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yWORK POWER ENERGY Vikasana – Bridge Course 2012 WORK - POWER - ENERGY work is said to be done by a force when it moves a body through a certain distance . Work done is measured as the product of component of force along the direction of displacement and the displacement Thus displacement. Vikasana – Bridge Course 2012 work done = { component of force x { displacement } along g the displacement } F S F cos θ θ Vikasana – Bridge Course 2012 People pulling a load at an angle with road Vikasana – Bridge Course 2012 If the application of force displaces the body at an angle ‘θ’ θ then work is Work = F cosθ x S = F S cos θ From this equation q we can draw some results. Vikasana – Bridge Course 2012 1 If the application of force and 1. displacement are along same direction then θ = 0 and cos θ = 1 Hence work becomes W = F S . work becomes maximum maximum. Ex. A person pushing a load or pulling lli a load l d on a horizontal h i t l road d makes maximum work. Vikasana – Bridge Course 2012 A person pulling a body horizontally Vikasana – Bridge Course 2012 Work is done along the direction of force hence the body gains the energy 2. If the application of force and displacement are mutually perpendicular then angle b t between F and d S becomes b 90 degree. d Thus Th θ = 90 and cos θ = 0 Vikasana – Bridge Course 2012 Work done = F S (0) = 0 (zero) work done is minimum or zero. Ex. A person carrying a suitcase on his head and moving horizontally will not make any work. F l d load s F = mg Vikasana – Bridge Course 2012 Vikasana – Bridge Course 2012 3. If the application of force and the displacement are in opposite direction then th angle the l between b t them th becomes b θ = 180 and cos180 = -1 work becomes W = - F S negative maximum. Work is done against the applied force . Hence the body looses the energy Vikasana – Bridge Course 2012 When brakes are applied the force is applied li d in i opposite it direction di ti to t displacement. Thus work becomes negative. ti Vikasana – Bridge Course 2012 Ex. When the brakes are applied to a vehicle the applied force and displacement are in opposite it di direction. ti The same thing happens if a body does th work the k against i t frictional f i ti l force f and d gravitational force. Vikasana – Bridge Course 2012 Work done against gravitational force is also negative as gravitational force acts down wards and body moves upwards. upward motion Gravitational force Displace p ment BALL THROWN UPWARDS DOES NEGATIVE WORK Vikasana – Bridge Course 2012 Work done is measured in terms of Joule or Nm N Work is a scalar quantity. The total work i equall to is t sum off works k done d . Ex. If a person pushes a body from one position to other position p p and brings g back to the same position then the amount of work is sum of works done. Vikasana – Bridge Course 2012 POWER ; The rate of doing work is called power. power Power is measured as the ratio of work done to the time taken to do the work. Vikasana – Bridge Course 2012 Power is energy exhausted per second Vikasana – Bridge Course 2012 If V= S /t is the constant velocity attained tt i d in i the th body b d due d to t force f then th Power = F V cosθ Power is a scalar quantity. SI unit of power is watt (W) or Js-1 Power is also measured in terms of horse power (HP). (HP) 1 HP = 746 Watt Vikasana – Bridge Course 2012 : ENERGY : The capacity of doing work by a body is called the energy of the body. It is measured by the work it can do. Energy of a body = work done by th body the b d Vikasana – Bridge Course 2012 Lets now understand these with an example. l There are two friends called Ramesh and Mahesh. Let us assign the work of taking 10 stones each of 2 kg from the compound to the terrace which is at a height 5 m , to both of them. 1. Ramesh picks every stone at a time and climbs the stairs and keeps p on the terrace. Vikasana – Bridge Course 2012 For keeping every stone he takes 2 minutes. i t Hence Ramesh totally takes 20 minutes to keep 10 stones on the terrace. 2. Now Mahesh starts the work . y time he p picks 2 stones and Every climbs the stairs to keep the stones on the terrace. He also takes 2 min for Vikasana – Bridge Course 2012 every two stones keeping. H Hence M Mahesh h h totally ll takes k 10 minutes to keep 10 stones on the terrace. The work done by Ramesh is Work = F x s = mg x h =2x9 9.8 8x5 = 98 J Vikasana – Bridge Course 2012 Now the work done by Mahesh is Work = F x S = m g h = 2 x 9.8 x 5 = 98 J Hence both of them do the same amount of work. Si Since th the energy is i equall to t the th amount of work done , Both spend same energy. Vikasana – Bridge Course 2012 Now consider the power they have Power of Ramesh = work done / time = 98 / 20 = 4.9 J / min Power of Mahesh = Work done / time = 98 / 10 = 9.8 J / min Vikasana – Bridge Course 2012 This shows that the power of Ramesh is less than Power of Mahesh Mahesh. Hence we can say that a person who d does the th work k in i less l time ti has h more power. Thus coming from home to college ll by b walk lk does d same work k as coming by running. But the difference i with is ith power. Running R i requires i more power than walking. Vikasana – Bridge Course 2012 y Thus a person who has more power can do the work in a short time. Vikasana – Bridge Course 2012 There are different forms of energy. They are 1. Mechanical energy 2. Electrical energy 3 Heat 3. H t energy 4. Sound energy 5. Wind energy etc All forms of energy are inter convertible. Vikasana – Bridge Course 2012 A generator converts heat energy to electricity or mechanical energy into electrical energy Vikasana – Bridge Course 2012 Wind energy(mechanical energy) converting to electricity Vikasana – Bridge Course 2012 Solar panels convert solar energy into electricity Vikasana – Bridge Course 2012 A fan converts electrical energy into mechanical h i l energy Vikasana – Bridge Course 2012 Mechanical energy are of two types. 1. Kinetic energy 2. Potential energy If a body b d possess both b th types t off energy then total energy of the body is s m of kinetic and potential energy. sum energ Vikasana – Bridge Course 2012 KINETIC ENERGY Kinetic energy gy is the capacity p y of a body to do work by virtue of its motion. The faster the object moves moves, the greater is the kinetic energy. When the object is stationary stationary, its kinetic energy is zero. Vikasana – Bridge Course 2012 A girl sliding down will possess P.E. Vikasana – Bridge Course 2012 If a body of mass ‘m’ moves with a velocity l it ‘V’ th then it will ill possess kinetic ki ti energy Kinetic energy = Ek = Examples of kinetic energy : A bullet fired from a gun , An arrow fired from bow , A vehicle running , a person running Vikasana – Bridge Course 2012 A fastly moving car possess kinetic energy Vikasana – Bridge Course 2012 Running girl posses kinetic energy Vikasana – Bridge Course 2012 POTENTIAL ENERGY Potential energy (PE) of a body is gy stored in the body y by y virtue the energy of its position of configuration in a field. Potential energy is measured by the amount of work to be done in taking a body from a standard position to given position Vikasana – Bridge Course 2012 A person at highest point possess P.E. Vikasana – Bridge Course 2012 Ex : a spring stretched / compressed, A b bow stretched t t h d , a body b d raised i d to t a height , Gravitational potential energy of a body is measured as potential energy = work done in raising = mgh m is the mass of the body g is i the th acceleration l ti due d to t gravity it Vikasana – Bridge Course 2012 h is the height to which body is raised Thus a body y which is at a larger g height g will have higher potential energy. Examples of gravitational P.E. : A stone t k keptt on tterrace , A An aero plane l at a height, water at the top of a fall Vikasana – Bridge Course 2012 Water in an overhead tank possess P.E. Vikasana – Bridge Course 2012 The water in a reservoir possess P.E. Vikasana – Bridge Course 2012 MECHANICAL ENERGY AND ITS CONSERVATION The mechanical energy gy E of a system y is the sum of its kinetic energy K and its potential energy p gy U. Total energy = Kinetic energy + potential energy E= K+U Vikasana – Bridge Course 2012 LAW OF CONSERVATION OF ENERGY In an isolated system the total mechanical energy of a body remains constant. The kinetic energy gy of a body y can be converted into potential energy and potential energy p gy can be converted into kinetic energy. In all the total energy remains constant . Vikasana – Bridge Course 2012 At highest point the boy possess only P.E. when he comes down P.E. is converted into K.E entirely. Vikasana – Bridge Course 2012 When stretched the bow gets P.E. When thread is released the P.E. is converted into K.E of arrow. The arrow moves fast. Vikasana – Bridge Course 2012 When water is stored in reservoir the water possess P.E. When gates are opened the water rushes out and gets enormous K.E. Vikasana – Bridge Course 2012 Thus a body y which is at highest g p point will have highest P. E. when released it g kinetic energy gy .As the starts attaining body comes down and down the kinetic gy g goes on increasing. g Just before energy reaching ground the body will have only gy kinetic energy. Vikasana – Bridge Course 2012 Consider an example of just leaving a pen off 10 gm ffrom an h helicopter li t which hi h is 800 m high. P.E = M g h = 10 x 10-3 x 9.8 x 800 = 78. 4 J When the pen comes to ground entire energy is converted into kinetic energy energy. this energy is sufficient to damage a car kept in open ground. Vikasana – Bridge Course 2012 :COLLISION: A collision is said to occur if the momentum or the kinetic energy of colliding bodies change. 1. ELASTIC COLLISION : Elastic collision is the one in which both momentum and kinetic energy of a system remains same (conserved) Vikasana – Bridge Course 2012 Kinetic energy before = kinetic energy after collision collision momentum before collision = momentum after collision Ex. Collisions between atomic and sub atomic particles Vikasana – Bridge Course 2012 If you add vectorially total momentum is conserved IN ELASTIC COLLISION : Inelastic collision is the one in which only momentum is conserved but kinetic energy is not conserved. Kinetic energy ≠ kinetic energy after B f Before C Collision lli i collision lli i Momentum before = momentum after Collision collision Vikasana – Bridge Course 2012 Ex. Collision between larger bodies like truck and car Vikasana – Bridge Course 2012 consider an example of lifting of water t from f a sump to t a ttank k and d filli filling it with 1000 litre which is on the top of th second the d floor fl att a height h i ht off 12 m from the ground. The amount of work done = P.E. in the water =mgh The volume of water = 1000 x 1000 cm3 Vikasana – Bridge Course 2012 mass of water = 106 cm3x density = 106 cm3x 10-3 Kg/cm3 = 1000 kg work done = m g h = 1000 x 9.8 x 12 = 117.6 117 6 x 10 3 = 1 . 176 x 10 5 J Vikasana – Bridge Course 2012 2. A cricket ball of mass 0.145 kg moving at 30 m/s has kinetic energy: K.E = ½ m V2 K E = ½×(0.145 K.E. ½ (0 145 k kg)×(30 ) (30 m/s) / )2 = 65.25 kg·m2/s2 ≈ 65 J 3 A mass = 0 3. 0. 5 k kg fli flipped d iinto t th the air i has h a speed on reaching your hand of about 5 m/s. The kinetic energy is: K.E. = ½×(0. 5 kg)×(5 m/s)2 = 6.25 6 25 J Vikasana – Bridge Course 2012 4. A 1000 kg car moving at 30 m/s will h have ki kinetic ti energy as K.E. = ½×(1000 kg)×(30 m/s)2 = 450000 kg·m2/s2 = 450 kJ 5. A 1000 kg car moving at 15 m/s will have kinetic energy as K.E. = ½×(1000 kg)×( 15 m/s)2 = 112500 kkg·m2/s / 2 = 112 kJ Vikasana – Bridge Course 2012 6. How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform? P.E=mgh = (70 kg)×(10 m/s2)×(10 m) = 7,000 kg·m kg m2/s2 = 7 kJ 7.What is the energy of a book of mass 2 kg k kept k t on a shelf h lf two t meters t off ff the th floor? P.E = 2 x 10 x 2 = 40 J Vikasana – Bridge Course 2012 8. How much p power does it take to lift 10 kg up 2 m in 2 seconds? work done = mgh = (10 kg)×(10 m/s2)×(2 m) = 200J power = work done /time = 200 / 2 = 100 W Vikasana – Bridge Course 2012 In this session we had learnt about 1. What is work ? 2. What is p power ? 3. What is energy ? 4 How to measure work , power and 4. energy ? 5 What 5. Wh t iis conservation ti off energy ? 6. How to convert energy from one form to another form ? Vikasana – Bridge Course 2012 WORK ENERGY THEOREM y Work done on a body (work done by a y) is equal q to the change g in energy gy body) of body. y Loss in kinetic energy = y If a bullet fired pierces a wooden plank and emerges out then loss in K.E. of bullet is equal to work done in drilling. drilling Vikasana – Bridge Course 2012