Class 9 Science - Chapter 10: Work and Energy

Work and Energy

Introduction to Work

In everyday language, the word "work" means any activity - mental or physical. But in science, particularly in physics, work has a very specific meaning.

Work: Work is said to be done when a force applied on an object causes a displacement in the object.

Two Conditions Must Be Satisfied:

A force must be applied on the object
The object must be displaced (moved) in the direction of force

Both conditions are essential. If either is absent, NO WORK is done!

Formula for Work:

W = F × s

Where:
W = Work done (Joule, J)
F = Force applied (Newton, N)
s = Displacement (meter, m)

SI Unit of Work: Joule (J)
1 Joule = 1 Newton × 1 meter
1 J = 1 N m

Work Done by a Force at an Angle

When force is applied at an angle θ to the direction of displacement:

W = F × s × cos θ

Where θ is the angle between force and displacement

Special Cases:
• θ = 0° (force along displacement): W = F × s × cos 0° = F × s (Maximum work)
• θ = 90° (force perpendicular): W = F × s × cos 90° = 0 (No work)
• θ = 180° (force opposite): W = F × s × cos 180° = -F × s (Negative work)

Types of Work

1. POSITIVE WORK:

When force and displacement are in the same direction (0° ≤ θ < 90°)

Examples: Pushing a cart forward, lifting an object upward, pulling a rope

2. NEGATIVE WORK:

When force and displacement are in opposite directions (90° < θ ≤ 180°)

Examples: Friction opposes motion, braking a vehicle, catching a ball

3. ZERO WORK:

When: (a) Force is perpendicular to displacement (θ = 90°), OR (b) No displacement (s = 0), OR (c) No force (F = 0)

Examples: Carrying load horizontally, centripetal force in circular motion, pushing a wall

Energy

Energy: The capacity or ability of a body to do work is called energy.

Energy is measured by the amount of work a body can do.

SI Unit: Joule (J) - same as work

Nature: Scalar quantity

Kinetic Energy

Kinetic Energy (KE): The energy possessed by a body by virtue of its motion is called kinetic energy.

KE = ½mv²

Where:
m = Mass of object (kg)
v = Velocity of object (m/s)
KE = Kinetic energy (Joule)

Key Points about Kinetic Energy:

Depends on both mass and velocity
KE ∝ m (directly proportional to mass)
KE ∝ v² (proportional to square of velocity)
Doubling velocity makes KE four times
Always positive (v² is always positive)
Zero for objects at rest (v = 0)

Potential Energy

Potential Energy (PE): The energy possessed by a body by virtue of its position or configuration is called potential energy.

Gravitational PE = mgh

Where:
m = Mass of object (kg)
g = Acceleration due to gravity (9.8 m/s²)
h = Height above reference level (m)
PE = Potential energy (Joule)

Key Points about Potential Energy:

Depends on position (height) above ground
PE ∝ m (directly proportional to mass)
PE ∝ h (directly proportional to height)
Zero at reference level (usually ground)
Increases with height
Stored energy that can be converted to KE

Other Forms of Energy

Chemical Energy: Stored in bonds of molecules (food, fuel, batteries)
Heat Energy: Energy due to temperature difference
Light Energy: Energy in the form of electromagnetic waves
Sound Energy: Energy carried by sound waves
Electrical Energy: Energy from flow of electric charges
Nuclear Energy: Energy stored in atomic nuclei
Elastic Potential Energy: Stored in stretched/compressed objects

Law of Conservation of Energy

Law of Conservation of Energy:

"Energy can neither be created nor destroyed. It can only be transformed from one form to another. The total energy of an isolated system remains constant."

Mathematical Form:

Total Energy (Initial) = Total Energy (Final)

E₁ = E₂

Examples of Energy Conservation:

Freely falling object: PE converts to KE, Total = PE + KE = constant
Pendulum: PE ↔ KE continuously
Electric bulb: Electrical energy → Light + Heat
Photosynthesis: Light energy → Chemical energy
Hydroelectric plant: PE of water → KE → Electrical energy

Power

Power: Power is the rate of doing work or the rate at which energy is transferred or converted.

Power = Work / Time
P = W / t

Also: P = Energy / Time = E / t

SI Unit: Watt (W)
1 Watt = 1 Joule / 1 second
1 W = 1 J/s

Larger Units of Power:

1 kilowatt (kW) = 1000 W = 10³ W
1 megawatt (MW) = 1,000,000 W = 10⁶ W
1 horsepower (hp) = 746 W

Commercial Unit of Energy

Kilowatt-hour (kWh): The commercial unit of electrical energy

1 kWh = Energy consumed when 1 kW power is used for 1 hour

Conversion:

1 kWh = 1000 W × 3600 s = 3,600,000 J = 3.6 × 10⁶ J

1 kWh = 3.6 MJ (megajoules)

Also called: 1 Unit of electricity

Your electricity bill is calculated based on kWh consumed!

Important Formulas - Summary

1. Work: W = F × s (or W = F × s × cos θ)

2. Kinetic Energy: KE = ½mv²

3. Potential Energy: PE = mgh

4. Conservation of Energy: PE + KE = constant (for freely falling body)
At any point: mgh + ½mv² = constant

5. Power: P = W/t = E/t

6. Energy from Power: E = P × t

7. Work-Energy Theorem: Work done = Change in KE
W = KE_final - KE_initial = ½m(v² - u²)

Work-Energy Theorem

Work-Energy Theorem:

"The work done by the net force acting on a body is equal to the change in kinetic energy of the body."

W = ΔKE = KE_final - KE_initial
W = ½mv² - ½mu² = ½m(v² - u²)

Free Fall and Energy Conservation

Object Dropped from Height 'h':

At height 'h' (top):

PE = mgh, KE = 0, Total Energy = mgh

At height 'x' (during fall):

PE = mgx, KE = mg(h-x), Total Energy = mgh

At ground (h = 0):

PE = 0, KE = mgh, Total Energy = mgh

Energy is conserved at every point!

Multiple Choice Questions (MCQ)

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Subjective Questions

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