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ICSE Class X Notes 2026 : Physics (Work, Energy and Power)

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Work, Energy, and Power Chapter 2 Page 1 ICSE NextGen (A) Work, Energy, and Power, their measurements and Units Part 1: Work De nition of Work Work is said to be done when a force is applied on a body and the body gets displaced in the direction of the force. Examples Work is done: 1. A boy pushes a trolley and it moves. 2. A girl lifts a bucket from the oor. 3. A person cycles uphill. Work is not done: 1. Holding a heavy suitcase stationary. 2. Trying to push a wall without moving it. 3. Sitting and reading a book. Measurement of Work Work is measured by the product of the force applied and the displacement produced in the direction of the force. Formula of Work Work (W)=Force (F) Displacement (S) cos W = F S cos Where: F = applied force S = displacement = angle between force and displacement Note: Work is a scalar quantity (it has magnitude but no direction). If displacement is zero, then work done is zero, even if force is applied. Expression for Work (based on vector components) Page 2 ICSE NextGen 1. By resolving displacement along force: W = F (S cos ) 1. By resolving force along displacement: W = (F cos ) S Conclusion: Work is the product of three factors: W=F S cos magnitude of force, magnitude of displacement, and the cosine of the angle between them. Special Cases of Work Case 1: Displacement in the direction of force =0 , cos =1 Formula: W=F x S x = F x S Work is positive Examples: 1. A man pulls a cart in the direction it moves. 2. A book falls freely under gravity. 3. A child slides down a slide. Case 2: Displacement perpendicular to force =90 , cos =0 Formula: W = F x S x 0 = 0 Work done is zero Examples: 1. A coolie carrying a load on his head while walking horizontally. 2. The circular motion of a satellite around Earth. 3. A centripetal force acting towards the center but object moving tangentially. Case 3: Displacement opposite to the direction of force =180 , cos = 1 Formula: W = F x S x (-1) = -(FS) Work is negative Examples: 1. Friction acting opposite to the motion of a sliding object. Page 3 ICSE NextGen 2. A person pulling a bucket out of a well (gravity does negative work). 3. Brakes applied in a moving car (retarding force). Two Conditions for Work Done by a Force to be Zero 1. No displacement: Force is applied, but the object does not move. e.g., pushing against a wall. 2. Displacement is perpendicular to force: Force and displacement are at 90 , so cos =0. e.g., carrying a load horizontally. Work Done by the Force of Gravity When an object is lifted vertically upward, the force applied to lift it is equal and opposite to the gravitational force (its weight). Let s say: Mass of the object = m Acceleration due to gravity = g Vertical displacement = h Then: Force applied to lift = Weight of the body = F=mg Displacement = h (in the direction of force) Derivation: Work done (W) = Force Displacement W = F S = mg h W = mgh This is the work done in lifting a body of mass m to a height h against gravity. Units of Work SI Unit of Work: Joule (J) De nition of 1 Joule: 1 joule of work is said to be done when a force of 1 newton displaces a body by 1 meter in the direction of the force. 1J=1N 1m CGS Unit of Work: Erg De nition of 1 Erg: Page 4 ICSE NextGen 1 erg of work is said to be done when a force of 1 dyne displaces a body by 1 cm in the direction of the force. 1 erg = 1 dyne 1 cm Relation Between SI and CGS Units: 1 joule = 107 Part 2: Power De nition of Power Power is de ned as the rate at which work is done or the rate of transfer of energy. Power (P)=Work done (W) / Time taken (t) Power is a scalar quantity it has magnitude but no direction. Measurement of Power Power is measured as the amount of work done per unit of time. Formula: P=W/t Where: P = Power W = Work done t = Time taken Factors on which Power Spent by a Source Depends 1. Amount of Work done More work = more power needed. 2. Time taken to do the work Less time = higher power required. Suppose: Person A does 100 J of work in 10 seconds Person B does the same 100 J of work in 5 seconds Then: Power of A: 100/10=10 =10W Power of B: 100/5=20 =20W Since Person B does the same work in less time, more power is spent by B. Page 5 ICSE NextGen Conclusion: If a machine or person does a given amount of work in less time, it uses more power. Derivation of P=F v Let: F = constant force applied V = constant velocity S = displacement in time t We know: Work done (W) = Force Displacement W=F S But if the object moves with constant velocity vvv, then: S=v t So, W=F v t Now, Power (P) = Work done / Time P = W / t = (F v t) / t So, P=F v This is used when a constant force moves a body with a constant velocity. Units of Power SI Unit of Power: Watt (W) De nition of 1 Watt: 1 watt is the power spent when 1 joule of work is done in 1 second. 1W=1J/1s CGS Unit of Power: erg/second 1 W = 10 erg/s Larger Units of Power: 1 kilowatt (kW) = 1000 W 1 megawatt (MW) = 10 W De nition of 1 Joule of Work: 1 joule is the amount of work done when a force of 1 newton displaces a body by 1 meter in the direction of the force. Page 6 ICSE NextGen 1J=1N 1m Horsepower (hp) Horsepower is a unit of power used mainly to measure the power output of engines, motors, pumps, and machines. It was originally de ned by James Watt to compare the power of steam engines with horses. It is still commonly used in the automobile industry to describe the power of cars, bikes, and other vehicles. 1 horsepower = 746 watts Work Power 1. Work is the product of force and 1. Power is the rate at which work is displacement in the direction of force. done. 2. Work is measured in joules (J). 2. Power is measured in watts (W). 3. Work depends on force and displacement but not on time. 3. Power depends on both work done and the time taken. Part 3: Energy De nition of Energy Energy is de ned as the capacity to do work. It is the ability of a body or system to perform work when acted upon by a force. Energy is a scalar quantity it has magnitude but no direction. No Transfer of Energy When Force is Normal to Displacement If a body is acted upon by a force perpendicular (normal) to the direction of its displacement, no work is done, and hence no energy transfer takes place. Example: When a person carries a bucket of water horizontally at a constant height, the upward force applied is perpendicular to the horizontal displacement. So, no work is done against gravity and no energy transfer occurs due to the vertical force. Units of Energy Page 7 ICSE NextGen SI and CGS Units SI unit of energy = Joule (J) 1 J =1 N 1 m CGS unit of energy = erg 1 erg = 1 dyne 1 cm Bigger Units of Energy Watt-hour (Wh): Energy consumed when power of 1 watt is used for 1 hour. 1 Wh = 3600 J Kilowatt-hour (kWh): Energy consumed when power of 1 kilowatt is used for 1 hour. 1 kWh = 1000 Wh = 3.6 106 Calorie (cal) The calorie is a unit of energy used in chemistry and food energy. It is de ned as the amount of heat energy required to raise the temperature of 1 gram of water by 1 C. 1 cal = 4.2 J Electron-volt (eV) The electron volt is a very small unit of energy used in atomic and nuclear physics. It is de ned as the energy gained or lost by an electron when it moves through a potential difference of 1 volt. 1 eV = 1.6 10 19 J (B) Different forms of Energy Mechanical Energy Mechanical Energy is the energy possessed by a body due to its motion or its position. It is the energy associated with the mechanical work that the body can perform. Types of Mechanical Energy: 1. Kinetic Energy (KE): Energy possessed by a body due to its motion. Page 8 ICSE NextGen 2. Potential Energy (PE): Energy possessed by a body due to its position or con guration. Note: The total mechanical energy of a body is the sum of its potential energy and kinetic energy. Part 1: Potential Energy (U) De nition: Potential Energy (U) is the energy possessed by a body due to its position or con guration. It represents the stored energy that has the potential to do work in the future. Symbol: U Examples of Potential Energy: A book kept on a table has potential energy due to its height above the ground. A stretched or compressed spring stores elastic potential energy. Water stored in a dam at height has potential energy. Forms of Potential Energy: 1. Gravitational Potential Energy (GPE) 2. Elastic Potential Energy (EPE) 1. Gravitational Potential Energy (GPE) Gravitational potential energy is the energy possessed by a body due to its position relative to the Earth s surface or any other reference point. It depends on the height of the body above the reference point (usually the ground). The higher the body is lifted, the more gravitational potential energy it gains because work is done against the force of gravity. Explanation: When you lift an object, you do work against gravity, and this work is stored as gravitational potential energy in the object. If the object falls, this stored energy converts into kinetic energy. Mathematical Expression: If a body of mass mmm is raised to a height h above the ground, the gravitational potential energy U is given by: U=mgh Where: m = mass of the body (in kg) Page 9 ICSE NextGen g = acceleration due to gravity (approx. 9.8 m/s2) h = height above the reference point (in meters) 2. Elastic Potential Energy (EPE) Elastic potential energy is the energy stored in an object when it is stretched or compressed from its normal shape. Common examples include stretched springs, rubber bands, or compressed balls. This energy is stored due to the elastic deformation of the object and is released when the object returns to its original shape. Part 2: Kinetic Energy (K) De nition: Kinetic energy is the energy possessed by a body due to its motion. It depends on the mass of the body and the square of its velocity. Symbol: K or KE Examples of Kinetic Energy: A moving car A ying bullet A falling ball A running person Expression for Kinetic Energy: Formula: K=1/2mv2 Explanation: A body in motion has kinetic energy. This energy increases if the body moves faster or has more mass. For example, a truck and a car moving at the same speed have different kinetic energies because the truck has more mass. Derivation: Let a body of mass m be initially at rest. Let a force F act on it, producing an acceleration a, and the body covers a distance s to reach nal velocity v. Work done, W = F s From Newton s second law, F = ma So, W = ma s Now using the equation of motion: v = u + 2as, and since u = 0: Page 10 ICSE NextGen v = 2as So, s = v / 2a Substitute s into the expression for W: W = ma (v / 2a) = 1/2 mv Hence, kinetic energy K = 1/2 mv Conclusion: The kinetic energy of a moving body is directly proportional to its mass and to the square of its velocity. Relationship Between Kinetic Energy and Momentum Momentum (p) is given by: p = mv We know: Kinetic Energy (K) = 1/2 mv Now, multiply and divide by m: K = 1/2 mv = (1/2) (m v ) / m = p / (2m) Therefore, K = p / (2m) This shows that kinetic energy is directly proportional to the square of momentum. Forms of Kinetic Energy: 1. Translational Kinetic Energy: Energy due to the straight-line motion of a body. Examples: A car moving on a road, a person running, a stone thrown in air. 2. Rotational Kinetic Energy: Energy due to the rotation of a body about an axis. Examples: A spinning wheel, a rotating fan, Earth spinning on its axis. 3. Vibrational Kinetic Energy: Energy due to the to-and-fro or back-and-forth motion of particles. Examples: Vibrating guitar string, vibrating tuning fork, atoms in a heated solid. Potential Energy Kinetic Energy Energy due to position or con guration Energy due to motion Depends on height or elastic condition Depends on mass and velocity Page 11 ICSE NextGen Formula: PE = mass gravity height (mgh) Formula: KE = one-half mass velocity squared Present even when object is at rest Present only when object is moving Part 3: Work-Energy Theorem De nition: The Work-Energy Theorem states that the net work done by all the forces acting on a body is equal to the change in its kinetic energy. In simple words, when a force does work on an object, it changes the object s speed, and thus its kinetic energy. Statement: Work done by the net force on a body = Final kinetic energy Initial kinetic energy That is, Work done (W) = KE KE Derivation: Let a body of mass m be moving with initial velocity u and it is acted upon by a force F, which causes it to accelerate and reach a nal velocity v over a distance s. From Newton's second law: F = ma Work done by the force: W = F s = ma s From the equation of motion: v = u + 2as s = (v u ) / 2a Now substitute s into the work formula: W = ma [(v u ) / 2a] W = m(v u ) / 2 W = 1/2 mv 1/2 mu So, W = Final KE Initial KE Conclusion: This proves the work-energy theorem: The work done on an object equals the change in its kinetic energy. Page 12 ICSE NextGen Part 4: Conversion of Potential Energy into Kinetic Energy Energy can change from one form to another. One of the most common transformations in nature and machines is the conversion of potential energy into kinetic energy. When a body loses height or moves from a position where it has stored potential energy, that energy gets converted into motion, which is kinetic energy. This transformation follows the law of conservation of energy, which states that energy can neither be created nor destroyed but only converted from one form to another. During this conversion, the total mechanical energy (PE + KE) remains constant if no energy is lost due to air resistance or friction. Examples: 1. Falling Ball: When a ball is held at a height, it has gravitational potential energy. As it is dropped, it begins to fall and gains speed. The potential energy decreases while kinetic energy increases. Just before hitting the ground, most of the energy has converted into kinetic energy. 2. Waterfall: Water stored at a height in a dam has potential energy. When it is released, the water ows downward, and its potential energy is converted into kinetic energy. This fastmoving water is then used to rotate turbines in hydroelectric power plants. 3. Swinging Pendulum: At its highest point, a swinging pendulum has maximum potential energy and zero kinetic energy. As it moves downwards, the potential energy decreases and is converted into kinetic energy. At the lowest point, the pendulum has maximum kinetic energy and minimum potential energy. 4. Roller Coaster Ride: When a roller coaster is pulled to the top of a hill, it gains potential energy. As it descends, this potential energy changes into kinetic energy, making the coaster speed up. The ride slows down again when it climbs the next hill, converting kinetic energy back into potential energy. Part 5: Conversion of different forms of Energy Energy is constantly changing from one form to another in our daily life and in machines. Below are important energy conversions with examples: 1. Mechanical Energy to Electrical Energy Example: Page 13 ICSE NextGen In hydroelectric power plants, moving water (mechanical energy) turns turbines connected to generators, producing electricity. Windmills convert wind energy into electrical energy. 2. Electrical Energy to Mechanical Energy Example: An electric fan converts electrical energy into the mechanical rotation of its blades. Electric vehicles use motors to convert electric energy into motion. 3. Electrical Energy to Heat Energy Example: Electric heaters and toasters convert electrical energy into heat. Electric irons and geysers also perform this conversion. 4. Heat Energy to Electrical Energy Example: In thermal power plants, heat produced by burning coal or gas is used to boil water into steam, which turns turbines to generate electricity. Thermoelectric generators convert temperature differences directly into electrical energy. 5. Electrical Energy to Sound Energy Example: Loudspeakers and headphones convert electrical signals into sound. Calling bells and buzzers also use this conversion. 6. Sound Energy to Electrical Energy Example: Microphones convert sound vibrations into electrical signals. Voice recognition systems use sound-to-electricity conversion for processing input. 7. Electrical Energy to Chemical Energy Example: In charging a battery, electrical energy is stored as chemical energy. Electrolysis stores energy in chemical bonds. 8. Chemical Energy to Electrical Energy Example: Dry cells and batteries convert chemical energy into electricity. Fuel cells used in spacecraft and electric cars perform this conversion. 9. Chemical Energy to Light Energy Example: Page 14 ICSE NextGen The burning of a candle or wood releases light and heat. Fireworks and crackers release bright light due to chemical reactions. 10. Light Energy to Chemical Energy Example: In photosynthesis, plants use sunlight to make food (glucose), storing light energy as chemical energy. Solar cookers heat food using sunlight, sometimes helping in slow chemical changes. 11. Electrical Energy to Light Energy Example: Electric bulbs, tube lights, and LED lamps convert electricity into light. Flashlights use batteries to power a light source. 12. Light Energy to Electrical Energy Example: Solar panels (photovoltaic cells) convert sunlight directly into electricity. Solar calculators work using this principle. 13. Heat Energy to Mechanical Energy Example: In steam engines, heat energy from steam moves pistons. Heat from combustion in a car engine pushes the pistons to create motion. 14. Chemical Energy to Heat Energy Example: Burning fuels like wood, coal, LPG, and petrol releases heat energy. Digesting food also releases heat inside our bodies. 15. Chemical Energy to Mechanical Energy Example: In a car engine, fuel combustion produces motion. Our muscles convert energy from food into movement when we run or lift objects. 16. Electrical Energy to Magnetic Energy Example: Electromagnets are created when current ows through a coil. Electric bells and magnetic cranes use this principle. 17. Nuclear Energy to Electrical Energy Example: In nuclear power plants, the energy released by the ssion of uranium atoms is used to generate electricity. Page 15 ICSE NextGen Nuclear submarines use this energy to power their systems. 18. Mechanical Energy to Heat Energy Example: When we rub our hands together, mechanical movement produces heat. Brakes in vehicles convert motion into heat energy through friction. No. Energy Conversion Example(s) 1 Mechanical Electrical Hydroelectric plant, windmill 2 Electrical Mechanical Electric fan, electric vehicles 3 Electrical Heat Electric heater, toaster, iron 4 Heat Electrical Thermal power plant, thermoelectric generator 5 Electrical Sound Loudspeaker, buzzer 6 Sound Electrical Microphone, voice input systems 7 Electrical Chemical Charging a battery, electrolysis 8 Chemical Electrical Dry cells, fuel cells 9 Chemical Light Fireworks, burning candle 10 Light Chemical Photosynthesis in plants, solar cooker 11 Electrical Light Bulbs, LEDs, tube lights 12 Light Electrical Solar panels, solar calculators 13 Heat Mechanical Steam engine, internal combustion engine Page 16 ICSE NextGen 14 Chemical Heat Burning of fuel, digestion 15 Chemical Mechanical Car engine, human body during movement 16 Electrical Magnetic Electromagnets, electric bell, magnetic crane 17 Nuclear Electrical Nuclear power plant, nuclear submarine 18 Mechanical Heat Rubbing hands, vehicle brakes Degraded Energy: Degraded energy is the form of energy that has become less useful or less capable of doing work. When energy changes from one form to another, some of it often changes into heat that spreads out and cannot be fully used again to perform useful work. This energy is said to be degraded because it loses its ability to do work ef ciently. Dissipation of Energy: Dissipation of energy refers to the process by which energy is lost or spread out, usually as heat, during energy transformations. For example, when a moving object slows down due to friction, some of its mechanical energy is converted into heat energy, which spreads into the surroundings and is no longer available for doing work. This spreading out and loss of usable energy is called dissipation. (C) Principle of Conservation of Energy De nition: Energy can neither be created nor destroyed; it only changes from one form to another. The total energy in an isolated system remains constant. Explanation: When a body moves or changes position, its energy continuously transforms between different forms, such as potential energy and kinetic energy. However, the sum of all forms of energy remains unchanged if there is no loss due to friction or other external forces. Example: A swinging pendulum has maximum potential energy at its highest point and maximum Page 17 ICSE NextGen kinetic energy at its lowest point. Throughout its motion, the total mechanical energy (sum of potential and kinetic energy) remains constant. Key Formula: Total Mechanical Energy = Potential Energy + Kinetic Energy Derivation of the Principle of Conservation of Energy (Using a Falling Object) Consider a body of mass m falling from a height h. At the top, potential energy (PE) = mgh and kinetic energy (KE) = 0 because the body is at rest. When the body has fallen a distance x, its height is (h - x). Potential energy at this point is PE = mg(h - x). Let the velocity at this point be v. Kinetic energy is KE = (1/2) m v . Using the equation of motion for a freely falling body, v = 2gx. Substitute this value of v into the kinetic energy formula: KE = (1/2) m (2gx) = mgx. Total mechanical energy at this point = PE + KE = mg(h - x) + mgx = mgh. This shows that total mechanical energy remains constant during the fall, proving the conservation of energy. Derivation of the Principle of Conservation of Energy (Using a Pendulum) Consider a pendulum bob of mass m suspended from a xed point. When the bob is at its highest point, it has maximum potential energy and zero kinetic energy because it momentarily stops before swinging back. Let the height of the bob above the lowest point be h. Potential energy at this point is PE = mgh, and kinetic energy KE = 0. When the bob swings down to the lowest point, its height is zero, so potential energy is PE = 0. At the lowest point, the bob has maximum speed v, so kinetic energy is KE = (1/2) m v . According to the conservation of energy, the total mechanical energy remains constant: Total energy at highest point = Total energy at lowest point mgh + 0 = 0 + (1/2) m v Simplifying, mgh = (1/2) m v This shows that potential energy lost by the bob is converted into kinetic energy. Page 18 ICSE NextGen Thus, total mechanical energy is conserved during the pendulum s motion. Stage Falling Object Pendulum Initial position Height = h Height = h (highest point) Potential Energy (PE) PE = mgh PE = mgh Kinetic Energy (KE) KE = 0 (at rest) KE = 0 (momentarily at rest) Intermediate point Height = (h - x) PE at intermediate PE = mg(h - x) Velocity at intermediate v = 2gx KE at intermediate KE = (1/2) m v = mgx Final position Height = 0 Height = 0 (lowest point) PE at nal PE = 0 PE = 0 KE at nal KE = (1/2) m v KE = (1/2) m v (maximum) Energy conservation PE + KE = mgh constant PE + KE = mgh constant Key formula mgh = (1/2) m v mgh = (1/2) m v Page 19 ICSE NextGen

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Additional Info : ICSE Class X Notes 2026 : Physics (Pawar Public School (PPS), Hadapsar, Pune) : Notes
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