NCERT Science Notes - Class 9
Chapter 10 - Work and Energy

Welcome to AJs Chalo Seekhen. This webpage is dedicated to Class 9 | Science | Chapter 10 - Work and Energy. The chapter introduces the concepts of work, energy, and power. It explains how work is done when a force moves an object in the direction of the force and defines energy as the capacity to do work. The chapter explores different forms of energy, such as kinetic energy (energy due to motion) and potential energy (energy due to position). The Law of Conservation of Energy is emphasized, stating that energy cannot be created or destroyed but can only change forms. The Work-Energy Theorem and the concept of power, the rate at which work is done, are also discussed.

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NCERT Science Notes - Class 9
Chapter 10 - Work and Energy

1. Work

• Definition: Work is done when a force acts on an object and causes it to move in the direction of the force.
• Formula: $$\text{Work (W)} = \text{Force (F)} \times \text{Distance (d)} \times \cos(\theta)$$
  
  • Where $\theta$ is the angle between the force and the direction of motion.
• Unit: The SI unit of work is the joule (J).

• Definition: Energy is the capacity to do work.
• Types of Energy:
  • Kinetic Energy: Energy possessed by an object due to its motion.
    • Formula: $$\text{Kinetic Energy (KE)} = \frac{1}{2} m v^2$$
      
      • Where $m$ is the mass and $v$ is the velocity.
  • Potential Energy: Energy possessed by an object due to its position or condition.
    • Formula: $$\text{Potential Energy (PE)} = mgh$$
      
      • Where $m$ is the mass, $g$ is the acceleration due to gravity, and $h$ is the height above the ground.

• Definition: Power is the rate at which work is done or energy is transferred.
• Formula: $$\text{Power (P)} = \frac{\text{Work (W)}}{\text{Time (t)}}$$
  
• Unit: The SI unit of power is the watt (W), where $1\text{W}=1\text{J/s}$

• Life Processes: All living beings require energy for survival and performing basic activities, known as life processes.
• Activities Requiring Energy:
  • Physical activities like playing, running, cycling, and jumping require varying amounts of energy.
  • Animals also engage in activities such as finding food, escaping threats, and moving to safe places, all of which require energy.

• Definition of Machines: Machines are devices that perform work using energy.
• Energy Requirements:
  • Machines require energy to function, often sourced from fuels (e.g., petrol, diesel) or electricity.
  • Understanding why machines need energy is crucial for their design and efficiency.

1. What is work, and how is it calculated?
   • Work is done when a force causes an object to move in the direction of the force. It is calculated using the formula $W = F \times d \times \cos(\theta)$
     
2. What is energy, and why is it important for living beings?
   • Energy is the capacity to do work, and it is essential for survival and performing daily activities.
3. What are the different forms of energy?
   • The two main forms of energy discussed are kinetic energy (due to motion) and potential energy (due to position).
4. What is power, and how is it related to work?
   • Power is the rate at which work is done or energy is transferred. It measures how quickly work can be performed.

10.1 - What is Work?

• Definition (Scientific): In science, work is defined as the application of force to an object that results in the displacement of the object in the direction of the applied force. $$\text{Work (W)} = \text{Force (F)} \times \text{Displacement (d)} \times \cos(\theta)$$
  • $\theta$ is the angle between the force and the direction of displacement.
  • Unit: The SI unit of work is the joule (J).
• Day-to-Day Usage vs. Scientific Definition:
  • In everyday life, work is any useful physical or mental effort. Examples include studying, drawing, attending classes, or talking with friends.
  • However, in science, work requires displacement. If no displacement occurs, no work is done, regardless of the effort involved.

10.1.1 - Not Much ‘Work’ in Spite of Working Hard!

10.1.2 - Scientific Conception of Work

To define work scientifically, we can analyze several scenarios where forces cause displacements:

1. Pushing a Pebble:
   • Description: When you push a pebble on a surface and it moves.
   • Force: You exerted a force on the pebble.
   • Displacement: The pebble is displaced.
   • Conclusion: Work is done.
2. Pulling a Trolley:
   • Description: A girl pulls a trolley and it moves through a distance.
   • Force: The girl exerts force on the trolley.
   • Displacement: The trolley moves; hence, work is done.
3. Lifting a Book:
   • Description: Lifting a book requires applying force to move it upwards.
   • Force: You apply an upward force on the book.
   • Displacement: The book rises; therefore, work is done.
4. Pulling a Cart:
   • Description: A bullock pulls a cart, and the cart moves.
   • Force: There is a force acting on the cart.
   • Displacement: The cart moves; thus, work is done.
     
     

1. A force must act on the object.
2. The object must be displaced.

Activity 10.2

Instructions:

• Think of daily life situations involving work.
• List them and discuss with friends whether work is being done.

1. Pushing a Door Open:
   • Force: You push the door.
   • Object: The door.
   • Displacement: The door moves; work is done.
2. Carrying a Backpack While Walking:
   • Force: The gravitational force acts downward.
   • Object: The backpack.
   • Displacement: The backpack is carried, but if you do not lift it, no work is done in lifting it.
3. Writing with a Pen:
   • Force: You apply pressure with your hand.
   • Object: The pen on the paper.
   • Displacement: The pen moves across the paper; work is done.

• What is the force acting on the object?
  • In pushing the door, the force is the push applied by your hand. In carrying a backpack, the force is gravity acting on the backpack.
• What is the object on which the work is done?
  • The object is the door in the first case and the backpack in the second.
• What happens to the object on which work is done?
  • The door opens when pushed (displacement occurs), and the backpack is lifted or carried while walking (force exerted in an upward direction).

Activity 10.3

Instructions:

• Think of situations where an object does not get displaced despite a force acting on it.
• Also consider situations where an object gets displaced without a force acting on it.

1. Object Not Displaced Despite Force:
   • Example: Pushing a wall.
     • Force: You exert force on the wall.
     • Displacement: The wall does not move; therefore, no work is done.
   • Example: Holding a book stationary.
     • Force: You hold the book up against gravity.
     • Displacement: If the book does not move, no work is done.
2. Object Displaced Without Force:
   • Example: A toy car rolling down a hill.
     • Force: Gravity acts on it.
     • Displacement: The car moves downwards; work is done by gravity, not by you.
   • Example: A balloon floating away.
     • Force: Air pushes it.
     • Displacement: The balloon moves; work is done by air.

• Is work done in the situations you listed? Why or why not?
  • For Pushing a Wall: No work is done because, although a force is applied, there is no displacement of the wall.
  • For Holding a Book: No work is done because the book remains stationary despite the force applied to hold it up.
• Explain the reasoning behind your answers based on the conditions for work.
  • In both cases, the condition for work (displacement) is not met. Work is defined scientifically by the relationship between force and displacement; without displacement, no work can be considered done, regardless of how much force is applied.

• Force: A push or pull acting on an object.
• Displacement: The distance and direction an object moves from its initial position.
• Work: The product of force and displacement in the direction of the force.

• For scientific work to be done, both force and displacement are essential.
• Activities involving force without displacement or displacement without force do not constitute work in the scientific sense.

10.1.3 - Work Done by a Constant Force

Definition of Work in Science

• Work: In science, work is defined as the product of the force applied to an object and the displacement of the object in the direction of that force. $$\text{Work Done (W)} = \text{Force (F)} \times \text{Displacement (s)}$$

• Work is done when a constant force acts on an object and causes displacement in the direction of the force.
• Work is a scalar quantity, meaning it has magnitude but no direction.
• The unit of work is newton metre (N m), also known as a joule (J).

• 1 Joule (J): The amount of work done when a force of 1 N displaces an object by 1 m along the line of action of the force.

• Work is done if:
  • A force acts on the object (F > 0).
  • The displacement of the object occurs (s > 0).
• If F = 0 (no force), or s = 0 (no displacement), then:
  • Work Done (W) = 0.

• Given: Force (F) = 5 N; Displacement (s) = 2 m.
• Calculation: $$W = F \times s = 5 \, \text{N} \times 2 \, \text{m} = 10 \, \text{N m} = 10 \, \text{J}$$

• When an object moves in the direction of the applied force, work is positive.
• When the applied force opposes the displacement, work is negative. The force is considered negative if it acts in the opposite direction of the displacement.

• When a retarding force is applied opposite to the direction of motion (angle = 180º):
  
  $$\text{Work Done} = F \times (-s) = -F \times s$$

Instructions:

1. Lift an object upwards.
2. Analyze the forces involved.

• Which force is doing positive work?
  • Answer: The force exerted by you on the object is doing positive work because it acts in the direction of displacement (upward).
• Which force is doing negative work?
  • Answer: The force of gravity is doing negative work because it acts in the opposite direction of the displacement (downward).

• Positive Work: Work is done when the force and displacement are in the same direction.
• Negative Work: Work is done when the force acts opposite to the direction of displacement.

• Problem: A porter lifts a luggage of mass 15 kg from the ground and puts it on his head at a height of 1.5 m. Calculate the work done.

1. Given:
   • Mass of luggage, $m=15\text{kg}$
   • Displacement, $s = 1.5 \, \text{m}$
     
   • Acceleration due to gravity, $g = 10 \, \text{m/s}^2$
     
2. Calculate Force: $$F = m \times g = 15 \, \text{kg} \times 10 \, \text{m/s}^2 = 150 \, \text{N}$$
3. Calculate Work Done: $$W = F \times s = 150 \, \text{N} \times 1.5 \, \text{m} = 225 \, \text{N m} = 225 \, \text{J}$$

• Work is defined as the product of force and displacement.
• The work can be positive or negative depending on the direction of the force relative to the displacement.
• Understanding work requires knowledge of force, displacement, and the conditions under which work is done.

10.2 - Energy

Importance of Energy

• Life and Energy: Life is impossible without energy. The demand for energy is constantly increasing.
• Primary Source: The Sun is the biggest natural source of energy for us.
• Other Sources:
  • Nuclei of atoms
  • Interior of the Earth
  • Tides
• Discussion: Think of other sources of energy beyond those listed.

1. Instructions:
   • List other sources of energy beyond the ones mentioned.
   • Discuss in small groups how certain sources of energy are derived from the Sun.
   • Identify sources of energy that are not derived from the Sun.

• In science, energy is defined as the capacity of an object to do work.
• When an object possesses energy, it has the capability to exert a force on another object and perform work.

1. Cricket Ball and Wicket: When a fast-moving cricket ball hits a stationary wicket, it transfers energy, causing the wicket to be displaced.
2. Raised Hammer: A hammer raised to a height gains potential energy and can do work when it falls, driving a nail into wood.
3. Winding a Toy: Winding a toy car gives it potential energy; when placed on the floor, it converts that energy to kinetic energy and moves.
4. Balloon: A balloon filled with air can return to its original shape when pressed gently (elastic potential energy). However, if pressed too hard, it can burst, demonstrating stored energy being released.

• An object that possesses energy can exert a force on another object, transferring energy and enabling work to be done.
• Energy Measurement: The energy possessed by an object is measured in terms of its capacity to do work.

• The unit of energy is the joule (J), the same as the unit of work.
  • 1 Joule (J): The energy required to do 1 joule of work.
  • Larger Unit: Kilojoule (kJ), where:
    • 1 kJ = 1000 J.

• Energy is essential for all life processes and activities.
• The capacity of an object to do work defines its energy.
• Energy can be transferred, and its measurement is crucial in both work and energy contexts.
• The primary source of energy for many systems is the Sun, but there are other sources as well.

10.2.1 - Forms of Energy

Different Forms of Energy - The world provides energy in various forms, which include:

1. Mechanical Energy
   • Definition: The sum of potential energy and kinetic energy.
   • Components:
     • Potential Energy: Energy stored in an object due to its position or configuration.
     • Kinetic Energy: Energy of an object due to its motion.
2. Heat Energy
   • Definition: Energy that is transferred between systems or objects with different temperatures (thermal energy).
3. Chemical Energy
   • Definition: Energy stored in the bonds of chemical compounds (e.g., food, fuels). This energy is released during chemical reactions.
4. Electrical Energy
   • Definition: Energy caused by the movement of electrons or the flow of electric charge.
5. Light Energy
   • Definition: Energy that is visible to the human eye, which travels in the form of electromagnetic waves.

• How do you know that some entity is a form of energy?
  • Considerations: Discuss with friends and teachers to identify characteristics or behaviors that indicate an entity possesses energy (e.g., ability to do work, transfer heat, etc.).

• Biography: James Prescott Joule was a renowned British physicist.
• Contributions:
  • Research in electricity and thermodynamics.
  • Formulated a law regarding the heating effect of electric current.
  • Experimentally verified the law of conservation of energy.
  • Discovered the mechanical equivalent of heat.
• Legacy: The unit of energy and work, joule (J), is named in his honor.

10.2.2 - Kinetic Energy

Definition of Kinetic Energy

• Kinetic Energy: The energy possessed by an object due to its motion.
  • Formula: $$\text{Kinetic Energy (KE)} = \frac{1}{2} mv^2$$where:
    • $m$ = mass of the object (in kilograms)
    • $v$ = velocity of the object (in meters per second)

Objective: To observe how the height from which a ball is dropped affects the depth of the depression created in sand, demonstrating kinetic energy.

Materials Needed

• A heavy ball
• Thick bed of sand (wet sand preferred)
• Measuring tape (optional for measuring depths)

1. Drop the Ball:
   • Drop the heavy ball from a height of approximately 25 cm onto the sand.
   • Observe and mark the depression created in the sand.
2. Increase the Height:
   • Repeat the dropping process from heights of 50 cm, 1 m, and 1.5 m.
   • Ensure that all depressions are distinctly visible and mark them to indicate the height from which the ball was dropped.
3. Compare Depressions:
   • Observe and compare the depths of the depressions made by the ball at different heights.

• Which depression is the deepest?
  • Answer: The depression created from the highest drop (1.5 m) is typically the deepest.
• Which depression is the shallowest?
  • Answer: The depression created from the lowest drop (25 cm) is usually the shallowest.
• Why do the depths differ?
  • Explanation: The depth of the depression is greater when the ball is dropped from a higher height due to increased kinetic energy at the point of impact. The greater the height, the faster the ball falls, leading to a higher velocity just before impact, and thus more kinetic energy.
• What has caused the ball to make a deeper dent?
  • Explanation: The ball creates a deeper dent due to the greater kinetic energy it possesses when dropped from a higher height. The energy transfer upon impact is more significant, resulting in a more pronounced depression in the sand.

• Conclusion: This activity illustrates that kinetic energy is directly related to the height from which an object falls. As the height increases, the kinetic energy at impact also increases, leading to a deeper depression in the sand. This demonstrates the principle that the energy of motion (kinetic energy) is dependent on both the mass of the object and its velocity.

• Kinetic energy is the energy of motion, calculated using mass and velocity.
• The activity provides a practical demonstration of how kinetic energy increases with height, affecting the impact on a surface.

Kinetic Energy

Definition of Kinetic Energy

• Kinetic Energy (KE): The energy possessed by an object due to its motion.
  • Key Points:
    • A moving object can perform work.
    • The faster an object moves, the more work it can do compared to an identical object moving slowly.
    • Examples of objects that possess kinetic energy:
      • Moving bullets
      • Blowing wind
      • Rotating wheels
      • Speeding stones
      • Falling coconuts
      • Speeding cars
      • Rolling stones
      • Flying aircraft
      • Flowing water
      • Running athletes

• The kinetic energy of an object increases with its speed.
• The kinetic energy of a moving body is defined as the work done on it to achieve its velocity.

1. Basic Equation:
   • For an object of mass $m$m moving with a uniform velocity $u$u, displaced through a distance $s$s under a constant force $F$F:
   $$W = F \times s$$where $W$ is the work done on the object.
2. Change in Velocity:
   • If the object's velocity changes from $u$u to $v$v due to acceleration $a$a:
   $$v^2 - u^2 = 2a s \quad (Equation \, of \, Motion)$$
3. Substituting Force:
   • From Newton's second law, $F = m \times a$, we can express work done as:
   $$W = F \times s = m \times a \times s$$
4. Work Done and Kinetic Energy:
   • Rearranging gives:
   $$W = \frac{1}{2} m (v^2 - u^2) \quad (10.3)$$
5. Stationary Position:
   • If the object starts from rest ( $u = 0$):
   $$W = \frac{1}{2} mv^2 \quad (10.4)$$
6. Final Kinetic Energy Expression:
   • Thus, the kinetic energy possessed by an object of mass $m$m and moving with velocity $v$ is:
   $$E_k = \frac{1}{2} mv^2 \quad (10.5)$$

Objective: To understand how kinetic energy changes with speed through real-life examples.

Procedure

1. Identify Moving Objects:
   • List examples from daily life where objects are in motion (e.g., cars, athletes, balls).
2. Analyze Motion:
   • Discuss how faster-moving objects perform more work than slower ones.
3. Explore Work Done:
   • Consider scenarios like a bullet piercing a target or wind moving windmill blades to illustrate kinetic energy in action.

• How does a bullet pierce a target?
  • Answer: The bullet possesses high kinetic energy due to its speed, allowing it to exert enough force to penetrate the target.
• How does the wind move the blades of a windmill?
  • Answer: The moving air has kinetic energy, which transfers to the blades of the windmill, causing them to rotate.

• Kinetic energy is crucial for understanding the dynamics of moving objects and their ability to perform work.
• The relationship between mass, velocity, and kinetic energy is fundamental in physics, emphasizing how energy transforms through motion.

Examples of Kinetic Energy and Work Done

Example 10.3: Kinetic Energy Calculation

Problem: An object of mass 15 kg is moving with a uniform velocity of 4 m/s. What is the kinetic energy possessed by the object?

Solution:

1. Given Data:
   • Mass of the object, $m = 15 \, \text{kg}$
     
   • Velocity of the object, $v = 4 \, \text{m/s}$
     
2. Kinetic Energy Formula:
   • Using the formula for kinetic energy:
   $$E_k = \frac{1}{2} mv^2 \quad (10.5)$$
3. Substituting Values: $$E_k = \frac{1}{2} \times 15 \, \text{kg} \times (4 \, \text{m/s})^2$$  $$E_k = \frac{1}{2} \times 15 \times 16 = \frac{240}{2} = 120 \, \text{J}$$ 
4. Final Answer:
   • The kinetic energy of the object is 120 J.

10.2.3 - Potential Energy

Definition of Potential Energy:

• Potential energy is the energy an object possesses due to its position or configuration. This type of energy is stored within an object when work is done on it, without causing a change in its velocity or speed.

1. Instructions:
   • Take a rubber band, hold it at one end, and stretch it by pulling from the other.
   • Release the band.
2. Observations:
   • The rubber band regains its original length after release, showing that it had energy stored when stretched.
3. Explanation:
   • The rubber band acquires potential energy in its stretched position because energy is transferred to it by doing work to stretch it.

1. Instructions:
   • Hold one end of a slinky while a friend holds the other.
   • Move away to stretch the slinky, then release it.
2. Observations:
   • The stretched slinky snaps back when released, showing it had stored energy.
3. Questions and Answers:
   • How did the slinky acquire energy when stretched?
     • Energy was transferred to the slinky when work was done to stretch it, storing potential energy in it.
   • Would the slinky acquire energy when compressed?
     • Yes, compressing the slinky also stores potential energy due to its change in configuration.

1. Instructions:
   • Wind a toy car using its key, then place it on the ground.
2. Observations:
   • The toy car moves once released, showing it has energy.
3. Questions and Answers:
   • From where did the car acquire energy?
     • The car acquired potential energy from the wound-up spring inside, which was wound through work done by the key.
   • Does the energy depend on the number of windings?
     • Yes, increasing the number of windings increases the stored potential energy, which can be tested by observing how far the car moves with different windings.

1. Instructions:
   • Lift an object to a certain height and then release it.
2. Observations:
   • The object falls when released, showing that it has energy at a height, which allows it to do work as it falls.
3. Questions and Answers:
   • From where did the object get the energy?
     • The energy was transferred to the object when work was done to lift it, storing it as gravitational potential energy.
4. Explanation:
   • An object raised to a height has potential energy because it can do work (falling due to gravity) if released. Lifting it to a higher position increases its potential energy, as more work is required to raise it.

1. Instructions:
   • Take a bamboo stick and create a bow.
   • Place a light stick (as an arrow) on the bow with one end supported by the stretched string.
   • Stretch the string and release the arrow.
2. Observations:
   • The arrow flies forward when the string is released, showing stored energy in the stretched bowstring.
3. Explanation:
   • Stretching the bowstring transfers potential energy into the string, which is then transferred to the arrow as kinetic energy when released.

• Potential energy is stored in objects due to their position (like height above ground) or configuration (like a stretched or compressed state).
• Examples include:
  • A stretched rubber band
  • A compressed or stretched slinky
  • A wound-up toy car
  • An object held at a height

10.2.4 - Potential Energy of an Object at a Height

Definition of Gravitational Potential Energy:

• Gravitational potential energy is the energy possessed by an object when it is raised to a certain height. This energy results from the work done against gravity to lift the object to that height.

• When an object is raised from the ground to a height, work is done on it against the force of gravity.
• This work done is stored as gravitational potential energy in the object.
• Formula: The gravitational potential energy, $E_p$Ep​, of an object with mass $m$m raised to a height $h$h from the ground, is given by: $$E_p = m \cdot g \cdot h$$where:
  • $m$ = mass of the object
  • $g$ = acceleration due to gravity (approx. $9.8 \, \text{m/s}^2$on Earth)
  • $h$ = height of the object above the ground

1. Consider an object with mass $m$m being lifted to a height $h$h.
2. Force required: The minimum force required to lift the object is equal to its weight, which is $mg$mg.
3. Work done (W): Since work done is the product of force and displacement, we calculate it as: $$W=\text{force}\times \text{displacement}=mg\times h=mgh$$
4. Potential energy: Since this work done is stored as potential energy in the object, we have: $$E_p=mgh$$

10.2.5 - Are Various Energy Forms Interconvertible?

10.2.6 - Law of Conservation of Energy

Activity 10.15: Calculating Potential and Kinetic Energy of a Falling Object

In this activity, we examine the potential and kinetic energy of an object with a mass of 20 kg as it falls from a height of 4 m. Use $g = 10 \, \text{m/s}^2$ for the calculations.

• Mass of object, $m = 20 \, \text{kg}$
  
• Initial height, $h = 4 \, \text{m}$
  
• Gravitational acceleration, $g = 10 \, \text{m/s}^2$
  

For each position, the potential energy (PE) and kinetic energy (KE) are calculated as follows:

1. Potential Energy (PE) at height $h$: $$\text{PE} = m \cdot g \cdot h$$ 
2. Kinetic Energy (KE), which is related to the object’s velocity $v$ as it falls:
   
   $$\text{KE} = \frac{1}{2} m v^2$$ 

10.3 - Rate of Doing Work

1.4 - Can Matter Change its State?

Example 10.7 Two girls, A and B, each weighing 400 N, climb a rope to a height of 8 m. Girl A takes 20 seconds, and girl B takes 50 seconds.

Solution:

1. Power expended by girl A:
   • Weight $mg = 400 \, \text{N}$
     
   • Displacement (height), $h=8\text{m}$
   • Time taken, $t = 20 \, \text{s}$
     
   Using the power formula: $$P = \frac{mgh}{t} = \frac{400 \, \text{N} \times 8 \, \text{m}}{20 \, \text{s}} = 160 \, \text{W}$$
   
2. Power expended by girl B:
   • Weight $mg = 400 \, \text{N}$m
   • Displacement (height), $h = 8 \, \text{m}$
     
   • Time taken, $t=50\text{s}$
   $$P = \frac{mgh}{t} = \frac{400 \, \text{N} \times 8 \, \text{m}}{50 \, \text{s}} = 64 \, \text{W}$$
   

Solution:

• Weight of the boy $mg = 50 \, \text{kg} \times 10 \, \text{m/s}^2 = 500 \, \text{N}$
  
• Height of the staircase $h = 45 \times \frac{15}{100} \, \text{m} = 6.75 \, \text{m}$
  
• Time taken $t = 9 \, \text{s}$
  

1. Objective: To monitor electricity usage in different periods.
2. Procedure:
   • Observe the electric meter in your house.
   • Record the meter reading daily at 6:30 am and 6:30 pm for one week.
3. Questions to Address:
   • How many units are consumed during the day?
   • How many units are consumed at night?
4. Tabulate and Compare:
   • Record the daily consumption in units.
   • Compare with the details provided in the monthly electricity bill.
   • You can also estimate the electricity consumption of individual appliances based on their wattage and usage time.

NCERT Science Notes - Class 9 Chapter 1 - Matter in our surroundings

NCERT Science Notes - Class 9 Chapter 1 - Matter in our surroundings