The Memory Trick
💡 KE = ½mv² and PE = mgh
Kinetic energy (KE) is the energy of motion: KE = ½mv². Because velocity is squared, doubling an object's speed quadruples its kinetic energy — not just doubles it. Gravitational potential energy (PE) is stored energy due to height: PE = mgh, where h is height above a chosen reference point.
Why It Works
Without friction or air resistance, total mechanical energy (KE + PE) stays constant — energy just converts back and forth between the two forms as an object rises and falls, speeds up and slows down.
Step by Step
Applying Energy Formulas
1
KE depends on speed squared
Because v is squared in ½mv², small changes in speed cause large changes in kinetic energy.
Doubling a car's speed from 30 to 60 mph doesn't double its stopping distance — it quadruples the kinetic energy that has to be dissipated.
2
PE depends on height above a reference
h in mgh is always measured relative to some chosen zero point — commonly the ground, but any reference level works as long as it's used consistently.
A 2 kg book on a 1.5 m shelf has PE = 2 × 9.8 × 1.5 ≈ 29.4 J relative to the floor.
3
Total mechanical energy is conserved (no friction)
As an object falls, PE converts to KE; as it rises, KE converts to PE. Without friction or air resistance, KE + PE stays constant throughout the motion.
A ball dropped from height h hits the ground with exactly the KE that equals its starting PE — mgh = ½mv².
🏥 Worked Example
A 0.5 kg ball is dropped from a height of 20 m (ignore air resistance). What is its speed just before hitting the ground?
1
Set up conservation of energy: all initial PE converts to KE at the bottom, since there's no friction: mgh = ½mv².
2
Cancel mass (it appears on both sides): gh = ½v², so v² = 2gh = 2 × 9.8 × 20 = 392.
3
Solve for v: v = √392 ≈ 19.8 m/s — notice mass never mattered, since it canceled out entirely.
📌 Exam Application
Exams test the ability to set up KE = PE conservation equations, correctly apply the squared relationship in KE, and recognize when mass cancels out of a problem entirely (as in free-fall speed calculations).
⚠️ Most Common Energy Formulas Mistakes
The most common trap is forgetting that velocity is SQUARED in the kinetic energy formula — doubling speed is often mistakenly assumed to double KE, when it actually quadruples it.
✓ Quick Self-Test
1) Write the formulas for kinetic and gravitational potential energy. KE = ½mv²; PE = mgh. 2) If an object's speed triples, what happens to its kinetic energy? It increases ninefold (3² = 9). 3) What quantity is h measured relative to in PE = mgh? A chosen reference point, often the ground, but any consistent level works. 4) Under what condition is total mechanical energy (KE + PE) conserved? When there is no friction or air resistance doing work on the system. 5) Why does mass cancel out when calculating the speed of a freely falling object? Because both KE (½mv²) and PE (mgh) contain mass as a simple multiplying factor, so it divides out of the equation.
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