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Work-Energy Theorem & Conservation of Mechanical Energy

动能定理与机械能守恒定律

Wnet​=ΔEk​=21​mv22​−21​mv12​,Ek1​+Ep1​=Ek2​+Ep2​

Theoretical Identity Description:

The net work done on an object equals the change in kinetic energy. When only conservative forces (gravity/elasticity) do work, total mechanical energy is conserved.

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Rigorous Derivation Tree

2 Logical Steps
Step 1check_circleValid Deduction
Wnet​=ΔEk​=21​mv22​−21​mv12​,Ek1​+Ep1​=Ek2​+Ep2​

Foundational identity statement defined under standard mathematical conditions.

Step 2check_circleValid Deduction
Wnet​=ΔEk​,mgh1​+21​mv12​=mgh2​+21​mv22​

Targeted algebraic evaluation and parameter substitution.

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CSCA Exam Triggers & Traps

High-Yield Exam Focus
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Use for curved trajectory motion, roller coasters, pendulum swings, and spring release dynamics.

errorCommon Examination Pitfalls

Friction and air resistance perform negative non-conservative work, dissipating mechanical energy into thermal energy: W_nc = ΔE_mech.

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