Ch 04: Work, Power & Energy | Exam Fusion Prep

🔨 Work — Introduction

Change in position of object by applying a force
Scalar quantity

W = F·s·cosθ

Joule (J)

SI / MKS Unit

erg

CGS Unit

1 J = 10⁷ erg

Conversion

1 erg = 1 dyne × 1 cm

CGS definition

📋 Types of Work

Type	Angle (θ)	Value	Example
Positive Work	0° ≤ θ < 90°	W = F·s (+ve)	Gravity on freely falling body
Negative Work	90° < θ < 270°	W = −F·s (−ve)	Gravity while lifting a body upward
Zero Work	θ = 90° or 270°	W = 0	Lifting load sideways; Circular motion

⚠ Exam Trap

Work done in circular motion = Zero (force ⊥ displacement). Work done against gravity while lifting = Negative. Work done by gravity while falling = Positive. cosθ determines the sign!

⚡ Worked Example

F=40N, s=10m, θ=30°
W = 40 × 10 × cos30° = 400 × (√3/2) = 346.41 J

⚖️ Conservative vs Non-Conservative Force

Feature	Conservative Force	Non-Conservative Force
Work depends on	Initial & final positions only	Initial, final positions AND path
Path dependence	Path independent	Path dependent
Closed path work	= 0 (zero)	≠ 0 (non-zero)
Examples	Gravitation, Electrostatic force, Magnetic force	Friction force, Viscous force

⚙️ Power

Time rate of work done by a machine or person
Scalar quantity

P = W / t = Work / Time

Watt (W)

SI Unit = J/s

1 HP = 746 W

Horse Power

1 kW = 10³ W

Kilowatt

1 MW = 10⁶ W

Megawatt

⚠ Exam Trap

1 Horse Power = 746 Watt (not 1000 W!). 1 kW = 10³ W. Power is Scalar quantity.

⚡ Worked Example

m=40kg, h=2m, t=4s
W = mgh = 40×9.8×2 = 784 J
P = 784/4 = 196 Watt

⚡ Energy — Introduction

Capacity of an object to do work
Scalar quantity
Unit: Joule (J) | Commercial unit: kilowatt-hour (kWh)

Unit	Equivalence in Joules
erg	10⁻⁷ J
Calorie	4.2 J
Kilowatt-hour (kWh)	3.6 × 10⁶ J
Electron-volt (eV)	1.6 × 10⁻¹⁹ J

🌈 Forms of Energy

Form	Description
Thermal Energy	Energy from heat
Electric Energy	Energy from flow of electric current
Chemical Energy	Energy from chemical reactions
Light Energy	Energy from sun and light sources
Sound Energy	Energy from sound sources / musical instruments
Nuclear Energy	Energy from fission or fusion of nuclei
Mechanical Energy	Energy from mechanical work (KE + PE)

⚠ Exam Trap

Nuclear energy = Fission OR Fusion. 1 calorie = 4.2 J (not 4 J, not 4.5 J). 1 kWh = 3.6 × 10⁶ J. eV = 1.6 × 10⁻¹⁹ J — used in atomic physics.

🏃 Kinetic Energy (KE)

Energy due to motion of an object
Proportional to mass and square of velocity
e.g. Wind mills, Bullet fired from gun

KE = ½mv²

KE-Momentum relation:KE = p²/2m = ½pv

⚠ Exam Trap

If momentum (P) of two objects is same → lighter object has MORE KE (KE = p²/2m — smaller m means larger KE). KE is always positive.

⚡ Worked Example

m=1500kg, v=72km/h = 20m/s
KE = ½ × 1500 × 20² = 3 × 10⁵ J

🏔️ Potential Energy (PE)

Energy due to position or configuration of a body

1. Gravitational PE

Body of mass m at height h

U = mgh

⚡ Example

m=40kg, h=5m, g=10
U = 40×10×5 = 2000 J

2. Elastic PE

Energy due to elastic deformation of spring
k = spring force constant
x = deformation / extension

U = ½kx²

e.g. Stretched bow string, Compressed spring

📊 KE vs PE — Quick Compare

Feature	Kinetic Energy	Potential Energy
Depends on	Mass + Velocity	Mass + Height (or configuration)
Formula	½mv²	mgh or ½kx²
Examples	Moving bullet, Running car	Water in dam, Stretched spring
Can be zero?	Yes (when v=0)	Yes (at reference point h=0)

♻️ Law of Conservation of Energy

"Energy can neither be created nor destroyed — only converted from one form to another"
Total energy of an isolated system remains constant

🎢 Free Fall — KE + PE = Constant

Position	KE	PE	Total
At highest point	Minimum (0)	Maximum	Constant
Midway	½ total	½ total	Constant
At lowest point	Maximum	Minimum (0)	Constant

KE + PE = Total Mechanical Energy = Constant

⚠ Exam Trap

At highest point: PE = max, KE = 0. At lowest: KE = max, PE = 0. Total always constant! Energy "created" or "destroyed" = impossible.

🔌 Energy Conversion Table

Equipment / Device	Energy Conversion
Solar cell	Solar (Light) → Electrical
Dynamo	Mechanical → Electrical
Electric Motor	Electrical → Mechanical
Microphone	Sound → Electrical
Loudspeaker	Electrical → Sound
Sitar	Mechanical → Sound
Bulb / Tube light / Heater	Electrical → Light + Thermal
Burning candle	Chemical → Light + Thermal
Burning coal	Chemical → Thermal
Electric cell (battery)	Chemical → Electrical
Engine	Thermal → Mechanical
Photoelectric cell	Light → Electrical

⚠ Exam Trap

Dynamo = Mechanical → Electrical (generator). Motor = Electrical → Mechanical (opposite of dynamo!). Solar cell + Photoelectric cell dono = Light → Electrical. Microphone + Loudspeaker = opposite conversions.

⚡ Quick Recall — Units Summary

Work = Energy = Joule. Power = Watt = J/s. 1 HP = 746 W. 1 J = 10⁷ erg. 1 cal = 4.2 J. 1 kWh = 3.6×10⁶ J.

⚡ Chapter 04 — Work, Power & Energy