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WORK AND ENERGY Another Way to Look at Motion The most important concept in science! What’s so Great About Energy? It’s a scalar; forget those vector headaches It’s useful in all of physics and in other sciences It’s conserved, meaning the total amount of it doesn’t change What is energy? Difficult to define precisely. Exists in many different forms Work The product of the magnitude of displacement times the component of force parallel to displacement W = Fd F d Work(more precisely) The product of the magnitude of displacement times the component of force parallel to displacement W = Fpd cos q F q d Units of Work and Energy SI unit – newton-meter = joule 1 J = 1 n –m Obsolete units you might run across: – In cgs system unit is erg = dyne-cm – In British system ft-lb – 1 J = 107 ergs = 0.7376 ft-lb Who Does More Work? A weightlifter holding up 200Kg A baby lifting a feather (Force, no displacement) (Small force, some displacement) Who Does More Work? A weightlifter holding up 200Kg A baby lifting a feather (Force, no displacement) No Work! (Small force, some displacement) Some work Work or no work? Lifting force is up, but displacement is horizontal; therefore…… No work is done on refrigerator Work or No Work A mass circles at constant speed, held by a string Force is along string, toward center Force is perpendicular to motion Therefore, no work is done Calculate the work 20 Kg crate is pulled 50m horizontally by a 100N force W = Fd = 100N x 50m = 5000Joules FN F = 100N mg Work to Climb a Mountain Work = force x distance How much work is required for a 70 Kg person to climb 1000 m up a peak? Hint: use F = mg Answer : 6.86 x 105 J Only up component of displacement contributes Work Done By Sun on Earth How much is there? NONE! FG v ENERGY The ability to do work (an imperfect definition) Many types exist: mechanical (potential, kinetic), heat, light, electrical, magnetic, nuclear They can change from one to another The sum of all of them (total energy)is conserved Energy Conversion Example What form of energy comes into the projector? Answer: electrical What forms are produced? Answer: light, heat, sound, kinetic, magnetic Common Forms of Energy Mechanical Kinetic – energy of motion Potential – energy of position A pendulum converts energy back and forth from potential to kinetic. Law of Conservation of Energy In any process total energy is neither decreased nor increased It can change from one form to another It can be transferred from one body to another, but IT CAN NOT BE CREATED NOR DESTROYED Kinetic Energy Energy of Motion Translational and rotational TRANSLATIONAL: KE = ½ m v2 Derivation of ½ mv2 Consider a mass accelerated uniformly from rest to velocity v Work done = W = F x d F = ma W = mad a = (v2 – v02)/2d v2 = v02 + 2ad; W = m d (v2 – v02)/2d = ½ mv2 (v0 = 0) Derivation of ½ mv2 Consider a mass accelerated uniformly from rest to velocity v Work done = W = F x d F = ma W = mad a = (v2 – v02)/2d v2 = v02 + 2ad; W = m d (v2 – v02)/2d = ½ mv2 (v0 = 0) Examples Find the kinetic energy of a 70 kg person walking at 1.0 m/s. KE = 1/2mv2 = 35kg x (1m/s)2 = 35J Find the kinetic energy of a 0.01 kg bullet traveling at 1000 m/s. KE = 1/2mv2 = 0.5 x 0.01 x (1000m/s)2 KE = 5000J Why is it so dangerous to get shot? Bullet deposits lots of energy in small area What about momentum (mv)? Find momentum of man 70 kg m/s Find momentum of bullet 10 kg m/s Why is a comet or asteroid crash on Earth so dangerous? Find the kinetic energy of a 1014 Kg asteroid whose speed is 50 km/sec. KE = ½ mv2 = 0.5 x 1014 x (5 x 104 m/s)2 = 12.5 x 1022 J = 1.25 x 1023 J Work-Energy Principle The net work done on an object equals the change in its kinetic energy Wnet = DKE Work that increases KE is positive Work that decreases KE is negative How Much Work? Is needed to give a car of mass 1000kg a speed of 10 m/s? W = Kinetic Energy gained W= ½ mv2 W = 0.5 x 1000kg x (10m/s)2 W = 50,000 J = 5 x 104 J Force Required What average force is needed to do this if the distance is 100m? W=FxD F = W/D = KE/D = 50,000 / 100 = 500N How Much Work… is required to accelerate a 1000Kg car from 30 to 40 m/s? Use W = 1/2mv22 - 1/2mv12 Answer: 3.5 x 105 joules Gravitational Potential Energy An object held high has the potential to do work PEgrav = mgy Reference level of zero PE is arbitrary How Much PE? How much PE does a 100kg crate get when raised 100m? PE = mgh use g = 10 N/kg PE = 100kg x 10N/kg x 100m PE = 100,000 J PE = 1.0 x 105 J Roller Coaster What speed will a frictionless roller coaster have at the bottom of a 40m high hill assuming zero speed at the top of the hill? PE lost = KE gained mgh = ½ mv2 2gh = v2 v = (2gh)1/2 v = (2 x 10 x 40)1/2 = (800)1/2 Answer v = 28 m/s Law of Conservation of Energy In any process total energy is neither decreased nor increased It can change from one form to another It can be transferred from one body to another, but IT CAN NOT BE CREATED NOR DESTROYED Conservation of Mechanical Energy In absence of friction or other nonconservative forces KE + PE = constant Conservative Force Work done does not depend on path taken Potential energy can be defined Example: lifting an object against gravity Non Conservative or Dissipative Force Work done depends on path No potential energy function can be defined Example: pushing an object against friction W = Fd = mFNd = mmgd Power The rate that work is done P = work/time = Fd/time = Fv Unit joules/sec = watt 746 watts = 1 horsepower Power The rate that work is done P = work/time = Fd/time = Fv Unit joules/sec = watt 746 watts = 1 horsepower Simple Machines Machines that make work easier by increasing force or increasing distance All simple machines trade force for distance; they can’t increase both Examples of Simple Machines Lever Inclined Plane Screw Gear Wheel and Axle Pulley Lever See saw Pry bar Screw driver used to pry Fork, pencil Paint brush Which of these increase force? Courtesy www.lkwdpl.org/schools/elempath/ simplemachines Inclined Plane Ramp Knife Road up hill Screwdriver pushed in Courtesy www.disabled.driverinfo.btinternet.co.uk / acctocar.html Screw Inclined plane wrapped around a cylinder Q: Is a screwdriver an example of a screw? Courtesy www.uen.org/.../ view_activity.cgi?activity_id=6528 Gear Wheel with teeth that mesh Changes speeds Increases or decreases force Used in auto and marine transmissions Wheel and Axle A lever wrapped in a circle Axle is normally fixed to wheel Pulley Axle turns freely Types: – Single fixed – Single moveable – One fixed one moveable – Block and tackle Courtesy www.conductortrain.com/.../apprentice/ skills/doc9.shtml Work In = Work Out In absence of friction the work you put into a simple machine equals the work that comes out Fin Din = Fout Dout Fout/ Fin = Din/ Dout Illustrates the trade-off between force and distance You can’t get “something for nothing without violating conservation of energy Mechanical Advantage Fout/ Fin is called “mechanical advantage,” actual mechanical advantage(AMA) to be exact. Din/ Dout is called ideal mechanical advantage (IMA) In a real machine AMA is always less than IMA because of friction Small and Large Mechanical Advantage Machines that increase force greatly are said to have large mechanical advantage – Example – pry bar Machines that increase distance and decrease force have mechanical advantage less than one – Example – paint brush Efficiency AMA = e x IMA e is called efficiency All machines have an efficiency less than one so as not to violate? Energy Conservation! Lever Example A certain lever lifts a weight of 20N with an effort force of only 5N. Assuming ideal efficiency, over what distance will the effort force act to lift the weight by 0.1 meter? Answer: 0.4m Pulley Example A pulley system has an ideal mechanical advantage of 2. – (a) What effort force will be required to lift 500N? 250 N – (b) if the efficiency is only 80%, would more force be required or less? more Review Why can’t a simple machine have an efficiency greater than 1 (100%) ? It would violate the law of conservation of energy. Compound Machines Many real machines are combinations of simple machines