THP Coaching Classes - Class 9 Physics: Work and Energy

📘 Introduction to Work

Work is said to be done when a force causes displacement of an object in the direction of the force.

W = F × S

Where:
W = Work done (in Joules)
F = Force applied (in Newtons)
S = Displacement in the direction of force (in meters)

Work is a scalar quantity - it has magnitude but no direction.

1 Joule (J) = 1 Newton (N) × 1 meter (m)

Definition of 1 Joule: If 1 N force is applied on an object and the displacement is 1 meter in the direction of force, then the work done is 1 J.

Conditions for Work to be Done

A force must be applied on the object
The object must be displaced
There must be a component of displacement in the direction of force

Types of Work

1. Positive Work: When force and displacement are in the same direction. Example: Pushing a box forward. Work Done: W > 0

2. Negative Work: When force and displacement are in opposite directions. Example: Friction slowing down a moving object. Work Done: W < 0

3. Zero Work: When there is no displacement or displacement is perpendicular to the force. Example: Pushing a wall that doesn't move. Work Done: W = 0

Diagram showing positive, negative, and zero work — Fig. 3 — Illustration of positive, negative, and zero work

Example 1: A force of 10 N is applied to move a box through a distance of 5 m in the direction of force. Calculate the work done.

Solution: W = F × S = 10 N × 5 m = 50 J

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Remember: Work = Force × Displacement (in the direction of force)
Positive work adds energy, negative work removes energy

⚡ Energy

Energy of a body is its capacity to do work. The SI unit of energy is Joule (J).

1 Joule of energy = Capacity to do 1 Joule of work

🔑 Key Points About Energy

Energy is a scalar quantity
SI unit is Joule (J)
Larger units: 1 kJ = 1000 J
Energy can be transformed from one form to another

Sources of Energy

The ultimate source of energy is the Sun. We also get energy from:

Nuclei of atoms (Nuclear energy)
Interior of the Earth (Geothermal energy)
Tides (Tidal energy)
Wind (Wind energy)

Forms of Energy

Form of Energy	Description	Examples
Mechanical Energy	Energy due to position or motion	Moving car, water in dam
Heat Energy	Energy due to temperature difference	Hot objects, geothermal
Chemical Energy	Energy stored in chemical bonds	Food, fuels, batteries
Electrical Energy	Energy due to moving charges	Electric current, lightning
Light Energy	Energy in the form of electromagnetic waves	Sunlight, lamps
Nuclear Energy	Energy stored in atomic nuclei	Nuclear reactors, stars

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Remember: The Sun is the ultimate source of energy for most life on Earth.
Energy can change forms but cannot be created or destroyed.

🏃 Kinetic Energy

Kinetic Energy is the energy possessed by an object due to its motion.

E_k = ½ mv²

Where:
E_k = Kinetic energy (in Joules)
m = Mass of the object (in kg)
v = Velocity of the object (in m/s)

Kinetic energy depends on both mass and velocity, but it's more sensitive to changes in velocity since velocity is squared in the formula.

Derivation of Kinetic Energy Formula

Consider an object of mass m, initially moving with velocity u. A force F is applied, producing acceleration a, and the object reaches velocity v after displacement S.

From equations of motion:

v² - u² = 2aS

Rearranging:

S = (v² - u²) / 2a

From Newton's second law:

F = ma

Work done on the object:

W = F × S = ma × (v² - u²) / 2a = ½ m(v² - u²)

If the object starts from rest (u = 0):

W = ½ mv²

This work done is stored as kinetic energy:

E_k = ½ mv²

Example 2: Calculate the kinetic energy of a car of mass 1000 kg moving with a velocity of 20 m/s.

Solution: E_k = ½ mv² = ½ × 1000 × (20)² = 500 × 400 = 200,000 J = 200 kJ

Kinetic Energy Diagram — Fig. 1 — Relationship between kinetic energy and velocity

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Remember: Kinetic energy depends on the square of velocity.
Doubling velocity quadruples kinetic energy: E_k ∝ v²

📈 Potential Energy

Potential Energy is the energy possessed by a body by virtue of its position or configuration.

E_p = mgh

Where:
E_p = Potential energy (in Joules)
m = Mass of the object (in kg)
g = Acceleration due to gravity (9.8 m/s²)
h = Height of the object above reference point (in meters)

Derivation of Potential Energy Formula

Consider an object of mass m raised to a height h from the ground. The minimum force required is equal to the weight of the object (mg).

Work done against gravity:

W = F × S = mg × h

This work is stored as potential energy:

E_p = mgh

The reference point for measuring height (h) is important. Potential energy is always measured relative to a reference level.

Example 3: A book of mass 2 kg is placed on a shelf 3 m above the ground. Calculate its potential energy. (Take g = 9.8 m/s²)

Solution: E_p = mgh = 2 × 9.8 × 3 = 58.8 J

Types of Potential Energy

1. Gravitational Potential Energy: Energy an object has due to its height or position in a gravitational field. Example: Water in a dam, a raised object.

2. Elastic Potential Energy: Energy stored in objects when stretched or compressed. Example: Stretched spring, compressed ball.

3. Chemical Potential Energy: Energy stored in chemical bonds of substances. Example: Food, fuels, batteries.

Potential Energy Diagram — Fig. 2 — Gravitational potential energy increases with height

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Remember: Potential energy depends on height, mass, and gravity.
More height = More potential energy

♻️ Law of Conservation of Energy

Law of Conservation of Energy states that energy can neither be created nor destroyed, but can be transformed from one form to another. The total energy before and after transformation remains constant.

Total Energy_initial = Total Energy_final

Examples of Energy Transformation

Process	Energy Transformation
Hydroelectric power plant	Potential → Kinetic → Electrical
Photosynthesis	Light → Chemical
Electric heater	Electrical → Heat
Burning of fuel	Chemical → Heat + Light
Solar cell	Light → Electrical

Example 4: A ball is dropped from a height of 10 m. Assuming no air resistance, calculate its velocity just before it hits the ground. (Take g = 10 m/s²)

Solution:
Potential energy at top = Kinetic energy at bottom
mgh = ½ mv²
gh = ½ v²
10 × 10 = ½ v²
100 = ½ v²
v² = 200
v = √200 = 14.14 m/s

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Remember: Energy is conserved - it changes form but the total amount stays constant.
In real systems, some energy is always "lost" as heat due to friction.

⚡ Power

Power is the rate of doing work or the rate of transfer of energy.

P = W / t

Where:
P = Power (in Watts)
W = Work done (in Joules)
t = Time taken (in seconds)

1 Watt (W) = 1 Joule (J) / 1 second (s)

Definition of 1 Watt: 1 watt is the power of an object which does work at the rate of 1 joule per second.

Commercial Unit of Energy

The commercial unit of energy is kilowatt-hour (kWh), commonly called a "unit".

Definition of 1 kWh: 1 kWh is the energy used in one hour at the rate of 1000 J/s (or 1 kW).

1 kWh = 1 kW × 1 hour = 1000 W × 3600 s = 3.6 × 10⁶ J

Example 5: A 100 W bulb is used for 5 hours daily. Calculate the energy consumed in kWh in 30 days.

Solution:
Power = 100 W = 0.1 kW
Time per day = 5 hours
Energy per day = 0.1 kW × 5 h = 0.5 kWh
Energy in 30 days = 0.5 × 30 = 15 kWh = 15 units

Unit	Equivalent	Conversion
1 Joule (J)	1 N·m	Basic SI unit of work/energy
1 Kilojoule (kJ)	1000 J	1 kJ = 10³ J
1 Watt (W)	1 J/s	SI unit of power
1 Kilowatt (kW)	1000 W	1 kW = 10³ W
1 Kilowatt-hour (kWh)	3.6 × 10⁶ J	Commercial unit of energy

Electricity meter showing kilowatt-hours (kWh) — Fig. — Electricity meter display of kilowatt-hours (kWh)

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Remember: Power measures how fast work is done.
1 kWh = 1 unit of electricity in our electricity bills.

🔢 Practice Problems

Numerical Problems

Problem 1: A force of 50 N is applied to move a box through a distance of 8 m in the direction of force. Calculate the work done.

Problem 2: A crane lifts a load of 2000 kg to a height of 25 m. Calculate the work done by the crane. (Take g = 10 m/s²)

Problem 3: Calculate the kinetic energy of a car of mass 1200 kg moving at 25 m/s.

Problem 4: A ball of mass 0.5 kg is thrown vertically upwards with a velocity of 20 m/s. Calculate the maximum height it reaches. (Take g = 10 m/s²)

Problem 5: A man does 600 J of work in 2 minutes. Calculate his power.

Problem 6: An electric heater of power 1500 W is used for 3 hours daily. Calculate the energy consumed in kWh in 15 days.

Conceptual Questions

Define work. Give an example of zero work.
Differentiate between kinetic energy and potential energy.
State the law of conservation of energy with an example.
Why is the work done by centripetal force zero?
Explain why a person carrying a load on his head does no work while walking on a horizontal road.
What is the commercial unit of energy? Express it in joules.

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Exam Tips:
- Always write formulas with proper notation
- Include units in calculations and final answers
- Draw diagrams where applicable
- Show all steps in numerical problems