Theory — Conservation of Mechanical Energy
Two Forms of Mechanical Energy
A moving object on a track has two kinds of mechanical energy: kinetic energy (energy of motion) and gravitational potential energy (stored energy of height). As the skater rolls up and down the track, energy continuously converts between these two forms.
PEg = m g h (energy of height)
m = mass (kg), v = speed (m/s), g = 9.8 m/s², h = height (m)
The Law of Conservation of Energy
Energy cannot be created or destroyed — only transformed. The total mechanical energy is the sum of kinetic and potential energy. On a frictionless track, with only gravity acting, mechanical energy is conserved: it has the same value at every point.
Frictionless: E_mech is the same at every point on the track
Non-Conservative Forces — Friction
When friction acts, the mechanical energy is not conserved: some of it is converted into thermal energy (heat). The skater does not return to its original height. But the total energy — mechanical plus thermal — is still conserved, in keeping with the first law of thermodynamics.
% Loss = (E_mech,initial − E_mech,final) / E_mech,initial × 100
At the top
Speed is zero, so KE = 0 and all the energy is potential (PEg maximum).
At the bottom
Height is zero, so PEg = 0 and all the energy is kinetic (KE maximum, fastest point).
With friction
Each pass loses mechanical energy to heat, so the skater rises a little less each time.
| Quantity | Formula | Notes |
|---|---|---|
| Kinetic energy | KE = ½mv² | maximum at the bottom |
| Potential energy | PEg = mgh | maximum at the top |
| Mechanical energy | E_mech = KE + PEg | constant if frictionless |
| With friction | E_mech,i = E_mech,f + E_thermal | mechanical energy drops |
Instructions — Running the Virtual Experiment
The Frictionless Track tab lets you verify that mechanical energy is conserved by reading KE, PEg, and ME at any point; the Friction Track tab shows mechanical energy draining into thermal energy. Record every reading in your lab report with screenshots of the bar graph and pie chart.
Simulation — Energy Skate Track
Skater & track
| Point | h (m) | v (m/s) | PEg (J) | KE (J) | E_mech (J) |
|---|---|---|---|---|---|
| Release the skater, pause, and click "Record this point" at P₁, P₂, P₃. | |||||
Friction track
Team Questions
Example Lab Report
Sample report demonstrating the expected format and level of detail. Use as a guide for your own submission, and include labelled screenshots of the bar graph and pie chart at each point.
Conservation of Energy
Physics | Section: [Your Section] | Date: [Date]
Lab Members: [Names of all members present]
Purpose
To verify the Law of Conservation of Mechanical Energy using a virtual skate track. In the frictionless case, the total mechanical energy (KE + PEg) is measured at three points and shown to be constant. In the friction case, the mechanical energy lost in one pass is measured and shown to equal the thermal energy generated.
Theory
Mechanical energy is E_mech = KE + PEg, with KE = ½mv² and PEg = mgh. With only gravity acting (no friction), E_mech is conserved. When friction acts, mechanical energy is converted to thermal energy, so E_mech,initial = E_mech,final + E_thermal and the percentage lost is (E_mech,i − E_mech,f)/E_mech,i × 100.
Friction: E_mech,i = E_mech,f + E_thermal (g = 9.8 m/s²)
Part 2 — Frictionless (m = 20 kg, h_start = 6.0 m)
| Point | h (m) | v (m/s) | PEg (J) | KE (J) | E_mech (J) |
|---|---|---|---|---|---|
| P₁ (start) | 6.0 | 0.00 | 1176 | 0 | 1176 |
| P₂ (bottom) | 0.0 | 10.84 | 0 | 1176 | 1176 |
| P₃ (mid) | 3.0 | 7.67 | 588 | 588 | 1176 |
The three E_mech values are identical (1176 J), confirming conservation in the frictionless system.
Part 3 — With Friction (m = 60 kg, h_start = 6.0 m)
E_mech,initial: mgh = (60)(9.8)(6.0) = 3528 J
After one pass (returns to ~4.0 m): E_mech,final = (60)(9.8)(4.0) = 2352 J
Thermal energy generated: 3528 − 2352 = 1176 J
% Loss: (3528 − 2352)/3528 × 100 = 33.3%
Discussion
On the frictionless track the total mechanical energy was the same — 1176 J — at the start, the bottom, and the midpoint, so it was conserved to within reading precision: the potential energy lost in descending was exactly matched by the kinetic energy gained. The skater was fastest at the bottom (10.84 m/s), where PEg = 0 and all the energy was kinetic, and momentarily at rest at the top, where all the energy was potential.
With friction, the bar graph and pie chart showed a growing red "thermal" slice as the skater moved, and the skater rose to a lower height on the far side. The mechanical energy fell from 3528 J to 2352 J — a 33.3% loss — and exactly that 1176 J appeared as thermal energy, illustrating the first law of thermodynamics: the energy was not destroyed but converted to heat. The skater's acceleration is largest where the track curves most sharply at the bottom of the U, where the net upward (centripetal) force is greatest.
Conclusion
Mechanical energy was conserved on the frictionless track (constant E_mech at every point) and not conserved with friction, where the lost mechanical energy was fully accounted for as thermal energy. The results confirm the Law of Conservation of Energy.
Practice Questions
Show all work and include units. Use g = 9.8 m/s², KE = ½mv², PEg = mgh.