Work and Energy

Work, Energy, and Power Explained: Formulas, Examples, and the Law of Conservation

πŸ”¬ Work, Energy & Power

Stop Confusing 'Hard Work' with 'Scientific Work'! Master the Physics That Changes Everything

Why Should You Care About Work, Energy & Power?

You probably hear the word "work" every day. Your teachers say "finish your homework," your parents say "work hard," but in physics, "work" has a very specific meaning. Understanding these concepts is the key to understanding how the world works—from why a car needs fuel to how your body gets energy from food.

πŸ’‘ Quick Fact: When you stand still holding a heavy backpack, you might feel exhausted, but according to physics, you haven't done any work! Work requires both force AND movement.

1️⃣ Work: The Scientific Rulebook

In everyday life, we use "work" for almost any effort. But in physics, work has two non-negotiable conditions:

✅ Work IS Done When:

  • A force acts on an object
  • The object moves (displacement)
  • Movement is in the direction of force

❌ Work Is NOT Done When:

  • No force is applied
  • Force is applied but object doesn't move
  • Force is perpendicular to movement

The Work Formula

W = F × s
Where: W = Work (Joules), F = Force (Newtons), s = Displacement (meters)
πŸ“Œ Definition of 1 Joule (J): When a force of 1 Newton moves an object 1 meter in the direction of the force, 1 Joule of work is done. It's named after James Prescott Joule, a brilliant physicist!
🎯 Three Scenarios: When Is Work Done?
✅ POSITIVE WORK
πŸ‘‹
Hand pulls toy car forward
Force & Motion = Same Direction
W = +10 J
❌ ZERO WORK
πŸšͺ
Person pushes wall (doesn't move)
No Displacement = No Work
W = 0 J
➖ NEGATIVE WORK
πŸ”™
Friction opposes motion
Force Opposite to Motion
W = -5 J

Work Example

πŸ“– Real-World Example
A porter lifts a 15 kg suitcase from the ground to his head (1.5 m above ground). How much work does he do?
Force needed = Weight = mg = 15 × 10 = 150 N
Distance = 1.5 m
Work = F × s = 150 × 1.5 = 225 Joules

2️⃣ Energy: The Capacity to Do Work

Have you ever wondered where your energy comes from to run, jump, and think? Energy is the ability to do work. When something has energy, it can make things happen.

🌟 Energy Definition: Energy is the capacity or ability of an object to do work. When an object does work, it loses energy. When work is done on an object, it gains energy.

The unit of energy is the same as work: Joules (J). This makes sense because energy is what allows things to do work!

Two Types of Mechanical Energy

⚡ Kinetic Energy (Motion)

Energy of movement. Faster objects have MORE kinetic energy.

Ek = ½mv²

Examples: Running athlete, flying ball, rolling stone, speeding car

πŸ“ Potential Energy (Position)

Energy stored due to position or shape. Higher = More energy.

Ep = mgh

Examples: Book on shelf, stretched rubber band, wound-up toy

Kinetic Energy in Action

⚡ Example 1: Moving Object
A 15 kg object moves at 4 m/s. What's its kinetic energy?
Ek = ½mv² = ½ × 15 × 4²
= ½ × 15 × 16
= 120 Joules

πŸ’‘ If the object moves twice as fast (8 m/s), kinetic energy becomes 480 J (4 times more!)
πŸ€” Think About It
Why does a speeding car cause more damage than a slow one? Because kinetic energy depends on velocity SQUARED (v²). Double the speed = 4 times the damage!

Potential Energy Examples

πŸ“ Example 2: Raised Object
A 10 kg object is raised to a height of 6 meters. What's its potential energy?
Ep = mgh = 10 × 9.8 × 6
= 588 Joules

πŸ’‘ This energy is waiting to be released when the object falls!
πŸ“Œ Key Insight: Potential energy depends on HEIGHT, not on the PATH taken. Whether you climb stairs or a slope, raising an object 10 meters requires the same work and gives the same potential energy.

3️⃣ The Ultimate Rule: Law of Conservation of Energy

This is one of the most important laws in physics: Energy can change forms, but it can NEVER be created or destroyed.

⚖️ Law of Conservation of Energy

✓ Energy transforms
From one form to another (potential → kinetic)
✗ Never disappears
Total energy stays the same
✗ Never appears from nothing
Energy must come from somewhere
✓ Always balanced
Energy in = Energy out

Free Fall: The Perfect Example

Imagine dropping a ball from a building:

Potential
MAX
Top of Building
All potential
Zero kinetic
Mixed
Energy
Mid-Fall
Some potential
Some kinetic
Kinetic
MAX
Just Before Impact
Zero potential
All kinetic
Etotal = Ep + Ek = Constant
Mechanical Energy is Always Conserved!
πŸ“Š Energy Conservation During Free Fall
Position Height (m) Potential Energy Kinetic Energy Total Energy
Top 10 m 1000 J ✅ 0 J 1000 J
Middle 5 m 500 J ✅ 500 J ⚡ 1000 J
Bottom 0 m 0 J 1000 J ⚡ 1000 J
πŸ€” Real Life Question
Why does a pendulum eventually stop swinging?
The law of conservation isn't broken! The pendulum's energy doesn't disappear—it converts to heat (friction) and sound. Energy is still conserved, just in different forms!

4️⃣ Power: The Rate of Doing Work

Imagine two students lifting the same backpack to the same height. One does it in 2 seconds, the other in 10 seconds. The work is the same, but the rate is different! This is where power comes in.

⏱️ Power Definition: Power measures HOW FAST work is done or how quickly energy is transferred. It's the rate of doing work.

The Power Formula

P = W / t
Where: P = Power (Watts), W = Work (Joules), t = Time (seconds)
πŸ“Œ Definition of 1 Watt (W): One watt means doing 1 Joule of work in 1 second. It's named after James Watt, who improved the steam engine!

Common Power Units:

  • 1 Watt (W) = 1 Joule per second
  • 1 Kilowatt (kW) = 1,000 Watts (used for household electricity)
  • Horsepower (hp) = 746 Watts (used for engines)

Power in Real Life

⏱️ Example: Two Girls Climbing
Two girls, each weighing 400 N, climb a rope 8 meters high. Girl A takes 20 seconds, Girl B takes 50 seconds. Who has more power?
Work done by both:
W = F × s = 400 × 8 = 3,200 J

Girl A (20 seconds):
P = W / t = 3,200 / 20 = 160 Watts ⚡⚡

Girl B (50 seconds):
P = W / t = 3,200 / 50 = 64 Watts

πŸ’‘ Girl A is MORE POWERFUL because she does the same work in LESS time!

πŸ’° Energy Analogy

Energy is like money in your bank account—what you have.

πŸ”„ Work Analogy

Work is like a transaction—what you did with the money.

⚡ Power Analogy

Power is like your spending rate—how fast you spend the money!

πŸ“Š Real-Life Power

A 100W bulb uses more energy per second than a 40W bulb.

🎯 Key Takeaways You Must Remember

The Core Concepts

πŸ“Œ Work (W = F×s)
Product of force and displacement. Unit: Joule (J)
⚡ Energy (E)
Ability to do work. Measured in Joules. Can be kinetic or potential.
⚡ Kinetic Energy (½mv²)
Energy of motion. Depends on mass and velocity squared!
πŸ“ Potential Energy (mgh)
Energy of position. Depends on height above ground.
⚖️ Conservation of Energy
Total energy stays constant. It transforms but never disappears.
⏱️ Power (P = W/t)
Rate of doing work. Unit: Watt (W). Faster = More powerful.

πŸ“ Quick Self-Check Questions

  1. Is work done when you hold a heavy box stationary? → No, because there's no displacement
  2. Which has more kinetic energy: a 2 kg ball at 5 m/s or a 5 kg ball at 2 m/s? → The 2 kg ball (12.5 J vs 10 J)
  3. Where does a falling object's potential energy go? → It converts to kinetic energy
  4. Can energy be created or destroyed? → No! Only converted to different forms
  5. Which person is more powerful: one lifting 100 kg in 5 seconds or 100 kg in 10 seconds? → The first person (same work, less time)

🌍 Where You See This Every Day

πŸš— Cars & Fuel

Fuel provides energy. The car's engine does work to move it. More powerful engines do this work faster!

⚽ Sports

A fast-moving ball has more kinetic energy than a slow one. That's why a hard throw goes further!

πŸ’‘ Electricity Bills

Your bill measures energy used (kWh). A 1000W heater uses more energy than a 100W LED bulb.

πŸ‹️ Your Body

Food provides energy. Exercise uses that energy. More intense exercise = More power!

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