Energy Diagrams and Potential Wells

Energy diagrams are abstract until students physically interact with forces and motion. Active learning makes these invisible concepts visible through hands-on simulations and physical models, building lasting intuition about equilibrium and binding energy.

• Grade 12
• Physics
• 4 activities
• 30 min–45 min

Learning Objectives

1. Analyze an energy diagram to identify and label points of stable and unstable equilibrium.
2. Explain the relationship between the depth of a potential well and the binding energy of a system.
3. Predict the subsequent motion of a particle given its initial position and energy relative to a potential well.
4. Compare the energy required to displace a particle from stable versus unstable equilibrium points.

Concept Mapping

⏱ 45 min·Small Groups

PhET Simulation Stations: Equilibrium Exploration

Assign small groups to PhET's 'Energy Skate Park' or 'Potential Energy' sims. Students adjust track shapes, release skaters from points, and sketch energy diagrams from motion data. Groups present one prediction versus observation to the class.

Prepare & details

Analyze an energy diagram to identify points of stable and unstable equilibrium.

Facilitation Tip: During PhET Simulation Stations, circulate with guiding questions: 'Why does the particle speed up as it moves downhill? How does changing the potential shape affect the motion?'

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Concept Mapping

⏱ 35 min·Pairs

Marble Track Labs: Physical Potential Wells

Provide foam tracks curved into wells and hills. Pairs release marbles from marked positions, time oscillations, and measure heights to plot custom energy diagrams. Discuss why marbles stay trapped or escape based on initial energy.

Prepare & details

Explain how a potential well describes the binding energy of a system.

Facilitation Tip: For Marble Track Labs, ask students to adjust track height and curve angles, then observe and record how marble motion changes with potential well depth.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Concept Mapping

⏱ 30 min·Whole Class

Whiteboard Prediction Rounds: Motion Scenarios

Project energy diagrams. Whole class votes on particle paths via whiteboard sketches, then reveals animations. Follow with pairs refining predictions using force arrows from slope analysis.

Prepare & details

Predict the motion of a particle based on its position within an energy diagram.

Facilitation Tip: In Whiteboard Prediction Rounds, require students to draw force arrows alongside energy curves, ensuring they connect slope to acceleration direction.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Concept Mapping

⏱ 40 min·Individual

Diagram Design Challenge: Binding Energies

Individuals draw potential wells for scenarios like molecular bonds. Small groups critique depths for realistic binding energies, then test with spring-mass models to verify stability.

Prepare & details

Analyze an energy diagram to identify points of stable and unstable equilibrium.

Facilitation Tip: During Diagram Design Challenge, provide a set of binding energy values and have groups create diagrams that match, then peer-review each other’s work for accuracy.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Teaching This Topic

Start with physical models before abstract diagrams to anchor ideas in experience. Avoid rushing to equations, as students need time to observe how potential energy relates to force and motion. Research shows that alternating between virtual and hands-on activities strengthens spatial reasoning and reduces misconceptions about equilibrium.

What to Expect

Students will confidently identify stable and unstable equilibrium by connecting energy diagram features to real motion, explaining why particles oscillate in wells and diverge from peaks, and quantifying binding energy through both virtual and physical systems.

Watch Out for These Misconceptions

Common Misconception

During Marble Track Labs, watch for students assuming marbles stop completely at the bottom of the track.

What to Teach Instead

Ask them to observe the marble’s motion after it reaches the bottom. Guide them to note that it rolls back up, illustrating oscillation rather than rest, and connect this to kinetic energy in the well.

Common Misconception

During Diagram Design Challenge, watch for students drawing flat-bottomed wells.

What to Teach Instead

Have peers compare their diagrams and identify the steepest slope at the well’s edge. Ask them to redraw with curved sides, linking slope steepness to restoring force strength.

Common Misconception

During PhET Simulation Stations, watch for students treating unstable equilibrium as just an upside-down stable point.

What to Teach Instead

Direct them to nudge particles near peaks and observe divergence. Ask them to describe how the motion differs from oscillation, emphasizing amplification versus restoration.

Assessment Ideas

Exit Ticket

After Marble Track Labs, provide a blank energy diagram and ask students to 1) mark stable and unstable points, 2) draw potential wells, and 3) explain how the marble’s motion reflects these features.

Quick Check

During Whiteboard Prediction Rounds, present the hill scenario and ask students to sketch an energy diagram on mini-whiteboards. Collect responses to identify students who draw flat curves versus those who show a peak and downward slopes.

Discussion Prompt

After Diagram Design Challenge, pose the discussion question and have students use their group diagrams to justify whether atoms form molecules or planets orbit stars based on binding energy depth.

Extensions & Scaffolding

• Challenge: Ask students to design a potential well that traps a particle with exactly 2.5 units of binding energy, then test it in the PhET simulation.
• Scaffolding: Provide pre-drawn energy curves with missing labels for students to complete during Marble Track Labs, focusing on one feature at a time.
• Deeper exploration: Have students research and present how potential wells explain molecular bonding or gravitational orbits, using their diagrams as evidence.

Key Vocabulary

Potential Energy Diagram	A graph plotting the potential energy of a system as a function of position, used to visualize forces and equilibrium states.
Stable Equilibrium	A state where a system, when slightly displaced, experiences a net force that tends to restore it to its original position, typically found at a potential energy minimum.
Unstable Equilibrium	A state where a system, when slightly displaced, experiences a net force that tends to move it further away from its original position, typically found at a potential energy maximum.
Potential Well	A region in an energy diagram where the potential energy is lower than surrounding areas, representing a bound system where energy must be added to separate components.
Binding Energy	The minimum energy required to separate the components of a bound system, often represented by the depth of a potential well.