In the previous unit, you learned that energy is conserved in a closed system and that it comes in many forms—most importantly kinetic and potential energy in classical mechanics.
Now we take the next step: What happens when forces like friction or air resistance come into play? How can we still apply the principle of energy conservation, even when mechanical energy appears to “disappear”?
This unit explores the concepts of mechanical energy, non-conservative forces, and how energy is transformed or “lost” in real-world systems.
1. Mechanical Energy – A Defined Subset
Mechanical energy is the sum of kinetic and potential energy in a system:
Emech=KE+PEE_{\text{mech}} = KE + PEEmech=KE+PEThis concept is useful because, in idealized systems (no friction or other dissipative forces), mechanical energy is conserved.
2. Conservative vs. Non-Conservative Forces
A conservative force is a force where the work done depends only on the starting and ending positions—not on the path taken. These forces store and release energy without loss.
Examples:
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Gravitational force
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Spring (elastic) force
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Electrostatic force
With conservative forces, energy can freely switch between KE and PE, and the total mechanical energy remains constant.
In contrast, non-conservative forces (like friction or air resistance) convert mechanical energy into other forms—typically thermal energy.
These forces depend on the path and always remove mechanical energy from the system.
3. Energy Dissipation – Where Does "Lost" Energy Go?
When mechanical energy decreases, it’s not actually lost—it’s transformed.
For example, sliding a box across a floor generates heat due to friction. That heat is energy, but it’s no longer “useful” for doing mechanical work.
This is why physicists distinguish between:
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Total energy (always conserved)
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Mechanical energy (can decrease due to non-conservative forces)
We can express this with:
Emech, final=Emech, initial−Elost (e.g., heat)E_{\text{mech, final}} = E_{\text{mech, initial}} - E_{\text{lost (e.g., heat)}}Emech, final=Emech, initial−Elost (e.g., heat)Or:
ΔEmech=−Wnc\Delta E_{\text{mech}} = - W_{\text{nc}}ΔEmech=−WncWhere WncW_{\text{nc}}Wnc is the work done by non-conservative forces.
4. Applying This in Practice
Let’s consider a real-world scenario:
A skateboarder rolls down a ramp.
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In a frictionless world, all gravitational PE becomes KE at the bottom.
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In reality, some energy is lost to friction and air resistance—so the final KE is less than expected.
By measuring the difference, you can estimate the energy dissipated by non-conservative forces.
5. Why This Matters
Understanding non-conservative forces helps you analyze real systems—where ideal assumptions don’t hold. This is critical in engineering, biomechanics, vehicle design, and any system where efficiency matters.
You’re now moving beyond idealized models into real-world physics—where energy conservation still applies, but in more subtle ways.
In this unit, you’ve learned:
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The meaning and importance of mechanical energy
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The difference between conservative and non-conservative forces
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How to account for energy “loss” through transformation into heat or other forms
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How to analyze real systems using energy conservation, even when friction is involved
Next up: We’ll explore power, efficiency, and work-energy theorems—key tools to describe how energy flows in dynamic systems over time.
