Page 1 WORK AND ENERGY Work Work is said to be done when force produces motion. Example An engine pulling bogies of train, horse pulling a cart etc. The work done by a force on a body depends on two factors: - 1. Magnitude of the force 2. Distance through which the body moves In other words, we can say that work is said to be done when the point of application of a force moves. Work done in moving a body is equal to the product of force exerted on the body in the direction of force. Work = Force × Distance Or W = F × S S. I. Unit Of Work W = F × S W = N × m = Nm Therefore, unit of work is Nm. 1Nm is 1 Joule. So, unit of work will be Joule. 1 Joule may be defined as, a force of 1N moving a body through a distance of 1 m in its own direction. In such case, the work done is known as 1 Joule. 1 Joule = 1Newton × 1metre 1J = 1Nm S.I. unit of work is joule denoted by J. Work is a scalar quantity. Note that work is said to be done only if there is a move in an object through some distance. If however, the distance moved is zero the work done on the body of man himself is not zero, because his muscles are stretched and his blood is displaced. Examples Of Work Done (i) Push a pebble lying on a surface. The pebble moves through a distance. You exerted the force on the pebble and the pebble is displaced. In this case the work is done. (ii) A girl pulls a trolley and the trolley moves through a distance. The girl has exerted a force and the trolley is displaced. The work is done. (iii) Lift a book through a height. The book rises up. There is a force applied on the book and the book has moved. The work is done. When Work Is Not Said To Be Done? (i) You are pushing a huge rock and the rock is not at all moving from its place. As there is no displacement in the rock even after applying force, work is not done. (ii) You stand still for a few minutes with a heavy load on your head. You get tired. No work is done on the load. Therefore work is not said to be done if there is no displacement even after the application of the force. Work Done Against Gravity Whenever work is done against gravity the amount of work done is equal to the product of weight of the body and the vertical distance through which the body is lifted. Work done by the person against gravity is positive. Work Done In Lifting A Body Upwards = Weight Of Body × Vertical Distance Or W = m × g × h When a body of mass m is lifted to a height h above the ground, work equal to mgh is done on the body. Work Done When A Body Moves At An Angle To The Direction Of Force In such cases, we cannot use the formula W = F × S, because the distance moved S is not exactly in the direction of force applied. In such case, the force is applied at certain angle to the horizontal ground but the body moves horizontally on the ground. Calculating The Work Done When A Body Moves At An Angle To The Direction Of Force In this case, all force F is not utilized in pulling the body, only the horizontal component of force F is pulling the body along the ground. The horizontal component of force F is F Cos? and distance moved is S. Thus, W = FS Cos ? Work Done By Force When A Body Moves In A Direction Different From That Of Force 1. When the displacement is in the direction of force i.e. when ? = 0° W=F S Cos ? W=F S Cos 0° = F S × 1 = F× S Page 2 WORK AND ENERGY Work Work is said to be done when force produces motion. Example An engine pulling bogies of train, horse pulling a cart etc. The work done by a force on a body depends on two factors: - 1. Magnitude of the force 2. Distance through which the body moves In other words, we can say that work is said to be done when the point of application of a force moves. Work done in moving a body is equal to the product of force exerted on the body in the direction of force. Work = Force × Distance Or W = F × S S. I. Unit Of Work W = F × S W = N × m = Nm Therefore, unit of work is Nm. 1Nm is 1 Joule. So, unit of work will be Joule. 1 Joule may be defined as, a force of 1N moving a body through a distance of 1 m in its own direction. In such case, the work done is known as 1 Joule. 1 Joule = 1Newton × 1metre 1J = 1Nm S.I. unit of work is joule denoted by J. Work is a scalar quantity. Note that work is said to be done only if there is a move in an object through some distance. If however, the distance moved is zero the work done on the body of man himself is not zero, because his muscles are stretched and his blood is displaced. Examples Of Work Done (i) Push a pebble lying on a surface. The pebble moves through a distance. You exerted the force on the pebble and the pebble is displaced. In this case the work is done. (ii) A girl pulls a trolley and the trolley moves through a distance. The girl has exerted a force and the trolley is displaced. The work is done. (iii) Lift a book through a height. The book rises up. There is a force applied on the book and the book has moved. The work is done. When Work Is Not Said To Be Done? (i) You are pushing a huge rock and the rock is not at all moving from its place. As there is no displacement in the rock even after applying force, work is not done. (ii) You stand still for a few minutes with a heavy load on your head. You get tired. No work is done on the load. Therefore work is not said to be done if there is no displacement even after the application of the force. Work Done Against Gravity Whenever work is done against gravity the amount of work done is equal to the product of weight of the body and the vertical distance through which the body is lifted. Work done by the person against gravity is positive. Work Done In Lifting A Body Upwards = Weight Of Body × Vertical Distance Or W = m × g × h When a body of mass m is lifted to a height h above the ground, work equal to mgh is done on the body. Work Done When A Body Moves At An Angle To The Direction Of Force In such cases, we cannot use the formula W = F × S, because the distance moved S is not exactly in the direction of force applied. In such case, the force is applied at certain angle to the horizontal ground but the body moves horizontally on the ground. Calculating The Work Done When A Body Moves At An Angle To The Direction Of Force In this case, all force F is not utilized in pulling the body, only the horizontal component of force F is pulling the body along the ground. The horizontal component of force F is F Cos? and distance moved is S. Thus, W = FS Cos ? Work Done By Force When A Body Moves In A Direction Different From That Of Force 1. When the displacement is in the direction of force i.e. when ? = 0° W=F S Cos ? W=F S Cos 0° = F S × 1 = F× S Work done is equal to F×S. It is positive work. Example A baby pulling a toy car parallel to the ground. 2. When the displacement is at right angles to that of force i.e., when ? = 90 0 W = F S Cos ? = F S Cos 90° = F × S × 0 = 0 No work is done by force. Also we can say that no work is done when a body is moving along a circular path. 3. When displacement is in the opposite direction to that of the force i.e ? =180° W=F S cos ? = F S cos 180° = F S×-1 = -F× S It is called negative work. Work done is negative or work done against the force is positive. POWER Power is the rate of doing work. Power = Taken Time Done Work or P = T W In other words, we can say that power is work done per unit time. Power is a scalar quantity. Units Of Power P = T W = Second Joules = s J = J/s or Js -1 Joules per second is called watt. The S.I. unit of power is watt. One watt is the rate of doing work at 1 joule per second. 1 Watt= Second 1 Joule 1 Or 1watt = s 1 J 1 = s J Another unit of power is Horse Power (h.p.) 1Horse Power = 746 Watts Or 1 h.p. = 746 W Work From the formula of power another formula of work done can be derived that is, Power = Taken Time Done Work ? Work Done = Power × Time Or W = P × t ENERGY Energy is the ability or capacity to do work. The amount of work possessed by a body is equal to the amount of work it can do when its energy is released. Energy is utilized to do work. Forms Of Energy 1. Mechanical Energy 2. Chemical Energy 3. Electrical Energy 4. Light Energy 5. Nuclear Energy 6. Heat Or Thermal Energy How Does An Object With Energy Do Work? An object that possesses energy can exert force on another object. When this happens energy is transferred from one object to another. The second object may move as it receives energy and therefore do some work. Thus the first object has the capacity to do work. This implies that any object that possesses energy can do work. Unit Of Energy S.I. unit of energy is Joule (J). Energy is a scalar quantity. The energy possessed by an object is measured in terms of its capacity of doing work. Therefore the units of both energy and work are same. Mechanical Energy The energy by which the body can do some mechanical work is called mechanical energy. Two forms of mechanical energy are: - 1. Kinetic Energy 2. Potential Energy Mechanical energy is equal to sum of kinetic and potential energy M.E. = K.E. + P.E. 1. Kinetic Energy The energy of a body due to its motion is called kinetic energy. A moving object possesses energy that is why it is capable of doing work. Example A fast moving ball, a stone thrown at a high speed high speed bullet, flowing wind and flowing water. Formula For Kinetic Energy To measure kinetic energy we have to measure the amount of work done because that is equal to kinetic energy. Work Done = Kinetic Energy â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦(i) Consider a body of mass m moving against the opposing force F with velocity v. Before its coming to rest after covering a certain distance work done by it will be given by W = F × S â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦(ii) But, because work done is equal to Kinetic Energy from (i) and (ii), we can say K.E. = F × S Now, assume that Initial Velocity = 0 Final Velocity = v Acceleration = a Distance = S (v) 2 â€“ (0) 2 = 2aS â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦(i) From Newtonâ€™s second law of motion F = m × a Page 3 WORK AND ENERGY Work Work is said to be done when force produces motion. Example An engine pulling bogies of train, horse pulling a cart etc. The work done by a force on a body depends on two factors: - 1. Magnitude of the force 2. Distance through which the body moves In other words, we can say that work is said to be done when the point of application of a force moves. Work done in moving a body is equal to the product of force exerted on the body in the direction of force. Work = Force × Distance Or W = F × S S. I. Unit Of Work W = F × S W = N × m = Nm Therefore, unit of work is Nm. 1Nm is 1 Joule. So, unit of work will be Joule. 1 Joule may be defined as, a force of 1N moving a body through a distance of 1 m in its own direction. In such case, the work done is known as 1 Joule. 1 Joule = 1Newton × 1metre 1J = 1Nm S.I. unit of work is joule denoted by J. Work is a scalar quantity. Note that work is said to be done only if there is a move in an object through some distance. If however, the distance moved is zero the work done on the body of man himself is not zero, because his muscles are stretched and his blood is displaced. Examples Of Work Done (i) Push a pebble lying on a surface. The pebble moves through a distance. You exerted the force on the pebble and the pebble is displaced. In this case the work is done. (ii) A girl pulls a trolley and the trolley moves through a distance. The girl has exerted a force and the trolley is displaced. The work is done. (iii) Lift a book through a height. The book rises up. There is a force applied on the book and the book has moved. The work is done. When Work Is Not Said To Be Done? (i) You are pushing a huge rock and the rock is not at all moving from its place. As there is no displacement in the rock even after applying force, work is not done. (ii) You stand still for a few minutes with a heavy load on your head. You get tired. No work is done on the load. Therefore work is not said to be done if there is no displacement even after the application of the force. Work Done Against Gravity Whenever work is done against gravity the amount of work done is equal to the product of weight of the body and the vertical distance through which the body is lifted. Work done by the person against gravity is positive. Work Done In Lifting A Body Upwards = Weight Of Body × Vertical Distance Or W = m × g × h When a body of mass m is lifted to a height h above the ground, work equal to mgh is done on the body. Work Done When A Body Moves At An Angle To The Direction Of Force In such cases, we cannot use the formula W = F × S, because the distance moved S is not exactly in the direction of force applied. In such case, the force is applied at certain angle to the horizontal ground but the body moves horizontally on the ground. Calculating The Work Done When A Body Moves At An Angle To The Direction Of Force In this case, all force F is not utilized in pulling the body, only the horizontal component of force F is pulling the body along the ground. The horizontal component of force F is F Cos? and distance moved is S. Thus, W = FS Cos ? Work Done By Force When A Body Moves In A Direction Different From That Of Force 1. When the displacement is in the direction of force i.e. when ? = 0° W=F S Cos ? W=F S Cos 0° = F S × 1 = F× S Work done is equal to F×S. It is positive work. Example A baby pulling a toy car parallel to the ground. 2. When the displacement is at right angles to that of force i.e., when ? = 90 0 W = F S Cos ? = F S Cos 90° = F × S × 0 = 0 No work is done by force. Also we can say that no work is done when a body is moving along a circular path. 3. When displacement is in the opposite direction to that of the force i.e ? =180° W=F S cos ? = F S cos 180° = F S×-1 = -F× S It is called negative work. Work done is negative or work done against the force is positive. POWER Power is the rate of doing work. Power = Taken Time Done Work or P = T W In other words, we can say that power is work done per unit time. Power is a scalar quantity. Units Of Power P = T W = Second Joules = s J = J/s or Js -1 Joules per second is called watt. The S.I. unit of power is watt. One watt is the rate of doing work at 1 joule per second. 1 Watt= Second 1 Joule 1 Or 1watt = s 1 J 1 = s J Another unit of power is Horse Power (h.p.) 1Horse Power = 746 Watts Or 1 h.p. = 746 W Work From the formula of power another formula of work done can be derived that is, Power = Taken Time Done Work ? Work Done = Power × Time Or W = P × t ENERGY Energy is the ability or capacity to do work. The amount of work possessed by a body is equal to the amount of work it can do when its energy is released. Energy is utilized to do work. Forms Of Energy 1. Mechanical Energy 2. Chemical Energy 3. Electrical Energy 4. Light Energy 5. Nuclear Energy 6. Heat Or Thermal Energy How Does An Object With Energy Do Work? An object that possesses energy can exert force on another object. When this happens energy is transferred from one object to another. The second object may move as it receives energy and therefore do some work. Thus the first object has the capacity to do work. This implies that any object that possesses energy can do work. Unit Of Energy S.I. unit of energy is Joule (J). Energy is a scalar quantity. The energy possessed by an object is measured in terms of its capacity of doing work. Therefore the units of both energy and work are same. Mechanical Energy The energy by which the body can do some mechanical work is called mechanical energy. Two forms of mechanical energy are: - 1. Kinetic Energy 2. Potential Energy Mechanical energy is equal to sum of kinetic and potential energy M.E. = K.E. + P.E. 1. Kinetic Energy The energy of a body due to its motion is called kinetic energy. A moving object possesses energy that is why it is capable of doing work. Example A fast moving ball, a stone thrown at a high speed high speed bullet, flowing wind and flowing water. Formula For Kinetic Energy To measure kinetic energy we have to measure the amount of work done because that is equal to kinetic energy. Work Done = Kinetic Energy â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦(i) Consider a body of mass m moving against the opposing force F with velocity v. Before its coming to rest after covering a certain distance work done by it will be given by W = F × S â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦(ii) But, because work done is equal to Kinetic Energy from (i) and (ii), we can say K.E. = F × S Now, assume that Initial Velocity = 0 Final Velocity = v Acceleration = a Distance = S (v) 2 â€“ (0) 2 = 2aS â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦(i) From Newtonâ€™s second law of motion F = m × a ? a = m F â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦(ii) By putting the value from (ii) in (i) we get v 2 - 0 = 2FS m ? v 2 = 2FS m ? F × S = 2 mv 2 Now, F × S = K.E. ? K.E. = 2 1 mv 2 Where m = mass of body v = velocity of the body Important Conclusion From The Formula K.E. = 2 1 mv 2 (i) As K.E. ? m, therefore if mass of the body is doubled then its kinetic energy also gets doubled and if mass of the body is halved its kinetic energy also gets halved. (ii) As K.E. ? v 2 , therefore if the velocity of the body is doubled then its kinetic energy becomes four times and if the velocity of body is halved, the kinetic energy become one fourth. 2. Potential Energy The energy of a body due to its position or change in shape is known as potential energy. The potential energy exists in two types: - 1. Gravitational Potential Energy The potential energy of a body due to its position above the ground is called gravitational potential energy. 2. Elastic Potential Energy The energy of a body due to a change in its shape and size is called elastic potential energy. Example (i) Water stored in an overhead tank. (ii) Coiled spring of a watch/clock. (iii) Raised hammer etc. The potential energy may be possessed by a body when it is not in motion, e.g. a stone lying on the top of the roof. Formula For Potential Energy Suppose a body of mass â€˜mâ€™ placed at a height â€˜hâ€™ above the ground and â€˜gâ€™ is the gravitational pull force acting on the body is gravitational pull of earth acting in downward direction is equal to m× g. Therefore, Force = m × g Displacement = h Work Done = Force × Distance W = m × g × h This work gets stored up in the body as potential energy. So, P.E. = m × g × h S. I. Unit Of Potential Energy P.E. = m × g × h P.E. = Kg × m/s 2 × m But, Kg × m/s 2 = N Therefore, P.E. = N × m = J S.I. unit of potential energy is Nm or J. Can a body possess both kinetic and potential energies at the same time? Certain bodies may possess both kinetic and potential energies at the same time. Examples (i) A man climbing a hill. (ii) An object rolling down a hill. (iii) A flying aeroplane. (iv) A flying bird. Transformation Of Energy The change of one form of energy into other form of energy is called transformation of energy. Example (i) When a body is released from a height then the potential energy of the body is gradually transformed into kinetic energy. (ii) The heat energy converted into K.E by a steam engine. (iii) The chemical energy of a firework is converted into thermal energy and light and sound energy when it explodes. (iv) A motor converts electrical energy into mechanical energy. Transformation In Case Of Mechanical Energy (i) When a body falls from a certain height its potential energy changes into kinetic energy. (ii) When a body is thrown upwards the kinetic energy of the body is changed into potential energy. Solar Energy The sun is a big store- house of energy. The solar energy gets changed into many other forms of energy which are very useful. Page 4 WORK AND ENERGY Work Work is said to be done when force produces motion. Example An engine pulling bogies of train, horse pulling a cart etc. The work done by a force on a body depends on two factors: - 1. Magnitude of the force 2. Distance through which the body moves In other words, we can say that work is said to be done when the point of application of a force moves. Work done in moving a body is equal to the product of force exerted on the body in the direction of force. Work = Force × Distance Or W = F × S S. I. Unit Of Work W = F × S W = N × m = Nm Therefore, unit of work is Nm. 1Nm is 1 Joule. So, unit of work will be Joule. 1 Joule may be defined as, a force of 1N moving a body through a distance of 1 m in its own direction. In such case, the work done is known as 1 Joule. 1 Joule = 1Newton × 1metre 1J = 1Nm S.I. unit of work is joule denoted by J. Work is a scalar quantity. Note that work is said to be done only if there is a move in an object through some distance. If however, the distance moved is zero the work done on the body of man himself is not zero, because his muscles are stretched and his blood is displaced. Examples Of Work Done (i) Push a pebble lying on a surface. The pebble moves through a distance. You exerted the force on the pebble and the pebble is displaced. In this case the work is done. (ii) A girl pulls a trolley and the trolley moves through a distance. The girl has exerted a force and the trolley is displaced. The work is done. (iii) Lift a book through a height. The book rises up. There is a force applied on the book and the book has moved. The work is done. When Work Is Not Said To Be Done? (i) You are pushing a huge rock and the rock is not at all moving from its place. As there is no displacement in the rock even after applying force, work is not done. (ii) You stand still for a few minutes with a heavy load on your head. You get tired. No work is done on the load. Therefore work is not said to be done if there is no displacement even after the application of the force. Work Done Against Gravity Whenever work is done against gravity the amount of work done is equal to the product of weight of the body and the vertical distance through which the body is lifted. Work done by the person against gravity is positive. Work Done In Lifting A Body Upwards = Weight Of Body × Vertical Distance Or W = m × g × h When a body of mass m is lifted to a height h above the ground, work equal to mgh is done on the body. Work Done When A Body Moves At An Angle To The Direction Of Force In such cases, we cannot use the formula W = F × S, because the distance moved S is not exactly in the direction of force applied. In such case, the force is applied at certain angle to the horizontal ground but the body moves horizontally on the ground. Calculating The Work Done When A Body Moves At An Angle To The Direction Of Force In this case, all force F is not utilized in pulling the body, only the horizontal component of force F is pulling the body along the ground. The horizontal component of force F is F Cos? and distance moved is S. Thus, W = FS Cos ? Work Done By Force When A Body Moves In A Direction Different From That Of Force 1. When the displacement is in the direction of force i.e. when ? = 0° W=F S Cos ? W=F S Cos 0° = F S × 1 = F× S Work done is equal to F×S. It is positive work. Example A baby pulling a toy car parallel to the ground. 2. When the displacement is at right angles to that of force i.e., when ? = 90 0 W = F S Cos ? = F S Cos 90° = F × S × 0 = 0 No work is done by force. Also we can say that no work is done when a body is moving along a circular path. 3. When displacement is in the opposite direction to that of the force i.e ? =180° W=F S cos ? = F S cos 180° = F S×-1 = -F× S It is called negative work. Work done is negative or work done against the force is positive. POWER Power is the rate of doing work. Power = Taken Time Done Work or P = T W In other words, we can say that power is work done per unit time. Power is a scalar quantity. Units Of Power P = T W = Second Joules = s J = J/s or Js -1 Joules per second is called watt. The S.I. unit of power is watt. One watt is the rate of doing work at 1 joule per second. 1 Watt= Second 1 Joule 1 Or 1watt = s 1 J 1 = s J Another unit of power is Horse Power (h.p.) 1Horse Power = 746 Watts Or 1 h.p. = 746 W Work From the formula of power another formula of work done can be derived that is, Power = Taken Time Done Work ? Work Done = Power × Time Or W = P × t ENERGY Energy is the ability or capacity to do work. The amount of work possessed by a body is equal to the amount of work it can do when its energy is released. Energy is utilized to do work. Forms Of Energy 1. Mechanical Energy 2. Chemical Energy 3. Electrical Energy 4. Light Energy 5. Nuclear Energy 6. Heat Or Thermal Energy How Does An Object With Energy Do Work? An object that possesses energy can exert force on another object. When this happens energy is transferred from one object to another. The second object may move as it receives energy and therefore do some work. Thus the first object has the capacity to do work. This implies that any object that possesses energy can do work. Unit Of Energy S.I. unit of energy is Joule (J). Energy is a scalar quantity. The energy possessed by an object is measured in terms of its capacity of doing work. Therefore the units of both energy and work are same. Mechanical Energy The energy by which the body can do some mechanical work is called mechanical energy. Two forms of mechanical energy are: - 1. Kinetic Energy 2. Potential Energy Mechanical energy is equal to sum of kinetic and potential energy M.E. = K.E. + P.E. 1. Kinetic Energy The energy of a body due to its motion is called kinetic energy. A moving object possesses energy that is why it is capable of doing work. Example A fast moving ball, a stone thrown at a high speed high speed bullet, flowing wind and flowing water. Formula For Kinetic Energy To measure kinetic energy we have to measure the amount of work done because that is equal to kinetic energy. Work Done = Kinetic Energy â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦(i) Consider a body of mass m moving against the opposing force F with velocity v. Before its coming to rest after covering a certain distance work done by it will be given by W = F × S â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦(ii) But, because work done is equal to Kinetic Energy from (i) and (ii), we can say K.E. = F × S Now, assume that Initial Velocity = 0 Final Velocity = v Acceleration = a Distance = S (v) 2 â€“ (0) 2 = 2aS â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦(i) From Newtonâ€™s second law of motion F = m × a ? a = m F â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦(ii) By putting the value from (ii) in (i) we get v 2 - 0 = 2FS m ? v 2 = 2FS m ? F × S = 2 mv 2 Now, F × S = K.E. ? K.E. = 2 1 mv 2 Where m = mass of body v = velocity of the body Important Conclusion From The Formula K.E. = 2 1 mv 2 (i) As K.E. ? m, therefore if mass of the body is doubled then its kinetic energy also gets doubled and if mass of the body is halved its kinetic energy also gets halved. (ii) As K.E. ? v 2 , therefore if the velocity of the body is doubled then its kinetic energy becomes four times and if the velocity of body is halved, the kinetic energy become one fourth. 2. Potential Energy The energy of a body due to its position or change in shape is known as potential energy. The potential energy exists in two types: - 1. Gravitational Potential Energy The potential energy of a body due to its position above the ground is called gravitational potential energy. 2. Elastic Potential Energy The energy of a body due to a change in its shape and size is called elastic potential energy. Example (i) Water stored in an overhead tank. (ii) Coiled spring of a watch/clock. (iii) Raised hammer etc. The potential energy may be possessed by a body when it is not in motion, e.g. a stone lying on the top of the roof. Formula For Potential Energy Suppose a body of mass â€˜mâ€™ placed at a height â€˜hâ€™ above the ground and â€˜gâ€™ is the gravitational pull force acting on the body is gravitational pull of earth acting in downward direction is equal to m× g. Therefore, Force = m × g Displacement = h Work Done = Force × Distance W = m × g × h This work gets stored up in the body as potential energy. So, P.E. = m × g × h S. I. Unit Of Potential Energy P.E. = m × g × h P.E. = Kg × m/s 2 × m But, Kg × m/s 2 = N Therefore, P.E. = N × m = J S.I. unit of potential energy is Nm or J. Can a body possess both kinetic and potential energies at the same time? Certain bodies may possess both kinetic and potential energies at the same time. Examples (i) A man climbing a hill. (ii) An object rolling down a hill. (iii) A flying aeroplane. (iv) A flying bird. Transformation Of Energy The change of one form of energy into other form of energy is called transformation of energy. Example (i) When a body is released from a height then the potential energy of the body is gradually transformed into kinetic energy. (ii) The heat energy converted into K.E by a steam engine. (iii) The chemical energy of a firework is converted into thermal energy and light and sound energy when it explodes. (iv) A motor converts electrical energy into mechanical energy. Transformation In Case Of Mechanical Energy (i) When a body falls from a certain height its potential energy changes into kinetic energy. (ii) When a body is thrown upwards the kinetic energy of the body is changed into potential energy. Solar Energy The sun is a big store- house of energy. The solar energy gets changed into many other forms of energy which are very useful. (i) Transformation of solar energy into wind energy. (ii) Transformation of solar energy into electrical energy. (iii) Transformation of solar energy into food energy. Law Of Conservation Of Energy Energy can neither be created nor destroyed; it is only transformed from one form into other. Whenever energy changes from one form to another, the total amount of energy remains constant or conserved. Whenever one form of energy disappears, an equivalent amount of energy in another form appears. Or we can say that whenever the energy gets transformed, the total energy before and after the transformation remains unchanged. Proof Of The Law Of Conservation Of Energy To prove this principle, let us consider kinetic energy, potential energy and T.E. (total energy) of the body falling freely under gravity. Consider an object of mass m, kept at rest at point A, which is height h, above the ground. We take the potential energy of the object at the ground to be zero. The potential energy of the object at A is U A = mgh K.E. A = 0 [Q v = 0, it is not moving] ? total energy (T.E.) A = U A + K.E. A = mgh + 0 = mgh The object is now allowed to fall freely under the action of gravity. It gains velocity as it comes down and its kinetic energy increases due to increase in the velocity. Let us consider a point C at any instant between A and B such that AC = x and v is the velocity of object at C. Then its kinetic energy will be 1 2 mv 2 and potential energy will be mg (h-x). Therefore total energy of the body will be T.E. = K.E. + P.E. T.E. = 1 2 mv 2 + mg (h-x) Using the third equation of motion v 2 = u 2 + 2gx; v 2 = 0 + 2gx ? v 2 = 2gx ? T.E. = 1 2 m 2gx + mg (h-x) = mgx + mgh â€“ mgx = mgh And finally when the object reaches the ground, height from the ground is zero and therefore the potential energy (U B ) = 0. If the velocity of body on reaching the ground is v, then K.E. = 1 2 mv 2 B Now from the 3 rd equation of motion v B 2 = u 2 â€“ 2 as v B 2 = (0) 2 + 2gh v B 2 = 2gh ?at B K.E. = 1 2 mv 2 B = 1 2 m (2gh) = 1 2 . 2 mgh ? T.E. B = v B + K.E. B = 0 + mgh = mgh Therefore the total energy of the object during the free fall remains constant at all positions. The form of energy however keeps on changing. At A the energy is entirely potential and at B it is entirely kinetic. In between A and B the energy is partiallt potential partially kinetic. But total energy remains constant throughout. When the body hits the ground and comes to rest, it looses all its kinetic energy, the loss of kinetic energy appears as sound, light and heat. When it hits the ground it produces sound, sparkling (light) and the point of contact becomes hot(heat). Example (i) Conservation of energy during the free fall of a body: As the ball falls downward its potential energy goes on decreasing whereas the kinetic energy increases in equal amount. So, total energy remains conserved. (ii) Energy of a ball thrown upwards is also conserved. (iii) A swinging simple pendulum is an example of conservation of energy. (iv) If a batsman hits a ball, the ball gets some velocity and at the same time the batsman looses some energy. The some total of energy in this universe is a constant quantity. Commercial Unit Of Energy The unit joule is too small and hence it is inconvenient to express large quantities of energy. A bigger unit of energy can be used that is kilowatt hour (kW h). The energy used in households, industries, and commercial establishments are usually expressed in kilowatt hour. For example electrical energy used during a month is expressed in terms of â€˜unitsâ€™. Here one â€˜unit â€˜ means 1 killowatt hour. 1 kW h is the energy used in one hour at the rate of one thousand joules per second or 1 kW. 1kW = 1000 W ? 1 h = 1000 W ? 3600 s = 3600000 Ws = 3600000 J 1kW = 3.6 ? 10 6 JRead More

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