Work and energy are central concepts in physics, explaining everything from human activity to machine operation to cosmic processes.
Feynman Lens
Start with the simplest version: this lesson is about Work and Energy. If you can explain the core idea to a friend using everyday language, examples, and one clear reason why it matters, you have moved from memorising to understanding.
Work and energy are central concepts in physics, explaining everything from human activity to machine operation to cosmic processes. Work measures how much a force accomplishes, while energy is the capacity to do work. Energy takes many forms—kinetic (motion), potential (position), thermal (heat), chemical, and more. The profound insight that energy is conserved—never created or destroyed, only transformed—unifies physics and explains why perpetual motion machines are impossible. This chapter explores work, energy types, power, and energy conservation, showing how these concepts apply to everyday life and technological systems.
What Is Work: Force and Displacement
Work: Energy transfer caused by a force acting on an object causing displacement.
Mathematical definition: W = F·d·cos(θ)
where:
W = work (Joules, J)
F = force magnitude (N)
d = displacement (m)
θ = angle between force and displacement
Special cases:
Force parallel to displacement (θ = 0°): W = Fd (maximum work)
Force perpendicular to displacement (θ = 90°): W = 0 (no work)
Force opposite to displacement (θ = 180°): W = -Fd (negative work)
Key insight: Work requires BOTH force and displacement in the force's direction.
Examples:
Lifting a 10 N box 2 m vertically: W = 10 × 2 = 20 J
Pushing a box 5 m horizontally with 8 N force: W = 8 × 5 = 40 J
Carrying a box 10 m with no change in height: W = 0 (vertical force, horizontal motion)
Historical context: "Work" in physics differs from everyday meaning. Holding a heavy box requires effort but does no work (no displacement).
Energy: The Capacity to Do Work
Energy: The capacity to do work or cause change.
Conservation of energy: Energy is never created or destroyed, only transformed from one form to another.
Types of energy:
Kinetic Energy (Energy of Motion)
KE = (1/2)mv²
Depends on mass and velocity squared
A 2x velocity increase gives 4x kinetic energy
Example: A 1000 kg car at 10 m/s has KE = (1/2)(1000)(10²) = 50,000 J
Potential Energy (Energy of Position)
Gravitational PE (near Earth): PE = mgh
Higher position = greater PE
Example: A 10 kg object 5 m above ground: PE = 10 × 9.8 × 5 = 490 J
Elastic PE: Energy stored in stretched springs or deformed objects
PE = (1/2)kx² where k is spring constant and x is deformation
Other Forms of Energy
Thermal energy: Heat; motion of atoms/molecules
Chemical energy: Stored in chemical bonds
Electrical energy: Energy of moving charges
Nuclear energy: Energy from atomic nucleus
Radiant energy: Light and electromagnetic radiation
Work-Energy Theorem
Statement: Work done on an object equals its change in kinetic energy.
W = ΔKE = (1/2)m(v_f² - v_i²)
Implication: A net force doing positive work increases an object's speed; negative work decreases speed.
Example: A 2 kg object accelerates from 5 m/s to 10 m/s.
ΔKE = (1/2)(2)(10² - 5²) = (1/2)(2)(75) = 75 J
Work done = 75 J
Power: Rate of Energy Transfer
Power: Rate at which work is done or energy is transferred.
P = W/t (average power)
Units: Watts (W) = Joules/second
1000 W = 1 kilowatt (kW)
P = F·v (instantaneous power)
Power depends on force and velocity
Examples:
A 100 W bulb transfers 100 J of energy per second
A 1500 W heater transfers 1500 J per second
Your body uses roughly 100 W at rest; athletes may use 1000+ W
Energy Conservation and Transformation
Mechanical energy: Sum of kinetic and potential energy in a system.
Law of conservation of mechanical energy: In absence of friction, total mechanical energy remains constant. KE + PE = constant
Example - Pendulum: At highest point, PE is maximum and KE = 0. At lowest point, KE is maximum and PE is minimum. Total energy stays constant.
Energy transformation: One form converts to another.
Chemical energy (fuel) → Thermal energy (heat) → Kinetic energy (motion)
Gravitational PE → Kinetic energy (falling object)
Electrical energy → Light energy (bulb)
Real-world energy loss: Friction converts mechanical energy to heat, "wasting" it.
Efficiency and Renewable Energy
Efficiency: Ratio of useful output to total input energy.
Efficiency = (Useful energy output / Total energy input) × 100%
Transportation: Fuel energy converted to kinetic energy; braking converts kinetic energy to heat.
Electronics: Electrical energy → light, heat, motion.
Renewable energy: Solar (radiant energy), wind (kinetic energy), hydroelectric (PE → KE).
Sports: Understanding energy transfer improves performance.
Connecting to Related Topics
Understanding work and energy prepares you for:
chapter-08-force-and-laws-of-motion: Forces do work
chapter-09-gravitation: Gravity does work on falling objects
chapter-07-motion: Kinetic energy relates to motion
Key Concepts and Definitions
Work: Energy transfer by force and displacement (W = Fd cos θ)
Joule (J): Unit of energy/work
Kinetic energy: Energy of motion; KE = (1/2)mv²
Potential energy: Energy of position
Power: Rate of energy transfer; P = W/t
Watt (W): Unit of power; 1 W = 1 J/s
Energy conservation: Energy is neither created nor destroyed
Efficiency: Ratio of useful output to total input
Mechanical energy: KE + PE
Socratic Questions
Work requires both force and displacement. A person holding a heavy box for an hour expends energy but does no work. Why is this counterintuitive?
Kinetic energy depends on v², so doubling velocity quadruples kinetic energy. Why does speed matter more than mass for kinetic energy?
A ball reaches the same height when thrown straight up at different initial velocities. Why don't faster-thrown balls go higher? (Hint: where does the extra kinetic energy go?)
Power is the rate of doing work. Two people climbing the same stairs at different speeds do the same work but at different powers. Why might more power consumption matter for the person?
Why is it impossible to create a "perpetual motion machine" that runs forever without external energy input? How does energy conservation make this impossible?
🃏 Flashcards — Quick Recall
Term / Concept
What is Work and Energy?
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Work and Energy is the central idea of this lesson. Use the chapter examples to explain what it means and why it matters.
Term / Concept
What is Work?
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Energy transfer caused by a force acting on an object causing displacement.
Term / Concept
What is Special cases?
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- Force parallel to displacement (θ = 0°): W = Fd (maximum work)
Term / Concept
What is Key insight?
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Work requires BOTH force and displacement in the force's direction.
Term / Concept
What is Examples?
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- Lifting a 10 N box 2 m vertically: W = 10 × 2 = 20 J
Term / Concept
What is Historical context?
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"Work" in physics differs from everyday meaning. Holding a heavy box requires effort but does no work (no displacement).
Term / Concept
What is Energy?
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The capacity to do work or cause change.
Term / Concept
What is Conservation of energy?
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Energy is never created or destroyed, only transformed from one form to another.
Term / Concept
What is Types of energy?
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### Kinetic Energy (Energy of Motion)
Term / Concept
What is KE = (1/2)mv²?
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- Depends on mass and velocity squared
Term / Concept
What is Elastic PE?
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Energy stored in stretched springs or deformed objects
Term / Concept
What is Thermal energy?
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Heat; motion of atoms/molecules
Term / Concept
What is Chemical energy?
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Stored in chemical bonds
Term / Concept
What is Electrical energy?
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Energy of moving charges
Term / Concept
What is Nuclear energy?
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Energy from atomic nucleus
Term / Concept
What is Radiant energy?
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Light and electromagnetic radiation
Term / Concept
What is Statement?
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Work done on an object equals its change in kinetic energy.
Term / Concept
What is W = ΔKE = (1/2)m(v_f² - v_i²)?
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Implication: A net force doing positive work increases an object's speed; negative work decreases speed.
Term / Concept
What is Example?
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A 2 kg object accelerates from 5 m/s to 10 m/s.
Term / Concept
What is Power?
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Rate at which work is done or energy is transferred.
Term / Concept
What is P = F·v?
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(instantaneous power)
Term / Concept
What is Mechanical energy?
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Sum of kinetic and potential energy in a system.
Term / Concept
What is Law of conservation of mechanical energy?
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In absence of friction, total mechanical energy remains constant. KE + PE = constant
Term / Concept
What is Example - Pendulum?
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At highest point, PE is maximum and KE = 0. At lowest point, KE is maximum and PE is minimum. Total energy stays constant.
Term / Concept
What is Energy transformation?
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One form converts to another.
Term / Concept
What is Real-world energy loss?
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Friction converts mechanical energy to heat, "wasting" it.
Term / Concept
What is Efficiency?
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Ratio of useful output to total input energy.
Term / Concept
What is Transportation?
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Fuel energy converted to kinetic energy; braking converts kinetic energy to heat.
Term / Concept
What is Electronics?
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Electrical energy → light, heat, motion.
Term / Concept
What is Renewable energy?
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Solar (radiant energy), wind (kinetic energy), hydroelectric (PE → KE).
Term / Concept
What is Sports?
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Understanding energy transfer improves performance.
Term / Concept
What is Joule (J)?
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Unit of energy/work
Term / Concept
What is Kinetic energy?
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Energy of motion; KE = (1/2)mv²
Term / Concept
What is Potential energy?
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: Energy of position
Term / Concept
What is Watt (W)?
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Unit of power; 1 W = 1 J/s
Term / Concept
What is Energy conservation?
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Energy is neither created nor destroyed
Term / Concept
What is the core idea of What Is Work: Force and Displacement?
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Work: Energy transfer caused by a force acting on an object causing displacement.
Term / Concept
What is the core idea of Energy: The Capacity to Do Work?
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Energy: The capacity to do work or cause change. Conservation of energy: Energy is never created or destroyed, only transformed from one form to another. Types of energy:
Term / Concept
What is the core idea of Kinetic Energy (Energy of Motion)?
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KE = (1/2)mv² - Depends on mass and velocity squared - A 2x velocity increase gives 4x kinetic energy - Example: A 1000 kg car at 10 m/s has KE = (1/2)(1000)(10²) = 50,000 J
Term / Concept
What is the core idea of Potential Energy (Energy of Position)?
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Gravitational PE (near Earth): PE = mgh - Higher position = greater PE - Example: A 10 kg object 5 m above ground: PE = 10 × 9.8 × 5 = 490 J Elastic PE: Energy stored in stretched springs or deformed objects - PE =…
40 cards — click any card to flip
📝 Quick Quiz — Test Yourself
Work requires both force and displacement. A person holding a heavy box for an hour expends energy but does no work. Why is this counterintuitive?
A Memorize the exact line without checking the reasoning.
B Use the chapter's evidence and explain the reasoning step by step.
C Ignore the examples and rely only on a keyword.
D Treat the idea as unrelated to the rest of the lesson.
Kinetic energy depends on v², so doubling velocity quadruples kinetic energy. Why does speed matter more than mass for kinetic energy?
A Memorize the exact line without checking the reasoning.
B Use the chapter's evidence and explain the reasoning step by step.
C Ignore the examples and rely only on a keyword.
D Treat the idea as unrelated to the rest of the lesson.
A ball reaches the same height when thrown straight up at different initial velocities. Why don't faster-thrown balls go higher? (Hint: where does the extra kinetic energy go?)
A Memorize the exact line without checking the reasoning.
B Use the chapter's evidence and explain the reasoning step by step.
C Ignore the examples and rely only on a keyword.
D Treat the idea as unrelated to the rest of the lesson.
Power is the rate of doing work. Two people climbing the same stairs at different speeds do the same work but at different powers. Why might more power consumption matter for the person?
A Memorize the exact line without checking the reasoning.
B Use the chapter's evidence and explain the reasoning step by step.
C Ignore the examples and rely only on a keyword.
D Treat the idea as unrelated to the rest of the lesson.
Why is it impossible to create a "perpetual motion machine" that runs forever without external energy input? How does energy conservation make this impossible?
A Memorize the exact line without checking the reasoning.
B Use the chapter's evidence and explain the reasoning step by step.
C Ignore the examples and rely only on a keyword.
D Treat the idea as unrelated to the rest of the lesson.
Which approach best shows that you understand Work and Energy?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Work?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Special cases?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Key insight?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Examples?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Historical context?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Energy?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Conservation of energy?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Types of energy?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand KE = (1/2)mv²?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Elastic PE?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Thermal energy?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Chemical energy?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Electrical energy?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Nuclear energy?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Radiant energy?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Statement?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand W = ΔKE = (1/2)m(v_f² - v_i²)?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Example?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Power?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand P = F·v?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Mechanical energy?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Law of conservation of mechanical energy?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Example - Pendulum?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Energy transformation?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Real-world energy loss?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Efficiency?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Transportation?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Electronics?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Renewable energy?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Sports?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Joule (J)?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Kinetic energy?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Potential energy?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
Which approach best shows that you understand Watt (W)?
A Repeat its name from memory.
B Explain it using a simple example and the reason it works.
C Skip the conditions where it applies.
D Use it only when the textbook wording is identical.
