University Physics I · Potential Energy & Conservation of Energy · 7.05
Potential-energy diagrams
Allowed regions, turning points, kinetic energy, total-energy lines, and small oscillations.
Build the model
Connect the measurement to the mechanism.
Allowed regions, turning points, kinetic energy, total-energy lines, and small oscillations. Treat this course-map statement as a claim to test rather than an invitation to import a familiar equation. In Potential Energy & Conservation of Energy, begin from system energy accounting, then state the system, observable, assumptions, and evidence before calculating.
- Simple definition
- Allowed regions, turning points, kinetic energy, total-energy lines, and small oscillations.
- Example
- A strong response uses potential-energy curves and states where the model stops being reliable.
A turning point occurs where K=0, so E=U.
Classical motion is allowed only where E ≥ U.
The turning points are symmetric about the minimum.
This relation is specific to a parabolic well.
The subsection's claim
Allowed regions, turning points, kinetic energy, total-energy lines, and small oscillations.
How to work with it
Start from system energy accounting. Then defining the system and reference level before invoking conservation. Select an equation only after its variables and assumptions match the stated system.
What evidence would decide
Over what extension range does elastic potential energy follow the ideal-spring model? Useful evidence includes force-extension data, integrated work, energy comparison, residuals, and a range claim.
Keep the boundary visible
This GioPhysics course map is an adaptable teaching sequence, not a claim of accreditation or a universal university syllabus. Departments can adjust the order, mathematical depth, laboratory hours, and optional fluids endpoint to match local requirements. A result should be checked against units, signs, limiting cases, and the conditions under which its model was derived.
Change one variable at a time
Make the relationship visible.
Change the curvature and excursion. Check that K=E−U is non-negative only between the two turning points.
TOTAL ENERGY0.60 relative
CENTRE KINETIC ENERGY0.60 relative
Live interpretationTOTAL ENERGY: 0.60 relative. CENTRE KINETIC ENERGY: 0.60 relative
Catch the common trap
Explain before calculating.
What identifies a classical turning point on an energy diagram?
Choose an answer to test the model.
Practice & worked examples
Reason from the model, then test the result.
Worked calculationA particle moves in U(x)=½kx² with k=4.0 N m⁻¹ and total energy 8.0 J. Find its turning points and maximum kinetic energy.
- At a turning point K=0, so E=U=½kx².
- x=±√(2E/k)=±√(16/4)=±2.0 m.
- At x=0, U=0, so Kₘₐₓ=E−U=8.0 J.
AnswerThe turning points are x=±2.0 m and the maximum kinetic energy is 8.0 J.
TransferDesign one observation that separates Potential-energy diagrams from Conservation of mechanical energy.
- Name the observable central to Potential-energy diagrams.
- Name the contrasting observable or condition in Conservation of mechanical energy.
- Choose a graph feature, sign, scale, or limiting case that would distinguish them.
AnswerThe comparison is useful only if the proposed observation could rule out at least one of the two accounts.