# CBSE Class 9 Science Revision Notes Chapter 11

## CBSE Class 9 Science Revision Notes Chapter 11 – Work and Energy

The Class 9 Science Chapter 11 Notes provides an overview of the concept of energy, work and power. After studying the chapter, you can review the concepts and understand them better by referring to Class 9 Chapter 11 Science Notes. A team of expert teachers have created the Chapter 11 Science Class 9 Notes while keeping in mind the most recent CBSE syllabus. Students will also learn about new concepts and different formulas related to work, energy, and power in Class 9 Science Notes Chapter 11 for solving mathematical problems. Students can download the CBSE revision notes in PDF format from the Extramarks website and use them for quick revision before exams.

In addition to the CBSE revision notes, students can access CBSE past years’ question papers and CBSE sample papers from the Extramarks website. Practising important questions, sample papers, past years’ question papers, and CBSE extra questions will help students understand the exam format and develop time-management skills to score better in the exam.

### Access Class 9 Science Chapter 11 – Work and Energy

Introduction

Energy is the ability to do work in daily life. According to scientific terminology, energy is quantifiable. It is the quantifiable quality that is transferred to a body or a physical system and is noticeable in the performance of work and in the form of heat and light.

In simple terms, work means an action that requires bodily or mental effort. However, this term means something different in Science. It represents a measurable quantity. When a force acts on an object and causes it to move in that direction, we say that the object has undergone work from the external force. We can further understand this with examples.

Ex 1: If a person attempts to push a textbook lying on a table, he is applying force to the book. The book then moves in the direction of the force, and we say that the force has done its job.

Ex 2: If a person attempts to push a wall, the person may get tired, but the wall will not move. Therefore, we can conclude that no work was done.

• Work and Measurement of Work

The work is said to be completed when a force acts on an object and the point of application shifts in its direction.

• Conditions to be Satisfied for Work to be Done
• Force must be applied to the object.
• The object must move in the force’s direction.
• The force is multiplied by the distance travelled to determine the amount of work.

W = F × S

Here W denotes the work done, F means the force exerted, and S is the distance travelled by the object. The amount of work done is a scalar quantity.

• Work Done When the Force is not Along the Direction of Motion

In the given figure, F is the constant force applied on a body, which results in a displacement S, as given in the figure. θ is the angle formed by the force and displacement directions.

Displacement in the direction where force is applied = Component of S along AX = AC

cos θ = adjacent side/ hypotenuse

cos θ = AC/S

AC = S cos θ

Displacement in the direction of force = S cos θ

Work done = Force × displacement in the direction force is applied.

W= FS cos θ

If S is the displacement towards the direction of the force, FS = 0, cos θ = 1.

Then, W = FS × 1

W = FS

If θ = 90°

cos 90°= 0

Therefore, W= FS × 0 = 0, the force applied did not result in work done on the body.

• The Centripetal Force is Activated When a Stone at the End of a String is Whirled Around in a Circle at a Constant Speed

If a rock is suspended at the end of a string and rotated in a circular motion at a constant speed, the centripetal force will act on the rock. Normally, this force will apply in the direction that the rock is acting in every time. Although this force is causing the rock to move, it does not produce any work.

• SI Unit of Work

W = F × S

SI unit of F is N (N=Newton)

SI unit of S is m

∴ SI unit of work = N × m

1 Nm is defined as 1 joule.

i.e., 1 joule= 1 Nm

∴ The SI unit of work is joule.

• One joule refers to the amount of work done when the point of application of a one-newton force moves one metre in the direction of the force.
• The term joule was named after the British scientist James Prescott Joule.
• The letter ‘J’ represents Joule.
• The higher units of work are joule and megajoule.

1 kilojoule = 1000 J

Or 1 kilojoule = 10³ J

1 megajoule = 1000,000 J

Or 1 megajoule = 10⁶ J

• Energy

Energy is referred to as the ability to do work. The amount of energy a body possesses determines the amount of work it can do. The SI unit of energy is the Joule.

• Different Forms of Energy

Examples of different types of energy are thermal energy, mechanical energy, electrical energy, and chemical energy. Mechanical energy is further divided into two types: kinetic energy and potential energy.

• Kinetic Energy

Kinetic energy is the energy that an object possesses due to its motion, and it is denoted by the letter T. It is present in all moving objects.

For example, a swiftly moving stone can shatter a window pane, falling water can turn turbines, and moving air can rotate windmills and drive sailboats. In all of these scenarios, energy is present in the moving body, and the work is done by the moving body. Moving objects possess energy called kinetic energy.

• Expression for Kinetic Energy of a Moving Body

Let us take an example of a body of mass ‘m’ that is initially at rest. When force denoted by ‘F’ is applied to the body, it will start to move with the velocity ‘v’ and travel a distance of ‘S’. The force will cause acceleration ‘a’ in the body.

The work that the force ′F′ produces when it moves the body over a distance ′S′ is stored in the body as kinetic energy.

By definition, W = F × S              ..(1)

F = ma                                      (Newton’s second law of motion)

W = mas                            …(2)

Also, v² – u² = 2aS                    (Newton’s third law of motion)

v² – 0 = 2aS                              (Initial velocity u = 0 as the body is initially at rest)

v² = 2aS

a = v2/2aS

If we substitute the value of ‘a’ in equation (2), we get:

Since the work done is stored in the body as kinetic energy, equation (3) can also be written as:

From the above calculation, it can be understood that the kinetic energy of a body is directly proportional to (1) its mass and (2) the square of its velocity.

• Momentum and Kinetic Energy

All moving objects have momentum. The body’s momentum can be defined as the product of a body’s mass and velocity.

Let’s look at the relationship between a body’s kinetic energy and momentum.

Let’s consider a body of mass ‘m’ moving with a velocity ‘v’. The momentum of the body will be p = mv.

Substituting the value of v in equation (1), we get,

• Potential Energy

Take a look at the following examples.

• Water in a reservoir can rotate the turbine at a lower level. Water stored in a reservoir possesses energy due to its location.
• If a nail is struck with a hammer, it moves, but if the hammer is just resting on the nail, it scarcely moves. The hammer possesses kinetic energy due to its position.
• A winding key-driven toy car: When we turn the key, the spring gets wound. The toy car moves if left on the floor because the spring unwinds as we release our grip, causing the wheels to start rolling. The wound spring becomes active. The location or state of the spring is thought to be responsible for the increase in energy.
• Potential energy is the energy that an object possesses because of its position or state.

#### Expression for Potential Energy

Let’s consider a mass ‘m’, which has been lifted to a height ‘h’ above the earth’s surface. The work done against gravity is saved in the object as the potential energy (gravitational potential energy).

Therefore, potential energy = work done lifting the object to a certain height ‘h’.

The object of Mass’ m’ is suspended at a height ‘h’.

Potential energy = F × S ….(1)

However, F = mg (Newton’s second law of motion)

S = h

If we substitute F and S in equation (1), we get

Potential energy = mg × h

∴ Potential energy= mgh

The equation shown above makes it clear that an object’s potential energy is proportional to its height above the ground.

#### Law of Conservation of Energy

Let’s look at the following examples.

• Steam engine: In a steam engine, coal is burned. The heat generated by burning coal converts water into steam. The locomotive is propelled by the force of steam on the engine’s piston. Chemical energy is transformed into heat energy, which is then converted to steam’s expansion power. When the train moves, this energy becomes kinetic energy.
• Hydroelectric power plant: Water in the reservoir is forced to fall on the turbine kept at a lower level, which is connected to the coils of an a.c generator. The potential energy of the water in the reservoir is converted to kinetic energy, and the kinetic energy of falling water is converted to turbine kinetic energy, which is ultimately converted into electrical energy. Hence, we can understand that when one form of energy vanishes, an equal amount of energy in a different form emerges, so the total amount of energy remains constant.

Law of Conservation of Energy

The law of conservation of energy states that energy can neither be created nor destroyed but can be transformed from one form to another.

Let’s look at an example to check whether the given law is applicable or not.

Let’s imagine a body of mass ‘m’ is suspended at a height ‘h’ above the earth. In this example, we will demonstrate that the body’s total energy (potential energy + kinetic energy) remains unchanged, i.e., potential energy is converted into kinetic energy.

At P,

Potential energy = mgh

Kinetic energy = 1/2mv2 = ½ x m x 0

Kinetic energy = 0 (velocity is zero as the object is initially at rest)

Total energy at P = Potential energy + kinetic energy

= mgh + 0

Total energy at P = mgh ….(1)

At Q,

Potential energy = mgh

= mg(h-x) (Height from the ground is (h-x))

Potential energy= mgh – mgx

Distance covered by the body is x with a velocity v. The third equation of motion can be used to obtain the body’s velocity.

v² – u² = 2aS

Here, u = 0, a is g, and S is x

v²- 0 = 2gx

v² = 2gx

Kinetic energy = mgx

∴ Total energy at Q = Potential energy + Kinetic energy

= mgh – mgx + mgx

Total energy at Q = mgh ….(2)

At R,

Potential energy = m × g × 0 (h=0)

Potential energy = 0

Kinetic energy = 1/2mv2

Distance covered by the body is h,

v² – u² = 2aS

Here, u is  0, a = g and S = h

v² – 0 = 2gh

v² = 2gh

Kinetic energy = 1/2m × 2gh

Kinetic energy = mgh

Total energy = mgh

∴ Total energy at R = Potential energy + Kinetic energy

= 0 + mgh

∴ Total energy at R = mgh…(3)

From the above equations 1, 2, and 3, we can conclude that the law of conservation of energy applies to a freely falling body.

• Power

The rate of work being done or the rate at which the energy is being transferred is known as Power. For example, two people are standing in front of 2 tracks, A and B, which are 100m in length from one end to the other. What will be the amount of work done by each person?

The work done will be the same, but the time taken to complete the work might vary.

To find out who completed the work faster, we must calculate the work done on time.

The total amount of work done and the total amount of work per unit of time are two separate quantities.

Work performed at a given time or at a given pace is referred to as power, which is represented by the letter ‘P’.

P = w/t, where w is the work done and t is the time taken.

Given that energy is the ability to do work, power can be defined as the amount of energy spent over a specified period.

P = E/t, where E is the energy consumed.

• SI unit of power

The SI unit of work is joule and the SI unit of time is second. So, the SI unit of power will be joule/second. 1 watt = 1 joule/second

If an agent performs one joule of work in one second, its power is measured in watts.

The higher power units are Kilowatts and Megawatts.

1 kilowatt (kW) = 10³ watts

1 Megawatt (MW) = 10⁶ watts

Another unit of power is horsepower.

1 horsepower= 746 watts

• Commercial Unit of Energy

Joule may not be sufficient to express a high amount of energy. As a result, we use a larger unit called a kilowatt-hour (kWh) to express energy.

1 kWh is the unit of energy used by an electronic device in one hour at the rate of 1000 J/s or (1kW).

A kilowatt-hour usually denotes energy consumed in households and industries.

• Numerical Relation Between SI and Commercial Unit of Electrical Energy

Joule is the SI unit of energy. The commercial unit of energy is denoted by kWh.

1 kWh = 1 kW × 1 h = 1000 W × 3600 s

1 kWh = 3600000 J

1 kWh = 3.6 × 10⁶ J

1 kWh = 1 unit

### Class 9 CBSE Science Revision Notes Chapter 11 – Work and Energy

We hear people talking about energy consumption in everyday life, and it is said that energy never gets destroyed; instead, it is transferred from one form to another, performing the work in the process. Some forms of energy are less useful to us than others, for example, low-level heat energy. Therefore, it is more beneficial to talk about the extraction or the consumption of energy resources, like oil, coal, or wind, than energy consumption by itself.

A fast-moving bullet has a measurable amount of energy known as kinetic energy. The bullet gains energy because work was done on it by a charge of gunpowder, which lost some potential chemical energy in this whole process.

Hot coffee has a measurable quantity of thermal energy obtained from work performed by a microwave oven, which uses electrical energy from the electrical grid.

Whenever work is done to move energy from one form to another, there is always some loss of energy to other forms of energy, such as heat and sound energy. For example, an old light bulb is only around 3% efficient at converting electrical energy to visible light, whereas humans are about half of 50, or 25% efficient, at converting chemical energy.

#### Measurement of Energy and Work

A Joule is the standard unit used to measure work and energy done in physics, and it is denoted by the symbol J. For example, in mechanics, 1 joule is the energy transferred when a force of 1 Newton is applied to an object, which moves it over a 1-metre distance.

The energy content of food is written in calories on the back of the packet of any food item. For example, a 60-gram chocolate bar contains about 280 calories. One calorie refers to the energy needed to raise 1 kg of water by 1 degree Celsius.

Why are we using kilograms here instead of grams?

Since there are 4184 joules in every calorie, one chocolate bar has 1.17 million joules, or 1.17 MJ of stored energy. So we can see that’s a lot of joules.

Holding an Object

People often get confused with the concept of work when thinking about holding a heavy-weight stationary above their heads against gravity. We are not moving the weight across any distance; hence no work is being done in relation to the weight. We might also accomplish this by placing the weight on a table, so it will be obvious that the table is not exerting any effort to maintain the weight in position. However, we are aware from prior experience that we become exhausted while performing the same task. What is happening then?

This is because our bodies work on our muscles to maintain the necessary tension that holds the weight up. The body accomplishes this by sending each muscle a series of nerve signals. The muscle temporarily releases and contracts in response to each stimulus. These events occur so quickly that we may only detect a small twist. However, eventually, the muscles won’t have enough chemical energy to keep us going. Then we start to tremble and temporarily rest. We are therefore working, but the job on the weight’s part is just not being done.

Work

Work is the process of energy being transferred to the motion of an object moving through the application of a force, which is expressed as the product of force and displacement. When a force is applied, and a component of that force is in the displacement direction of the application, the force is said to do positive work.

For example, when a ball is held above the ground and then dropped down, the work done on the ball by the gravitational force as it falls is equal to the ball’s weight. When the force (F) is constant, and the angle between the displacement and force is θ, then the work done is given by the formula:

W = Fs cosθ

### 1. A pair of bullocks exerts a force of 150 N on a plough cart. The field being ploughed is 15 m long. Calculate the work done in ploughing the length of the field.

Work done by the bulls is given by the expression:

W= F × d

Where applied force (F) = 150 N

Displacement (d) = 15 m

W = 150 x 15 = 2250 J

Therefore, 2250 J of work is done in ploughing the length of the field.

### 2. The K.E of an object of mass m accelerating with a velocity of 5 m/s is 25 J. Calculate the kinetic energy when its velocity is doubled and tripled.

Given K.E. of the object = 25 J

Velocity of the object (v) = 5 m/s

K.E. = (½) mv2

25 = (½) m (5)2

50 = 25 x m

m = 50/25

m = 2 kg

When velocity is doubled, then

v = 10 m/s

m = 2 kg

K.E. = (½) x 2 x (10)2

K.E. = 100 J

When velocity is increased three times, then

v = 15 m/s

m = 2 kg

K.E. = (½) x 2 x (15)2

K.E. = 225 J

### 3. A lamp consumes 2000 J of electrical energy in 20 s. Calculate its power.

Power = Work/Time

P = W/T

Time = 10 s

Work done = energy used by the lamp = 1000 J

Power = 2000/20 = 200 Js-1 =200 W

Therefore, the power of the lamp is 200 W