🎓 Prepared by students from Boğaziçi University

What is the Law of Conservation of Energy?

The law of conservation of energy states that energy cannot be created or destroyed — only transformed from one form to another. In a closed mechanical system, the total of kinetic and potential energy stays constant even as it converts between the two.

Short answer

Total mechanical energy is conserved: E_total = KE + PE = constant. As an object falls, potential energy converts into kinetic energy, and their sum never changes (ignoring friction and air resistance).

Energy transformation during free fall (m = 10 kg, h₀ = 10 m)

x: height (m) · y: energy (J)Potential EnergyKinetic Energy

Try it: interactive calculator

Total mechanical energy E

980J

= 0.5*10*0*0 + 10*9.8*10

Mass m10 kgVelocity v0 m/sHeight h10 mGravitational acceleration g9.8 m/s²

Step-by-step worked examples

A ball is dropped from 20 m (g = 9.8 m/s²). Find its speed just before hitting the ground, ignoring air resistance.

mgh = ½mv²
v = √(2gh) = √(2×9.8×20)
v = √392 ≈ 19.8 m/s

A roller coaster starts from rest at the top of a 30 m hill. Find its speed at the bottom.

mgh = ½mv²
v = √(2gh) = √(2×9.8×30)
v = √588 ≈ 24.2 m/s

A pendulum is released from a height of 0.2 m. Find its maximum speed at the bottom of the swing.

mgh = ½mv²
v = √(2gh) = √(2×9.8×0.2)
v = √3.92 ≈ 1.98 m/s

Flashcards

Quick quiz

Q1.In an isolated system, total mechanical energy…

Correct answer: C. With no external forces like friction, E_total = KE + PE is conserved.

Q2.As a ball falls freely, its potential energy…

Correct answer: B. Height decreases (PE falls) while speed increases (KE rises); their sum stays constant.

Q3.The law of conservation of energy states that energy…

Correct answer: C. Energy only changes form; the total amount never changes.

Q4.In real systems with friction, why does mechanical energy seem to decrease?

Correct answer: B. Friction converts mechanical energy into thermal and sound energy; total energy is still conserved.

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Common mistakes

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Believing energy disappears when friction acts. — Correct: Friction converts mechanical energy into heat and sound — it isn't destroyed.

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Only accounting for kinetic energy and ignoring potential energy. — Correct: Total mechanical energy includes both KE and PE; both must be tracked.

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Applying conservation of energy while ignoring external forces doing work. — Correct: The law applies strictly only to isolated systems with no external work input or loss.

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Confusing conservation of energy with conservation of momentum. — Correct: These are separate laws — momentum is mv, energy includes ½mv² and mgh among other forms.

FAQ

What is the law of conservation of energy?

It states that the total energy of an isolated system stays constant — energy only changes form, such as potential to kinetic.

What is the conservation of energy formula?

E_total = KE + PE = constant, for a system where only gravity does work.

What are examples of conservation of energy?

A swinging pendulum, a roller coaster, a bouncing ball, and a falling object all demonstrate energy converting between potential and kinetic forms.

How do you calculate speed using conservation of energy?

Set initial PE equal to final KE (mgh = ½mv²) and solve for v = √(2gh), assuming no friction.