WORK & ENERGY Another Way to Look at Motion

What’s so Great About Energy? It’s a scalar; forget those vector headaches It’s a scalar; forget those vector headaches It’s useful in all of physics and in other sciences It’s useful in all of physics and in other sciences It’s conserved, meaning the total amount of it doesn’t change It’s conserved, meaning the total amount of it doesn’t change

Work The product of the magnitude of displacement times the component of force parallel to displacement The product of the magnitude of displacement times the component of force parallel to displacement W = Fd W = Fd F d

Work (more precisely) The product of the magnitude of displacement times the component of force parallel to displacement The product of the magnitude of displacement times the component of force parallel to displacement W = F p d cos cos cos W = F p d cos  cos    cos    F d 

Units of Work and Energy SI unit – newton-meter = joule SI unit – newton-meter = joule 1 J = 1 n –m (kg m/s 2 ·m) 1 J = 1 n –m (kg m/s 2 ·m) Obsolete units you might run across: Obsolete units you might run across: –In cgs system unit is erg = dyne-cm (spring scales) –In British system ft-lb (torque wrench) –1 J = 10 7 ergs = ft-lb

Who Does More Work? A weightlifter holding up 200Kg A weightlifter holding up 200Kg (Force, no displacement) (Force, no displacement) A baby lifting a feather (Small force, some displacement)

Who Does More Work? A weightlifter holding up 200Kg A weightlifter holding up 200Kg (Force, no displacement) (Force, no displacement) No Work! No Work! A baby lifting a feather (Small force, some displacement) Some work

Work or no work? Lifting force is up, but displacement is horizontal; therefore…… No work is done

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 20 Kg crate is pulled 50m horizontally by a 100N force W = Fd = 100N x 50m = 5000Joules W = Fd = 100N x 50m = 5000Joules F = 100N mg FNFN

Work to Climb a Mountain How much work is 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 10 5 J Work = force x distance

Work Done By Sun on Earth How much is there? How much is there? v FGFG

ENERGY The ability to do work (an imperfect definition) The ability to do work (an imperfect definition) Many types exist: potential, kinetic, heat, electrical, magnetic, nuclear Many types exist: potential, kinetic, heat, electrical, magnetic, nuclear They can change from one to another They can change from one to another The sum of all of them (total energy)is conserved The sum of all of them (total energy)is conserved

Energy Conversion Example What form of energy comes into the projector? What form of energy comes into the projector? What forms are produced? What forms are produced? Answer: electrical Answer: light, heat, sound, kinetic, magnetic

Common Forms of Energy Kinetic – energy of motion Kinetic – energy of motion Potential – energy of position 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 In any process total energy is neither decreased nor increased It can change from one form to another It can change from one form to another It can be transferred from one body to another, but It can be transferred from one body to another, but IT CAN NOT BE CREATED NOR DESTROYED IT CAN NOT BE CREATED NOR DESTROYED

Kinetic Energy Energy of Motion Energy of Motion Translational and rotational Translational and rotational KE = ½ m v 2 KE = ½ m v 2

Derivation of ½ mv 2 Consider a mass accelerated uniformly from rest to velocity v Consider a mass accelerated uniformly from rest to velocity v Work done = W = F x d Work done = W = F x d F = ma F = ma W = mad W = mad v 2 = v ad; v 2 = v ad; W = m d (v 2 – v 0 2 )/2d W = m d (v 2 – v 0 2 )/2d = ½ mv 2 (v 0 = 0) a = (v 2 – v 0 2 )/2d

Examples Find the kinetic energy of a 70kg person walking at 1.0 m/s? Find the kinetic energy of a 70kg person walking at 1.0 m/s? KE = 1/2mv 2 = 35kg x (1m/s) 2 = 35J KE = 1/2mv 2 = 35kg x (1m/s) 2 = 35J Find the kinetic energy of a 0.01kg bullet traveling at 1000m/s Find the kinetic energy of a 0.01kg bullet traveling at 1000m/s KE = 1/2mv 2 = 0.5 x 0.01 x (1000m/s) 2 KE = 1/2mv 2 = 0.5 x 0.01 x (1000m/s) 2 KE = 5000J KE = 5000J

Work-Energy Principle The net work done on an object equals the change in its kinetic energy The net work done on an object equals the change in its kinetic energy W net =  KE W net =  KE Work that increases KE is positive Work that increases KE is positive Work that decreases KE is negative Work that decreases KE is negative

How Much Work? Is needed to give a car of mass 1000kg a speed of 10 m/s? Is needed to give a car of mass 1000kg a speed of 10 m/s? W = Kinetic Energy gained W = Kinetic Energy gained W= ½ mv 2 W= ½ mv 2 W = 0.5 x 1000kg x (10m/s) 2 W = 0.5 x 1000kg x (10m/s) 2 W = 50,000J W = 50,000J

How Much Work… is required to accelerate a 1000Kg car from 30 to 40 m/s? is required to accelerate a 1000Kg car from 30 to 40 m/s? Use W = 1/2mv /2mv 1 2 Use W = 1/2mv /2mv 1 2 Answer: 3.5 x 10 5 joules Answer: 3.5 x 10 5 joules

Gravitational Potential Energy An object held high has the potential to do work An object held high has the potential to do work PE grav = mgy PE grav = mgy Reference level of zero PE is arbitrary Reference level of zero PE is arbitrary

How Much PE? How much PE does a 100kg crate get when raised 100m? How much PE does a 100kg crate get when raised 100m? PE = mgh use g = 10 N/kg PE = mgh use g = 10 N/kg PE = 100kg x 10N/kg x 100m PE = 100kg x 10N/kg x 100m PE = 100,000 J PE = 100,000 J PE = 1.0 x 10 5 J PE = 1.0 x 10 5 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? 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 PE lost = KE gained mgh = ½ mv 2 mgh = ½ mv 2 2gh = v 2 2gh = v 2 v = (2gh) 1/2 v = (2gh) 1/2 v = (2 x 10 x 40) 1/2 = (800) 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 In any process total energy is neither decreased nor increased It can change from one form to another It can change from one form to another It can be transferred from one body to another, but It can be transferred from one body to another, but IT CAN NOT BE CREATED NOR DESTROYED IT CAN NOT BE CREATED NOR DESTROYED

Conservation of Mechanical Energy In absence of friction or other non- conservative forces In absence of friction or other non- conservative forces KE + PE = constant KE + PE = constant

Simple Machines Machines that make work easier by increasing force or increasing distance 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 Lever Inclined Plane Inclined Plane Screw Screw Gear Gear Wheel and Axle Wheel and Axle Pulley Pulley

Lever See saw See saw Pry bar Pry bar Screw driver used to pry Screw driver used to pry Fork, pencil Fork, pencil Paint brush Paint brush Which of these increase force? Which of these increase force? Courtesy simplemachines

Inclined Plane Ramp Ramp Knife Knife Road up hill Road up hill Screwdriver pushed in Screwdriver pushed in Courtesy / acctocar.html

Screw Inclined plane wrapped around a cylinder Inclined plane wrapped around a cylinder Courtesy view_activity.cgi?activity_id=6528 Q: Is a screwdriver an example of a screw?

Gear Wheel with teeth that mesh Wheel with teeth that mesh Changes speeds Changes speeds Increases or decreases force Increases or decreases force Used in auto and marine transmissions Used in auto and marine transmissions

Wheel and Axle A lever wrapped in a circle A lever wrapped in a circle Axle is normally fixed to wheel Axle is normally fixed to wheel

Pulley Axle turns freely Axle turns freely Types: Types: –Single fixed –Single moveable –One fixed one moveable –Block and tackle Courtesy 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 In absence of friction the work you put into a simple machine equals the work that comes out F in D in = F out D out F in D in = F out D out F out / F in = D in / D out F out / F in = D in / D out Illustrates the trade-off between force and distance Illustrates the trade-off between force and distance You can’t get “something for nothing without violating conservation of energy You can’t get “something for nothing without violating conservation of energy

Mechanical Advantage F out / F in is called “mechanical advantage,” actual mechanical advantage(AMA) to be exact. F out / F in is called “mechanical advantage,” actual mechanical advantage(AMA) to be exact. D in / D out is called ideal mechanical advantage (IMA) D in / D out is called ideal mechanical advantage (IMA) In a real machine AMA is always less than IMA because of friction 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 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 Machines that increase distance and decrease force have mechanical advantage less than one –Example – paint brush

Efficiency AMA =  x IMA AMA =  x IMA  is called efficiency  is called efficiency All machines have an efficiency less than one so as not to violate? 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? 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 pulley system has an ideal mechanical advantage of 2. –(a) What effort force will be required to lift 500N? –(b) if the efficiency is only 80%, would more force be required or less? 250 N more

Review Why can’t a simple machine have an efficiency greater than 1 (100%) ? 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 Many real machines are combinations of simple machines

Power The rate that work is done The rate that work is done P = work/time = Fd/time = Fv P = work/time = Fd/time = Fv Unit joules/sec = watt Unit joules/sec = watt 746 watts = 1 horsepower 746 watts = 1 horsepower

Power to Climb a Hill A 60 Kg student climbs a 100m high hill in three minutes. Find the student’s power in watts and horsepower. A 60 Kg student climbs a 100m high hill in three minutes. Find the student’s power in watts and horsepower. Answer 326w, 0.44hp

Power Needed by a Car A 1400 Kg car runs over level ground at 30m/s. If 1000N force is needed to keep it moving, what power is required (watts and HP) A 1400 Kg car runs over level ground at 30m/s. If 1000N force is needed to keep it moving, what power is required (watts and HP) P = Fv = P = Fv = 1000N x 30m/s = 30,000 watts= 1000N x 30m/s = 30,000 watts= 30,000w ÷ 746 w/HP = 40HP 30,000w ÷ 746 w/HP = 40HP