Physics HL · Chapter 3: Work, Energy and Power
3.4 Conservation, Dissipation, and Real Systems
Apply conservation of mechanical energy and then extend to realistic cases with resistive transfer.
Estimated time: 30 minutes
Mechanical Energy Conservation
When only conservative interactions act, the sum of kinetic and potential energy stays constant. In gravitational and spring settings, this allows direct endpoint solutions for speed or height without solving acceleration as a function of time.
Use this only when non-conservative transfers (like friction or drag) are negligible.
Including Friction as Energy Transfer
In practical systems, friction and drag convert mechanical energy into internal/thermal energy. Mechanical energy then decreases, but total energy is still conserved if those thermal pathways are included in the bookkeeping.
A robust template is: initial mechanical energy + external input = final mechanical energy + dissipated energy. This equation prevents the common mistake of treating "lost" mechanical energy as vanished rather than transferred.
Simulation Sequence: Conservative to Dissipative
Run these presets as a controlled sequence. Keep your focus on two readouts each time: final speed and friction thermal gain. Before changing sliders freely, compare outcomes against your qualitative prediction from conservation ideas.
Preset A (low friction baseline): this should look close to a mechanical-energy-conservation case, with most initial potential + kinetic ending in final kinetic.
Simulation A: Low-Friction Baseline
Check near-conservative behavior first, then compare later presets against this baseline.
Work-Energy Lab
Ramp-body energy scene
Sankey energy flow
Initial mechanical
55.58 J
Friction transfer
5.89 J
Final kinetic
49.69 J
Final speed
7.05 m/s
Read the Sankey as a conservation diagram: one incoming stream splits into useful kinetic output and thermal dissipation, with widths proportional to actual computed energy.
Interpretation for A: if friction thermal gain is small and final speed is high, your result matches the expectation that little mechanical energy is diverted away from translational kinetic output.
Preset B (idealized limit): set friction to zero. This gives a direct numerical check of the chapter claim that gravitational work depends only on vertical drop in the near-Earth model.
Simulation B: Zero-Friction Limit
Use an idealized no-friction run to verify full conversion from initial mechanical energy to final kinetic energy.
Work-Energy Lab
Ramp-body energy scene
Sankey energy flow
Initial mechanical
85.06 J
Friction transfer
0.00 J
Final kinetic
85.06 J
Final speed
8.42 m/s
Read the Sankey as a conservation diagram: one incoming stream splits into useful kinetic output and thermal dissipation, with widths proportional to actual computed energy.
Interpretation for B: the friction thermal bar should collapse to zero, so any increase in final kinetic comes entirely from initial potential plus initial kinetic. If you double mass while keeping height and speed fixed, the energies scale up proportionally, but the percentage split remains unchanged.
Preset C (strong dissipation): increase friction and initial speed together. The higher initial energy can still yield a lower final speed if thermal transfer grows strongly enough.
Simulation C: High-Dissipation Ramp
Observe how strong friction can dominate the energy budget even when the object starts with more total mechanical energy.
Work-Energy Lab
Ramp-body energy scene
Sankey energy flow
Initial mechanical
37.38 J
Friction transfer
31.10 J
Final kinetic
6.28 J
Final speed
3.00 m/s
Read the Sankey as a conservation diagram: one incoming stream splits into useful kinetic output and thermal dissipation, with widths proportional to actual computed energy.
Interpretation for C: compare with A and B. A larger thermal-transfer share means a lower useful kinetic fraction, illustrating why real transport systems invest heavily in reducing resistive losses.
Interpreting the Simulation Outputs
Across all three presets, separate two ideas: absolute energy and efficiency ratio. Changing mass rescales nearly every energy bar, but changing friction coefficient primarily reshapes the output split. That distinction mirrors textbook efficiency discussions: high-energy systems are not automatically high-efficiency systems.
Did You Know?
In many transport systems, small efficiency gains matter because repeated cycles multiply the saved energy over long operating times.