done against gravity increases GPE.
- 4
GPE is a scalar quantity, and can be positive or negative.
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 5.2.1
Derive, using , the formula for gravitational potential energy changes in a uniform gravitational field
- 5.2.2
Recall and use the formula for gravitational potential energy changes in a uniform gravitational field
- 5.2.3
Derive, using the equations of motion, the formula for kinetic energy
- 5.2.4
Recall and use
Explore the concept
Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.
Step-synced diagram — highlights what to look for in the simulation above.
GPE = mgh (near Earth’s surface); KE = ½mv².
GPE = mgh (near Earth’s surface); KE = ½mv².
13 more simulations for this topic — run them in the Simulations section below
Simulations
Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.
13 simulations · 5 to start with
Start herein this order — each one shows a different piece of the topic
- 3JCN PhysicsStart here · 19702 5.1 · 9702 5.2 · IB A.3
Conservation of Energy (CoE)
Drop or launch an object and watch KE, PE and total energy bars update in real time
Why this one: Drop or launch an object and watch the KE and PE bars swap while their sum stays flat.
Try this
- Drop the object and watch the KE, PE and total energy bars.
- Launch it instead and compare the bars at the top of the flight.
Look for KE and PE trade off but their sum stays constant.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- The Physics ClassroomStart here · 29702 5.1 · 9702 5.2 · IB A.3
Stopping Distance
Skid a car to a stop from different speeds and compare the stopping distances
Why this one: Double the speed and the skid is four times longer: KE goes as v².
Try this
- Stop from one speed and read the distance.
- Double the speed and stop again.
- Compare the two distances.
Look for Stopping distance scales with the square of the speed.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- 3JCN PhysicsStart here · 39702 5.1 · 9702 5.2 · IB A.3
CoE on an Inclined Ramp
Slide a block down a ramp with chosen height and friction; track energy transfers
Why this one: Add friction and the KE at the bottom falls short of the PE lost by the work done against it.
Try this
- Set a height with no friction and slide the block; track the energy transfers.
- Add friction and compare the KE at the bottom.
Look for Without friction PE converts fully to KE; with friction the missing KE equals the work done against friction.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- The Physics ClassroomStart here · 49702 5.2 · 9702 5.1 · IB A.3
Roller Coaster Model
Build a first drop, a loop, or dips and hills and study the coaster's energy and speed along the track
Why this one: Speed is lowest at the highest point of the track; KE + PE is constant all the way round.
Try this
- Build a single drop and watch the speed.
- Add a loop and find where the speed is lowest.
- Add hills and compare their heights with the speed.
Look for Kinetic plus potential energy stays constant along the track.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- 3JCN PhysicsStart here · 59702 5.1 · 9702 5.2 · 9702 17.1
Energy Conservation Demonstration
Swing a pendulum and watch PE convert to KE and back through the cycle
Why this one: A pendulum has maximum PE at the extremes and maximum KE at the bottom; the total is constant.
Try this
- Swing the pendulum and watch PE and KE through one cycle.
- Note the energies at the extremes and at the lowest point.
Look for PE is maximum at the extremes, KE is maximum at the bottom, and the total stays constant.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
More simulations8 more on this topic — core ones first
- oPhysicsCore9702 5.1 · 9702 5.2 · 9702 17.2
Conservation of Mechanical Energy: Mass on a Vertical Spring
Mass oscillating on a vertical spring with live KE / GPE / EPE bar graphs; adjust mass and spring constant
Try this
- Watch the three bars through one full oscillation.
- Increase the mass and compare the bar heights.
- Increase the spring constant and compare the period.
Look for KE, GPE and EPE trade against each other while their total stays constant.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- The Physics ClassroomCore9702 5.1 · 9702 5.2 · IB A.3
Kinetic Energy
Relate the work done on an object to the kinetic energy it acquires, and see what friction changes
Try this
- Apply a force and read the kinetic energy gained.
- Add friction and compare the kinetic energy.
Look for Net work done equals the change in kinetic energy.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- The Physics ClassroomCore9702 5.1 · 9702 5.2 · IB A.3
It's All Uphill
Drive a car up a gently-sloped hill and a steep hill to the same summit and compare the work and energy
Try this
- Drive up the gentle hill and read the work done.
- Drive up the steep hill to the same summit.
- Compare the two values.
Look for Work done against gravity depends only on the height gained, not on the slope.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- SimuPhysicsCore9702 5.1 · 9702 5.2 · IB A.3
Work-Energy Theorem
Apply a force over a distance and track the work done and the kinetic energy as the motion proceeds
Try this
- Apply a force and read the work done.
- Compare the work with the kinetic energy gained.
- Double the distance and compare.
Look for Work done by the net force equals the change in kinetic energy.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- 3JCN PhysicsCore9702 3.3 · 9702 5.1 · 9702 5.2
Ballistic Pendulum
Fire a bullet into a hanging block; use swing height to find the bullet speed
Try this
- Fire the bullet into the hanging block and read the swing height.
- Use the height to find the bullet speed.
- Double the bullet speed and compare the swing height.
Look for Momentum is conserved in the impact and energy in the swing, so the swing height scales with the square of the bullet speed.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- 3JCN PhysicsCore9702 5.1 · 9702 5.2 · 9702 4.1
Antigravity?
Roll a double cone up a diverging V-track; see why its centre of mass actually falls
Try this
- Release the double cone on the diverging V-track and watch which way it rolls.
- Follow the centre of mass as the cone moves along the track.
Look for The cone rolls toward the wider end because its centre of mass drops as the track diverges, so gravitational potential energy still falls.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
Key formulas
Tap any symbol to reveal exactly what it means and its units.
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Full topic notes
Formal explanation with the rigour you need for the exam.
Kinetic Energy: The Energy of Motion
Any object that is moving possesses kinetic energy. The faster an object travels and the more mass it has, the greater its kinetic energy. This energy is a scalar quantity, meaning it only has magnitude, not direction. Think of a bullet fired from a gun, a car on a motorway, or even electrons moving in a circuit - they all have kinetic energy!
Where:
- is kinetic energy (Joules, J)
- is the mass of the object (kilograms, kg)
- is the speed of the object (metres per second, m s\textsuperscript{-1})
Derivation of Kinetic Energy
The kinetic energy of an object is equal to the work done on the object to accelerate it from rest to its final speed. We can derive this from the definitions of work and acceleration. Consider an object of mass at rest () that is accelerated by a constant force over a distance . The work done is . From Newton's second law, . Substituting this gives . Using the kinematic equation , and since , we have , which rearranges to . Substituting this into our work equation gives . Since the work done is equal to the kinetic energy gained, we arrive at the formula .
Gravitational Potential Energy: Stored Height Energy
Gravitational potential energy (GPE) is the energy an object has stored due to its position within a gravitational field, specifically its vertical height. When you lift an object, you do work against gravity, and this work is stored as GPE in the object. This stored energy is ready to be converted into other forms, like kinetic energy, if the object is allowed to fall.
$GPE = mgh$
Where:
- is gravitational potential energy (Joules, J)
- is the mass of the object (kilograms, kg)
- is the acceleration due to gravity (metres per second squared, m s\textsuperscript{-2})
- is the vertical height above a chosen reference point (metres, m)
Derivation of Gravitational Potential Energy
The change in gravitational potential energy is defined as the work done to move an object vertically against a uniform gravitational field. To lift an object of mass to a vertical height , a force must be applied that is at least equal to its weight, . The work done () is the product of this force and the vertical distance moved, . Therefore, . This work done against the gravitational field is stored as gravitational potential energy. Thus, the change in GPE is given by $\Delta E_p = mgh$.
GPE depends on mass, gravity, and vertical height.
The reference point for 'h' is arbitrary; it defines where GPE is zero.
Work done against gravity increases GPE.
GPE is a scalar quantity, and can be positive or negative.
GPE formula $mgh$ is valid for uniform gravitational fields (near Earth's surface).
The Principle of Conservation of Energy
One of the most fundamental laws in physics is the Principle of Conservation of Energy. It states that in a closed, isolated system, the total amount of energy remains constant. Energy cannot be created or destroyed; it can only be transformed from one form to another. In the context of mechanics, if there are no non-conservative forces like friction or air resistance, the total mechanical energy (the sum of GPE and KE) is conserved. This means that as an object moves, its GPE can become KE, or vice versa, while the total stays the same.
Total energy in a closed system is constant.
Energy transforms, e.g., GPE KE.
Falling objects convert GPE to KE.
Rising objects convert KE to GPE.
This ideal applies when resistive forces are negligible.
The Role of Resistive Forces
In real-world scenarios, perfectly conserved mechanical energy (GPE + KE) is rare. Resistive forces, such as air resistance or friction, are non-conservative forces that do work on moving objects. This work done against resistance converts some of the mechanical energy into internal energy (heat and sound), which is dissipated into the surroundings. Therefore, the total energy of the universe is still conserved, but the mechanical energy of the specific system decreases. The energy lost is equal to the work done by the resistive forces.
Work done by resistive forces = Change in mechanical energy
Where
Resistive forces reduce mechanical energy.
Air resistance and friction are common examples.
Mechanical energy converts into internal energy (heat).
Total energy is always conserved, but not always mechanical energy.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
A 2.0 kg ball is dropped from a height of 15 m above the ground. Calculate its speed just before it hits the ground, assuming negligible air resistance. (Take m s\textsuperscript{-2})
- 1
Principle: By the principle of conservation of energy, the initial GPE is converted into final KE.
A box of mass 5.0 kg is pushed up a rough slope inclined at 30° to the horizontal. It is given an initial speed of 8.0 m/s at the bottom and travels 4.0 m up the slope before coming to rest. Calculate the work done against the resistive forces. (Take m s\textsuperscript{-2})
- 1
Initial Energy: Calculate the total mechanical energy at the bottom of the slope. We define the initial height as .
How it all connects
The big idea sits in the middle — tap a linked idea to explore the link.
Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.
Glossary
Key terms for this topic — skim now; the Check step will test them.
- Gravitational potential energy (GPE)
Gravitational potential energy (GPE) is the energy an object has stored due to its position within a gravitational field, specifically its vertical height.
- Principle of Conservation of Energy
One of the most fundamental laws in physics is the Principle of Conservation of Energy. It states that in a closed, isolated system, the total amount of energy remains constant.
- air resistance
Resistive forces, such as air resistance or friction, are non-conservative forces that do work on moving objects. This work done against resistance converts some of the mechanical energy into internal energy (heat and sound), which is dissipated into the surroundings.
- internal energy
This work done against resistance converts some of the mechanical energy into internal energy (heat and sound), which is dissipated into the surroundings.
Quick check
Write your answer first, then compare it with the model one — the gap is what you would have lost.
Teach it back
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Teach it back
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Revision flashcards
Guess first, then flip — retrieval beats re-reading.
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
GPE depends on mass, gravity, and vertical height.
The reference point for 'h' is arbitrary; it defines where GPE is zero.
Work done against gravity increases GPE.
GPE is a scalar quantity, and can be positive or negative.
GPE formula $mgh$ is valid for uniform gravitational fields (near Earth's surface).
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
Calculate the kinetic energy of the α-particle.
Show that the increase in gravitational potential energy of the car in a time of 1.0s is 46 000 J.
Extra simulations & links
PhET, GeoGebra and other curated tools — open in a new tab.
Frequently asked
Checkpoint
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Reading it isn’t knowing it — prove it.
Before you move on: do 9702/22 · Q6(c)(ii) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.
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