VARDAAN LEARNING INSTITUTE | POWERED BY VARDAAN COMET

Work and Energy

CBSE Class 9 Science • Chapter 10 • Detailed Master Notes

Chapter Overview:

Physics defines work differently from our daily usage. This chapter links the concept of Work with Energy, exploring its forms (Kinetic & Potential), the Law of Conservation of Energy, and the rate of doing work, which is Power.

1. Work

In ordinary language, reading, thinking, or standing with a load is considered work. But in Science:

Scientific Definition of Work:

Work is said to be done by a force on an object if:

A force acts on the object.
The object undergoes displacement.

We define Work done ($W$) as the product of magnitude of force ($F$) and displacement ($s$).

$$ W = F \times s $$

SI Unit: Joule (J) or Newton-meter ($N m$).
1 Joule: 1 J is the work done when a force of 1 N moves an object by 1 m in the direction of force.
Work is a Scalar Quantity (Has magnitude, no direction).

Nature of Work Done

Depending on the direction of Force and Displacement, work can be:

1. Positive Work: Force and displacement are in the same direction ($\theta = 0^\circ$).

Example: A lifting a book upward (Work by lifting force); A horse pulling a cart.

2. Negative Work: Force and displacement are in opposite directions ($\theta = 180^\circ$).

Example: Work done by Friction when a car stops; Work done by Gravity when lifting an object.

3. Zero Work:

No displacement ($s=0$): Pushing a wall.
Force is perpendicular to displacement ($\theta = 90^\circ$): ($W = Fs \cos 90^\circ = 0$).
Example: A coolie carrying a load and walking on a level road (Force of gravity acts down, displacement is horizontal).

2. Energy

The sun is the biggest natural source of energy. In science, energy is a quantitative property.

Definition: The capacity of a body to do work is called its Energy.

An object having energy can exert force on another object to move it.
The unit of Energy is same as Work: Joule (J).
Examples: Mechanical, Heat, Chemical, Electrical, Light energy.

3. Forms of Mechanical Energy

Mechanical Energy is the sum of Kinetic Energy and Potential Energy.

(a) Kinetic Energy ($E_k$)

Definition: The energy possessed by an object due to its motion. Moving bullet, blowing wind, rotating wheel have KE.

Formula Derivation:

Consider an object of mass $m$ at rest ($u=0$).
A force $F$ acts on it, causing displacement $s$ and final velocity $v$.
Work Done $W = F \times s$.
From Newton's Law: $F = ma$.
From 3rd Equation of Motion: $v^2 - u^2 = 2as \Rightarrow s = \frac{v^2}{2a}$ (since $u=0$).
Substitute $F$ and $s$ in Work equation:
$$ W = (ma) \times (\frac{v^2}{2a}) = \frac{1}{2} mv^2 $$

So, the work done becomes Kinetic Energy.

$$ E_k = \frac{1}{2} mv^2 $$

(b) Potential Energy ($E_p$)

Definition: The energy possessed by an object due to its position or configuration (shape/size).

Examples: Stretched rubber band (Elastic PE), Water growing in a dam (Gravitational PE).

(c) Gravitational Potential Energy

Work done in lifting an object of mass $m$ to a height $h$ against gravity ($g$).

Force required = Weight of object = $mg$.
Displacement = Height = $h$.
Work Done $W = \text{Force} \times \text{Displacement} = mg \times h$.

$$ E_p = mgh $$

Key Note: Work done by gravity depends only on the initial and final vertical heights, not on the path taken.

4. Law of Conservation of Energy

Statement: 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 conserved.

Example (Free Fall):

At Max Height: $v=0 \Rightarrow KE=0$. $h$ is max $\Rightarrow PE=mgh$. Total = $mgh$.
During Fall: Height decreases (PE decreases), Velocity increases (KE increases).
Just before Ground: $h=0 \Rightarrow PE=0$. $v$ is max $\Rightarrow KE$ is max. Total = $mgh$.

At any point, $KE + PE = \text{Constant}$.

5. Power

Doing work at a faster rate requires more power.

Definition: Rate of doing work or rate of transfer of energy.

$$ Power (P) = \frac{\text{Work (W)}}{\text{Time (t)}} $$

SI Unit: Watt ($W$).
$1 Watt = 1 Joule/second$.
Average Power = Total Energy Consumed / Total Time Taken.

Commercial Unit of Energy

Joule is a very small unit. For household/industry, we use Kilowatt-hour ($kWh$).

1 Unit = 1 kWh

This is the energy consumed when 1 kW appliance is used for 1 hour.

Relation with Joule:

$1 kWh = 1 kW \times 1 h$
$= 1000 W \times 3600 s$
$= 3,600,000 J$

$$ 1 kWh = 3.6 \times 10^6 J $$

Practice Zone

Q1: A porter lifts a luggage of 15 kg from the ground and puts it on his head 1.5 m above the ground. Calculate work done.

Ans: $m = 15 kg, h = 1.5 m, g = 9.8 m/s^2$ (approx $10$).
$W = mgh = 15 \times 10 \times 1.5 = 225 J$.

Q2: Two girls A and B each weigh 400N. They climb up a rope 8m high. Girl A takes 20s, girl B takes 50s. What is the power expended by each?

Ans: Weight ($mg$) = 400 N. Height ($h$) = 8 m.
Work done by both $= mgh = 400 \times 8 = 3200 J$.
Power of A $= W/t = 3200/20 = 160 W$.
Power of B $= W/t = 3200/50 = 64 W$.

Q3: An electric bulb of 60 W is used for 6 hours per day. Calculate the 'units' of energy consumed in one day.

Ans: Power $= 60 W = 0.06 kW$. Time $= 6 h$.
Energy $= P \times t = 0.06 \times 6 = 0.36 kWh = 0.36 \text{ Units}$.