Slide 1

23/02/14371Norah Ali Al - moneef Slide 2 6-1 Work In physics, work has a very specific meaning. In physics, work represents a measurable change in a system, caused by a force. Work is done on a system where an applied force results in some net displacement force that results in no displacement does no work A displacement that results with no applied force has had no work done 23/02/14372Norah Ali Al - moneef Slide 3 What do forces do? They change the speed of a mass They do work on a mass They change the energy of a mass 23/02/14373Norah Ali Al - moneef Work (force is parallel to distance) W = F x d Distance (m) Force (N) Work (joules) Slide 4 23/02/14374Norah Ali Al - moneef Slide 5 W = F d cos definition of work Work d - the displacement of the point of application of the force - is the angle between the force and the displacement vectors 23/02/14375Norah Ali Al - moneef Slide 6 Work Relates force to change in energy Scalar quantity Independent of time Units of Work and Energy SI unit = Joule 1 J = 1 N m = 1 kg m 2 /s 2 23/02/14376Norah Ali Al - moneef Slide 7 Work W = F d cos A force does no work on the object if the force does not move through a displacement The work done by a force on a moving object is zero when the force applied is perpendicular to the displacement of its point of application cos 90 = 0 23/02/14377Norah Ali Al - moneef Slide 8 The Scalar Product of Two Vectors Our definition of work: W = F d cos is messy because of the cosine factor What we are actually doing is performing an operation with two vectors called the scalar product: 23/02/14378Norah Ali Al - moneef It is also called the dot product is the angle between A and B Slide 9 More About Work The sign of the work depends on the direction of the displacement relative to the force Work is positive when the projection of F onto d is in the same direction as the displacement Work is negative when the projection is in the opposite direction Work zero: W = 0 if = 90 Work maximum if = 0 Work minimum if = 180 23/02/14379Norah Ali Al - moneef Slide 10 W > 0 W < 0 W = 0 23/02/143710Norah Ali Al - moneef Slide 11 Example: When Work is Zero A man carries a bucket of water horizontally at constant velocity. The force does no work on the bucket Displacement is horizontal Force is vertical cos 90 = 0 23/02/143711Norah Ali Al - moneef Slide 12 Work can be positive or negative Man does positive work lifting box Man does negative work lowering box Gravity does positive work when box lowers Gravity does negative work when box is raised Work is done on the books when they are being lifted, but no work is done on them when they are being held or carried horizontally. 23/02/143712Norah Ali Al - moneef Slide 13 Work Done by a Constant Force Example: Work done on the bag by the person.. Special case: W = 0 J a) W = F d cos ( 90 o ) b) W g = m g d cos ( 90 o ) Nothing to do with the motion 23/02/143713Norah Ali Al - moneef Slide 14 23/02/143714Norah Ali Al - moneef Slide 15 example 23/02/143715Norah Ali Al - moneef Slide 16 16 Work - Example The normal force,, and the gravitational force, mg, do no work on the object cos = cos 90 = 0 The force does do work on the object There is a component along the direction of motion W = F d cos 23/02/1437Norah Ali Al - moneef Slide 17 Example : A horizontal force F pulls a 10 kg carton across the floor at constant speed. If the coefficient of sliding friction between the carton and the floor is 0.30, how much work is done by F in moving the carton by 5m? The carton moves with constant speed. Thus, the carton is in horizontal equilibrium. F = f = k N = k mg. Thus F = 0.3 x 10 x 9.8 = 29.4 N Therefore work done W = FS =(29.4 Cos 0 o ) =147 J 23/02/143717Norah Ali Al - moneef Slide 18 23/02/143718Norah Ali Al - moneef Slide 19 23/02/143719Norah Ali Al - moneef Three student push their car which run out of gas. If each student pushes with a force of 500 N and the car pushed a distance of 40 m, find the work done by the student s Example A student pushes on a heavy box with a force of 400 N and moves it a distance of 5 m. If the force applied at an angle of 37 shown below, find the work done by the student A man exert a horizontal force 160 N on a car that moves a distance of 10m calculate the work done by the force Slide 20 Work Done by a Varying Force We know that for a constant force the work is just But if the force is not constant in space we have a problem We will use an approach similar to that used to determine net displacement given a time varying velocity! Consider a force in the x- direction with a magnitude that changes depending on the exact position. We can carve that (the displacement x f -x i ) displacement up into a bunch of small (very small) displacements. 23/02/143720Norah Ali Al - moneef Slide 21 Work Done by a Varying Force For each of these small displacements, the force will be nearly constant, in that case, W 1 F x x (the area of the rectangle) This will be true for all the intervals so we can form 23/02/143721Norah Ali Al - moneef Slide 22 Work Done by a Varying Force, cont Again, we make the intervals vanishingly small; Therefore, The work done is equal to the area under the curve When more than one force acts on an object: or 23/02/143722Norah Ali Al - moneef Slide 23 example An Eskimo returning pulls a sled as shown. The total mass of the sled is 50.0 kg, and he exerts a force of 1.20 10 2 N on the sled by pulling on the rope. How much work does he do on the sled if = 30 and he pulls the sled 5.0 m ? 23/02/143723Norah Ali Al - moneef Slide 24 23/02/1437 Work and Multiple Forces Suppose k = 0.200, How much work done on the sled by friction, and the net work if = 30 and he pulls the sled 5.0 m ? Slide 25 Energy and Conservation of Energy Energy is the ability to make things change. A system that has energy has the ability to do work. Energy is measured in the same units as work because energy is transferred during the action of work. 23/02/143725Norah Ali Al - moneef What are important kinds of energy? 1. Kinetic Energy Energy of a mass in motion Kinetic is moving energy (Dynamics) Dependant on velocity Slide 26 6- 2 Kinetic Energy: F x A force F = 10 N pushes a box across a frictionless floor for a distance x = 5 m. The speed of the box is v 1 before the push and v 2 after the push. xxxx F v1v1 v2v2i m 23/02/143726Norah Ali Al - moneef Slide 27 23/02/143727Norah Ali Al - moneef The quantity is so important that we give it a special name. The kinetic energy K of an object of mass m moving with a speed v is: Kinetic energy is the energy of a particle due to its motion. Kinetic energy is a scalar and has the same units as work (Joules) Kinetic energy and the Work-Kinetic energy theorem Slide 28 Kinetic Energy Energy of motion is called kinetic energy. The kinetic energy of a moving object depends on two things: mass and speed. Kinetic energy is proportional to mass. 23/02/143728Norah Ali Al - moneef Mathematically, kinetic energy increases as the square of speed. If the speed of an object doubles, its kinetic energy increases four times. (mass is constant) Slide 29 An objects kinetic energy depends on its mass and its speed. The faster something is moving and the heavier it is, the more work it can do, so 2 If v quadruples, 23/02/143729Norah Ali Al - moneef then KE will increase by 9 times. If v tripled then KE will increase by 16 times Slide 30 example 23/02/143730Norah Ali Al - moneef M= 4 kg Slide 31 23/02/143731Norah Ali Al - moneef Slide 32 A change in kinetic energy is one possible result of doing work to transfer energy into a system. If the net work done on a particle is positive, the speed (and hence the kinetic energy) of the particle increases. If the net work done on a particle is negative, the speed (and hence the kinetic energy) of the object decreases. Kinetic Energy and the Work-Kinetic Energy Theorem 23/02/143732Norah Ali Al - moneef Slide 33 23/02/143733Norah Ali Al - moneef Slide 34 23/02/143734Norah Ali Al - moneef Slide 35 23/02/143735Norah Ali Al - moneef M=6.00 kg Slide 36 23/02/143736Norah Ali Al - moneef Slide 37 Example 3 : A 6.0-kg block initially at rest is pulled to the right along a horizontal, frictionless surface by a constant horizontal force of 12 N. Find the speed of the block after it has moved 3.0 m. W =F d cos 0 =12x 3x1 = 36J k = w 0.5m V 2 =W =36 J 23/02/143737Norah Ali Al - moneef Slide 38 Example What acceleration is required to stop a 1000kg car traveling 28 m/s in a distance of 100 meters?. 23/02/143738Norah Ali Al - moneef Slide 39 Example A car traveling 60.0 km/h to can brake to a stop within a distance of 20.0 m. If the car is going twice as fast, 120 km/h, what is its stopping distance ? (a) (b) 23/02/143739Norah Ali Al - moneef (1) W net = F d (a) cos 180 o = - F d (a) = 0 m v (a) 2 / 2 - F x (20.0 m) = - m (16.7 m/s) 2 / 2 (2) W net = F d (b) cos 180 o = - F d (b) = 0 m v (b) 2 / 2 - F x (d ) = - m (33.3 m/s) 2 / 2 (3) F & m are common. Thus, d = 80.0 m Slide 40 example 23/02/143740Norah Ali Al - moneef Slide 41 example 23/02/143741Norah Ali Al - moneef Slide 42 23/02/143742Norah Ali Al - moneef k= Slide 43 23/02/143743Norah Ali Al - moneef Slide 44 6 3 potential energy and conservative forces Potential Energy Potential energy is associated with the position of the object within some system Potential energy is a property of the system, not the object A system is a collection of objects or particles interacting via forces or processes that are internal to the system - Potential is stored energy (Statics) Dependant on height 23/02/143744Norah Ali Al - moneef Slide 45 Potential Energy Gravitational potential energy is simple to calculate Gravitational Potential Energy = weight X height 23/02/143745Norah Ali Al - moneef Work done against gravity W =mgh Height object raised (m) Gravity (m/sec 2 ) Work (joules) Mass (k g) Slide 46 23/02/143746Norah Ali Al - moneef Slide 47 Ball slows down Ball speeds up 23/02/143747Norah Ali Al - moneef Slide 48 Work Done by Gravity l ball up W g = (mg)(S) S =h f -h 0 W g =-mg(h f -h 0 ) = u pot,initial u pot,final Y i = h f Y f = h 0 mgS y x l Drop ball Y i = h Y f = h f W g = (mg)(S) S =h f -h 0 W g = mg(h f -h 0 ) = mg(h f -h 0 ) = E pot, final E pot, initial y x Y i = h 0 mg S y x,initial 23/02/143748Norah Ali Al - moneef Slide 49 Work Done by the Gravitational Force Work done on the ball by the gravity is: If an object is moving down, If an object is moving up, Work done by the gravity only depends on the change of height, not depends on the path. 23/02/143749Norah Ali Al - moneef Slide 50 U = - w Lift mass m with constant velocity Work done by gravity = mg.(-h) = -mgh Potential Energy The change in potential energy is equal to minus the work done BY the conservative force ON the body. Therefore change in PE is U = - w h mg U grav = +mgh 23/02/143750Norah Ali Al - moneef Slide 51 What is the potential energy of a 12 kg mass raised from the ground to a to a height of 25 m? example Potential Energy = weight x height change Weight = 12 x 10 = 120 N Height change = height at end - height at start = 25 - 0 = 25 m Potential energy = 120 x 25 = 3000 J 23/02/143751Norah Ali Al - moneef Slide 52 How much potential energy is lost by a 5Kg object to kinetic energy due a decrease in height of 4.5 m PE = mgh PE = (5Kg)(10 m/s 2 )(4.5 m) PE = 225 Kg m 2 /s 2 PE = 225 J example 23/02/143752Norah Ali Al - moneef Slide 53 example 23/02/143753Norah Ali Al - moneef Slide 54 23/02/143754Norah Ali Al - moneef Slide 55 23/02/143755Norah Ali Al - moneef Slide 56 Conservative Forces -g Each step height= h = -mg( h 1 + h 2 + h 3 +) = -mgh Same as direct path (-mgh) Work done by gravity w = -mg h 1 + -mg h 2 +-mg h 3 + h A force is conservative if the work done by it on a particle that moves between two points is the same for all paths connecting these points: otherwise the force is non-conservative. 23/02/143756Norah Ali Al - moneef Slide 57 23/02/143757Norah Ali Al - moneef Slide 58 Work Done by Gravity l Slide block down incline W g = (mg)(S)cos S = h/cos W g = mg(h/cos )cos W g = mgh with h= h 0 -h f h mg S Work done by gravity is independent of path taken between h 0 and h f => The gravitational force is a conservative force. h0h0 h f 23/02/143758Norah Ali Al - moneef Slide 59 23/02/143759Norah Ali Al - moneef Slide 60 Who is going faster at the bottom? Assume no friction Assume both have the same speed pushing off at the top same 23/02/143760Norah Ali Al - moneef Slide 61 23/02/143761Norah Ali Al - moneef Slide 62 23/02/143762Norah Ali Al - moneef Slide 63 Doing Work to Decrease Energy When you catch a ball, its kinetic energy is reduced (or absorbed) by the negative work you do on it Your muscles do negative work on your limbs and absorb energy when you land from a jump or fall Average force you must exert to absorb energy in catching a ball or landing from a jump or fall depends on how much energy must be absorbed and the displacement over which the force is absorbed 23/02/143763Norah Ali Al - moneef Safety and protective equipment used in many sports utilizes the work/energy principle to reduce potentially damaging impact forces Examples of shock absorbing or energy absorbing materials Landing pads (gymnastics, high jumping, and pole vaulting) increase displacement of the athlete during the impact period Sand (long jumper), water (diver), midsole material in shoes (runner) Slide 64 Law of Conservation of Energy As energy takes different forms and changes things by doing work, nature keeps perfect track of the total. No new energy is created and no existing energy is destroyed. 23/02/143764Norah Ali Al - moneef Slide 65 U + K = 0 Lets check this for a body of mass m moving under gravity. xixi xfxf h mg w = K = K f - K i K = mv f 2 mv i 2 For motion under gravity you know v 2 = u 2 + 2as v f 2 = v i 2 - 2gh mult by m m v f 2 = mv i 2 -mgh w g = - u = -mgh +ve w = - U = K so U + K = 0 vfvf vivi 23/02/143765Norah Ali Al - moneef Slide 66 Work-Energy Theorem The work done on an object is equal to the change in its kinetic energy. Work = KE If you know the height of the block, you can predict its speed at the bottom of the ramp! (doesnt matter how LONG the ramp is) Gives the same answer as above. 23/02/143766Norah Ali Al - moneef Slide 67 Weight =500 N 23/02/143767Norah Ali Al - moneef Slide 68 example At B At C 23/02/143768Norah Ali Al - moneef Slide 69 Example A skier slides down the frictionless slope as shown. What is the skiers speed at the bottom? H=40 m L=250 m start finish 28.0 m/s 23/02/143769Norah Ali Al - moneef Slide 70 A truck of mass 3000 kg is to be loaded onto a ship using a crane that exerts a force of 31 kN over a displacement of 2m.Find the upward speed of truck after its displacement. 23/02/143770Norah Ali Al - moneef Slide 71 23/02/143771Norah Ali Al - moneef Slide 72 Work-Energy Theorem If we do work on an object and set it into motion without changing the objects potential energy, the work done appears as kinetic energy of the object 23/02/143772Norah Ali Al - moneef Slide 73 Work done on a system by external force 23/02/143773Norah Ali Al - moneef Slide 74 Work Energy Principle & Mechanical Energy Conservation If we ignore non conservative forces (friction and the such), the implication is that no non-mechanical energies are present (heat, sound, light, etc) therefore As energy takes different forms and changes things by doing work, nature keeps perfect track of the total. No new energy is created and no existing energy is destroyed. 23/02/143774Norah Ali Al - moneef Slide 75 Work and Energy If a force (other than gravity) acts on the system and does work Need Work-Energy relation or 23/02/143775Norah Ali Al - moneef Slide 76 Types of Forces There are two general kinds of forces Conservative Work and energy associated with the force can be recovered Non conservative The forces are generally dissipative and work done against it cannot easily be recovered 23/02/143776Norah Ali Al - moneef Slide 77 Conservative Forces A force is conservative if the work it does on an object moving between two points is independent of the path the objects take between the points The work depends only upon the initial and final positions of the object Any conservative force can have a potential energy function associated with it Examples of conservative forces include: Gravity Spring force Electromagnetic forces 23/02/143777Norah Ali Al - moneef Slide 78 Non conservative Forces A force is non conservative if the work it does on an object depends on the path taken by the object between its final and starting points. Examples of non conservative forces kinetic friction 23/02/143778Norah Ali Al - moneef Slide 79 F f d Work done by me = F.d Work done by friction = -f.d = -F.d Total work done = 0 What happens if I let go?NOTHING!! Gravity is Conservative Friction is NOT!! Moving a block against friction at constant velocity 23/02/143779Norah Ali Al - moneef Slide 80 Example Suppose the initial kinetic and potential energies of a system are 75J and 250J respectively, and that the final kinetic and potential energies of the same system are 300J and -25J respectively. How much work was done on the system by non- conservative forces? 1. 0J 2. 50J 3. -50J 4. 225J 5. -225J correct Work done by non-conservative forces equals the difference between final and initial kinetic energies plus the difference between the final and initial gravitational potential energies. W = (300-75) + ((-25) - 250) = 225 - 275 = -50J. 23/02/143780Norah Ali Al - moneef Slide 81 6-4 Dissipative forces Friction as a Non conservative Force The friction force is transformed from the kinetic energy of the object into a type of energy associated with temperature (internal energy) the objects are warmer than they were before the movement Internal Energy is the term used for the energy associated with an objects temperature 23/02/143781Norah Ali Al - moneef Work can be done by friction The energy lost to friction by an object goes into heating both the object and its environment Some energy may be converted into sound For now, the phrase Work done by friction will denote the effect of the friction processes on mechanical energy alone Slide 82 Friction Depends on the Path The blue path is shorter than the red path The work required is less on the blue path than on the red path Friction depends on the path and so is a non-conservative force 23/02/143782Norah Ali Al - moneef Mechanical Energy Conservation with energy lost Slide 83 example a- B - 23/02/143783Norah Ali Al - moneef Slide 84 23/02/143784Norah Ali Al - moneef Slide 85 23/02/143785Norah Ali Al - moneef Slide 86 23/02/143786Norah Ali Al - moneef Slide 87 23/02/143787Norah Ali Al - moneef Slide 88 example 23/02/143788Norah Ali Al - moneef Slide 89 23/02/143789Norah Ali Al - moneef Slide 90 23/02/143790Norah Ali Al - moneef Slide 91 23/02/143791Norah Ali Al - moneef Slide 92 23/02/1437Norah Ali Al - moneef92 A ) W gra =F gra s cos 180 = - (mg sin 20) s =- 10 x 9.8 x5 x sin 20 = - 168 J OR W gra = -mg ( h-h 0 ) = - 10 x 9.8 x s sin 20 = - 10 x9.8 x5 x sin 20= - 168 J B ) w friction = F friction s cos 180= -( mg cos 20 )s = -10 x9.8 x5 cos 20 = - 184 J C ) w app = F s cos o = 100 x5 = 500 J w net = w app + W gra + w friction = 500 168 184 = 148 J D ) K = w net = 148 J E ) K K 0 = 148 J Another solution Slide 93 23/02/143793Norah Ali Al - moneef Slide 94 23/02/143794Norah Ali Al - moneef Slide 95 23/02/143795Norah Ali Al - moneef Slide 96 23/02/143796Norah Ali Al - moneef Slide 97 example s 23/02/143797Norah Ali Al - moneef Slide 98 23/02/143798Norah Ali Al - moneef Slide 99 23/02/143799Norah Ali Al - moneef Slide 100 OR 23/02/1437100Norah Ali Al - moneef Slide 101 23/02/1437101Norah Ali Al - moneef Slide 102 23/02/1437102Norah Ali Al - moneef Slide 103 23/02/1437103Norah Ali Al - moneef Slide 104 example You are towing a car up a hill with constant velocity. A )The work done on the car by the normal force is: 1. positive 2. negative 3. zero W T FNFN V The normal force is perpendicular to the displacement, hence, does no work. correct b )The work done on the car by the gravitational force is: 1. positive 2. negative 3. zero correct With the surface defined as the x-axis, the x component of gravity is in the opposite direction of the displacement, therefore work is negative. C ) The work done on the car by the tension force is: 1. positive 2. negative 3. zero correct Tension is in the same direction as the displacement. 23/02/1437104Norah Ali Al - moneef Slide 105 6-9 power 23/02/1437105Norah Ali Al - moneef Slide 106 Power Takes more power to run up the stairs than to walk up the stairs, but the energy consumed is the same in either case Unit is the WATT A Watt is a newton--meter per second Bigger units are kilowatts and megawatts Utility sells energy in kilowatt-hours 1 KWh = 1000 Joules/second times 3600 Seconds = 3.6 X 10 6 Joule 23/02/1437106Norah Ali Al - moneef Slide 107 23/02/1437107Norah Ali Al - moneef Slide 108 Killer whales are able to accelerate up to 30 mi/h in a matter of seconds. Disregarding the considerable drag force of water, calculate the average power a killer whale with mass 8000 kg would need to generate to reach a speed of 12.0 m/s in 6.00 s? Example: 23/02/1437108Norah Ali Al - moneef Slide 109 A 100-watt light bulb that is on 10-hours a day for 30 days. How much energy will it use? How much did it cost to operate that lamp if the price is $.09053 per kWh? example 10 hours per day x 10 days = 300 hours (energy is all about time of operation) 300 Hours x 100 Watts = 30,000 watt hours (energy is also about connected load or Watts) A kilowatt (kW) is 1000 watts 30,000 watt hours 1000 watts = 30 kilowatt hours (kWh as on the electric bill 30 kWh x $.09053 per kWh = $2.72 cost of operation 23/02/1437109Norah Ali Al - moneef Slide 110 A 1000-kg elevator carries a maximum load of 800 kg. A constant frictional force of 4000 N retards its motion upward. What minimum power must the motor deliver to lift the fully loaded elevator at a constant speed of 3 m/s? Power Delivered by an Elevator Motor M= 1000+800=1800 Kg where M = total mass of the system Since the speed is constant, so a = 0 23/02/1437110Norah Ali Al - moneef Slide 111 example OR 23/02/1437111Norah Ali Al - moneef Slide 112 A 5 Kg Cart is pushed by a 30 N force against friction for a distance of 10m in 5 seconds. Determine the Power needed to move the cart. example 23/02/1437112Norah Ali Al - moneef Slide 113 In a rifle barrel, a 15.0 g bullet is accelerated from rest to a speed of 780 m/s. a)Find the work that is done on the bullet.? example Using Work-Kinetic Energy Theorem, W = KE W = KE f - KE i W = 1/2(0.015 kg)(780 m/s) 2 - 0 W = 4.56 kJ b) If the rifle barrel is 72.0 cm long, find the magnitude of the average total force that acted on the bullet. Using W = Fcosd, F = (4.56 kJ) / (0.72 m) F = 6.33 kN 23/02/1437113Norah Ali Al - moneef Slide 114 The minimum work required to raise a 800 N person up 10 m, is: Example : W = F d W = (800 N) (10 m) = 8000 J If this work is done in 60 sec, then what is the power? 23/02/1437114Norah Ali Al - moneef Slide 115 example 23/02/1437115Norah Ali Al - moneef m/s F k= A car of mass 500 kg is traveling along a horizontal road.the engine of the car is working at a constant rate of 5kw.the total Resistance to motion is constant and is 250 N. What is the acceleration of the car when its speed is 5 m/s Slide 116 example 23/02/1437116Norah Ali Al - moneef Slide 117 23/02/1437117Norah Ali Al - moneef Slide 118 Summary of Chapter 6 Work: Kinetic energy is energy of motion: Work-energy principle: The net work done on an object equals the change in its kinetic energy. Conservative force: work depends only on end points Gravitational potential energy: U grav = mg (h h 0 ). Total mechanical energy is the sum of kinetic and potential energies. Additional types of energy are involved when nonconservative forces act. Total energy (including all forms) is conserved. Power: rate at which work is done, or energy is transformed: or k = - u K+u =k o +u o K+u =k o +u o + w a 23/02/1437118Norah Ali Al - moneef