Work and Energy Class 9 Notes Science Chapter 11

Conditions that must satisfied for work to be done:

1. A force should act on an object.
2. The object must be displaced.
3. The direction of Force must not be perpendicular to the displacement

Types of Work

A) Positive Work

• When the force acts in the same direction as the displacement
• Angle θ = 0°, so cos(0°) = 1
• Work done is positive

Examples: A person pushing a box across the floor

Therefore: W=F×s

B) Negative Work

• When the force acts opposite to the direction of displacement
• Angle θ = 180°, so cos(180°) = -1
• Work done is negative

Examples: Braking force on a moving car

Therefore: W=−F×s

C) Zero Work

• When force acts perpendicular to displacement
• Angle θ = 90°, so cos(90°) = 0
• No work is done even though force is applied

Examples:

• A coolie carrying luggage on his head while walking horizontally (force is vertical, displacement is horizontal)
• A person pushing against a wall without moving it
• Earth’s gravitational force acting on a satellite orbiting at constant height

Therefore: $=0$

Energy

Definition of Energy

Energy is the capacity or ability of a body to do work.

• Energy is a scalar quantity
• SI Unit: Joule (J)
• 1KJ = 1000 J
• Energy can be transferred from one object to another
• Energy can be transformed from one form to another
• The total energy in an isolated system remains constant

Forms of Energy

Energy exists in various forms:

1. Mechanical energy (Kinetic energy + Potential energy )
2. Heat energy
3. Chemical energy
4. Electrical energy
5. Light energy
6. Nuclear energy
7. Solar energy, etc.

Kinetic Energy

Kinetic energy is the energy of an object due to its motion.

A faster object has more kinetic energy.

Formula

\( KE = \frac{1}{2}mv^2\)

Where:

• KE = Kinetic Energy (in Joules, J)
• m = Mass of the object (in kg)
• v = Velocity of the object (in m/s)

Derivation:

Let us consider a body of mass ‘m’ moving with initial velocity ‘u’. Let a force ‘F’ is applied on the body so that its velocity changes to ‘v’ and it covers ‘s’ distance. Let the force causes acceleration ‘a’.

We know,

\( F=m\times a \)————(i)

Also,
\( W=F\times s \)————(ii)

From the Third Equation of Motion

\( v^2 – u^2 = 2as\)

Let the object start from rest, so initial velocity u=0
Then,

\( v^2 = 2as\)

\(s = \frac{v^2}{2a}\)​

From the equation (i) and (ii), we have

\(W = ma \left(\frac{v^2}{2a}\right)\)

\(W = m \times \frac{v^2}{2}\)​

So,

\(W = \frac{1}{2}mv^2\)

Properties of Kinetic Energy:

• Kinetic energy is always positive (since v² is always positive)
• Kinetic energy is directly proportional to mass
• Kinetic energy is directly proportional to the square of velocity
• If velocity is doubled, kinetic energy increases by a factor of 4

Examples: A moving car

Potential Energy (PE)

Definition: Potential energy is the energy possessed by a body due to its position or shape.

Types of Potential Energy:

A) Gravitational Potential Energy:
B) Elastic Potential Energy:

Gravitational Potential Energy:

• When an object is raised through a height, work is done on it against gravity. The energy present in such an object is called gravitational potential energy.
• GPE is defined as the work done in raising the object from the ground to that point against gravity.
• The minimum force required to raise an object of mass $m$ is equal to its weight, $mg.$

Formula:
PE=mgh

Where:

• PE = Potential Energy (in Joules, J)
• m = Mass of the object (in kg)
• g = Acceleration due to gravity (≈ 9.8 m/s² or 10 m/s²)
• h = Height above reference level (in meters, m)

Derivation of Potential Energy:

Let us consider an object mass m raised upto a height h from the ground. Let F be the force required to raise the object up to that height.

Then, work done in doing so is given by—–

W=F×s —————-(i)

By Newton’s second law of motion,

The force required is given by

F = mg ——————(ii)

From (i), we have

W = mgh ( Since, displacemet = height)