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Work, Energy and Power In text: Ch 5 Do you already know these words? • Work – • Energy – • Power – Looking a little deeper at… Work • First a demo: • One volunteer • Hold a couple of books and walk across the room. • How much work was done to the book? • Any? A lot? A little? None? Looking a little deeper at… Work: • Is the product of the magnitude of the displacement and the component of the force acting in the direction of the displacement • Is the force applied over a distance • When a force acts upon an object to cause a displacement of the object • two key ingredients: • Force • displacement Looking a little deeper at… Work: • Everyday examples: • a horse pulling a plow through the field • a father pushing a grocery cart down the aisle of a grocery store • a weightlifter lifting a barbell above his head • Olympian launching the shot-put • Can you identify the three parts in each example? Looking a little deeper at… Work: • Are these examples of work? 1. A teacher applies a force to a wall and becomes exhausted. 2. A book falls off a table and free falls to the ground. 3. A waiter carries a tray full of meals above his head by one arm straight across the room at constant speed. 4. A rocket accelerates through space. Looking a little deeper at… Work: • Or… W = F d cosΘ • d is displacement or Δx • F is force applied • Θ is the angle between the force and the displacement vector Looking a little deeper at… Work: • Notice that the application of a force alone does not constitute work. • Work can only be done when looking at the force applied parallel to the displacement. • Most of the time F is in the direction of d so θ = 0° and cos 0° = 1 so… it all works out. Looking a little deeper at… Work: • Consider theta: • Three basic situations Looking a little deeper at… Work: • Consider theta: • Be careful!! • Pay attention to the direction of the displacement and the applied force. • Ex. A car being pushed up a ramp Looking a little deeper at… Work: • Consider “the sign”: • If force and displacement are in the… • Same directions, + W • Opposite directions, - W • Perpendicular directions, W = 0 See fig. 3 pg 162 Looking a little deeper at… Work: • Consider “the sign”: • Ex. car skidding to a stop on a roadway surface • Ex. a baseball runner sliding to a stop on the infield dirt Looking a little deeper at… Work • From all that we can say that the total work done is dependant on the total force applied. So…. • Wnet = Fnet d cosΘ • So, what are the units? • • • • If we break it down W=F*d ?=N*m J=N*m • Basic question: • What work is done to lift your Physics book (m=12kg) up 1 m? • What work is done to carry the book 1 m across the room? • Try this: What is the work done on a vacuum cleaner pulled 3m by a force of 50N at an angle of 30° above the horizontal? Working solution… • The angle of the force means we have to find the force acting in the direction that the bag moves. • It moves in the x-position, so we will use the Fx component • The upward component doesn’t do any work as the y-position doesn’t change. • Pg 162 Practice A A few more: • A 20kg suitcase is raised vertically 3m above a platform by a conveyor belt. How much work is done on the suitcase? • A 100 N force is applied to move a 15kg object a horizontal distance of 5m at constant speed. • A 100N force is applied at an angle of 30° to the horizontal to move a 15kg object at a constant speed for a horizontal distance of 5m. • An upward force is applied to lift a 15kg object to a height of 5m at constant speed. How ‘bout those angles: • How far did a flying shark pull a box if it exerted a force of 100N at an angle of 25°. It also did 1200J of work. • You are at the beach and notice somebody in trouble about 30m away from you. You throw a rope to them and pull them in to the beach at an angle of 15° above the horizontal. You did 7500J of work. What is the force you used? • You are pulling your little red wagon at an angle of 53.1° You pull it for a distance of 15m and do 90J of work. Answers: A.588J B.500J C.433J D.735J Energy – Flow Chart Energy Mechanical Kinetic Non-mechanical Potential Linear Rotational Gravitational Elastic Sound Heat Light Chemical Electric Looking a little deeper at… Energy • In general Energy is the ability to do work and create change. • We will look at two basic types of energy. • Kinetic • Potential • We will also look at the conservation of energy. Kinetic • Associated with objects in motion • Depends on both an objects speed and mass • It is a scalar quantity Kinetic • Kinetic energy = 1/2 *mass*speed2 • KE=1/2 mv2 • The unit of KE is joule(J) • If the speed is doubled the energy is quadrupled. Kinetic • A bowling ball and a volleyball roll at the same speed. • Which has more kinetic energy? Kinetic • A 7kg bowling ball moves at 3 m/s. How fast must a 2.45 g ping pong ball move to have the same kinetic energy as the bowling ball? • KE=1/2 mv2 Practice: • Determine the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s. • If the roller coaster car in the above problem were moving with twice the speed, then what would be its new kinetic energy? • Missy Diwater, the former platform diver for the Ringling Brother's Circus, had a kinetic energy of 12 000 J just prior to hitting the bucket of water. If Missy's mass is 40 kg, then what is her speed? • A 900-kg compact car moving at 60 mi/hr has approximately 320 000 Joules of kinetic energy. Estimate its new kinetic energy if it is moving at 30 mi/hr. (HINT: use the kinetic energy equation as a "guide to thinking.") Answers: A.105,000J B.419,000J C.24.5m/s D.80,000J Potential • Associated with an object that has the potential to move because of its position • Depends on the interaction with its environment • store energy as the result of its position Potential • Gravitational potential energy • Potential energy due to gravity • the energy stored in an object as the result of its vertical position or height. • PEg = mass*free-fall acceleration*height • PEg = mgh Potential • PEg = mgh • Notice that PEg is dependant on free-fall acceleration being constant. • Also notice that g and h aren’t properties of the actual object. Potential • PEg = mgh • The higher that an object is elevated, the greater the gravitational potential energy • a doubling of the height will result in a doubling of the gravitational potential energy Potential • Is it possible to have a negative potential energy? • Can an object have both a positive potential energy and a negative potential energy? Potential • How is h defined? • Relative to a “zero” • What can be a “zero”? • Anything can be defined as “zero” • Discussion: A ball that falls from one building rooftop to another buildings rooftop. Where is zero? Potential Springs!!! Potential Springs: • a device which can store elastic potential energy due to either compression or stretching • force is required to compress a spring • the amount of force is directly proportional to the amount of stretch or compression • Equilibrium position – when a spring isn’t being stretched or compressed Potential • Springs: • Fspring = k * x • k is the spring constant • x is the amount stretched or compressed Potential • Relaxed length • Length of spring when no external forces are acting on it. • Nothing is pulling or pushing it. • Spring Constant • Small for flexible springs • Large for stiff springs • Units of (N/m) • PEtotal = PEg + PEspring Potential • Elastic Potential energy • Stored in any compressed or stretched object • PEelastic = ½*spring constant*(distance compressed or stretched)2 • PEelastic = ½kx2 Practice: • Pg 166 practice B # 1-5 • Pg 172 practice D # 1-3 Practice: • A 70kg stuntman is attached to a bungee cord with an unstretched length of 15m. He jumps off a bridge spanning a river from a height of 50m. When he finally stops, the cord has a stretched length of 44m. Treat the stuntman as a point mass, and disregard the weight of the bungee cord. Assuming the spring constant of the bungee cord is 71.8N/m, what is the total potential energy relative to the water when the man stops falling? Practice: 1. Mr. B got a new fish tank. As he moves it he uses 200J of work. He pushes it with a force of 50N at an angle of 30°. How far did he push the tank? 2. The mass of the fish tank is 50kg. How fast did Mr. B push the tank? 3. Once the tank is set up the water has a height of 1.8m and a mass of 150kg. How much potential energy does the water have? 4. A mass is hung from a slinky it stretchs the slinky .4m. The slinky has a spring constant of .3N/m. How much potential energy does the spring have? Answers: A.13.2J B.13.2J C.34,300J Energy – Flow Chart Energy Mechanical Kinetic Non-mechanical Potential Linear Rotational Gravitational Elastic Sound Heat Light Chemical Electric HEAT AND TEMPERATURE Temperature • Temperature: A measure of how hot (or cold) something is • Specifically, a measure of the average kinetic energy of the particles in an object. Concept Check • What is the relationship between the temperature of a substance and the speed of its molecules? • High temperature = _____ KE (high or low)? Thermometers a. • Thermometer: an instrument that measures and indicates temperature b. c. Bimetallic strip Temperature Scales • Kelvin • International System (SI) of measurement • Fahrenheit • Celsius Kelvin and Absolute Zero • The Kelvin scale is based on absolute zero • Absolute Zero: the temp at which molecular movement stops • 0 K on the Kelvin scale = -273.16ºC What is heat? • Heat: the transfer of energy between objects that are at different temperatures. • All matter has heat. • Measured in JOULES Heating and Cooling • If an object has become hotter, it means that it has gained heat energy. • If an object cools down, it means it has lost energy Endothermic and Exothermic Processes • Endothermic Process – heat is absorbed from the surroundings • Endo = Into HEAT Endothermic and Exothermic Processes • Exothermic process – heat is released into the surroundings • Exo = Exit HEAT Heating and Cooling cont… • Heat energy always moves from: HOT object COOLER object ex1. Cup of water at 20 °C in a room at 30°C gains heat energy and heats up – its temperature rises ex2. Cup of water at 20 °C in a room at 10°C loses heat energy and cools down – its temperature will fall. ARE HEAT AND TEMP THE SAME THING? • NO….although the two quantities are related. Example: a beaker of water at 60 °C is hotter than a bath of water at 40 °C BUT the bath contains more joules of heat energy Review What is the difference between heat and temperature? • HEAT is energy that transfers from one object/substance to another • TEMPERATURE is a measure of the amount of energy an object/substance has (how quickly the molecules are moving around) Measuring Heat Flow Two Common Units • Joule • calorie 4.184 J = 1 cal 1Calorie = 1 kilocal = 1000 cal Concept Check • What causes heat to flow? Energy Transfer • The transfer of heat is normally from a high temperature object to a lower temperature object. 1) Conduction • Thermal Conduction: the transfer of heat within a substance, molecule by molecule. 2) Convection • Convection: the movement of matter due to the differences in density that are caused by temp. variations applet 3) Radiation • Radiation: the energy that is transferred as electromagnetic waves, Doesn’t need matter • Most radiation comes from the sun Conductor vs. Insulator • Conductor: any material through which energy can be transferred as heat • Insulator: poor conductors Energy Definition of Energy • The ability to do work • Potential energy is the energy of position • Kinetic energy is the energy of motion (depends on speed and mass) • Mechanical energy= Potential + Kinetic energy The Law of Conservation of Energy • States that energy can be neither created nor destroyed, it is conserved • Energy can transform from one form to another, but it always adds up to the same amount. Energy conversion • Mechanical energy is converted into thermal energy whenever you bounce a ball. Each time the ball hits the ground, some of the energy of the ball's motion is converted into heating up the ball, causing it to slow down at each bounce Forms of energy • Energy can neither be created nor destroyed, but it can be changed into different forms of energy… • This is energy transformation. • The forms include: thermal (heat), chemical, electrical, sound, light, nuclear Conservation of Energy • What does it mean to conserve something? • Think about: • Recycling • Money • H2O Lingo to Know • Mechanical Energy is: • the energy which is possessed by an object due to its motion or due to its position. • the total kinetic energy and potential energy associated with an object • ME = KE + PEtotal • Mechanical energy is just a classification, not another type of energy. Lingo to Know • Nonmechanical energy: • Other forms of energy • Ex. light, sound, heat Conservation of Energy With that said: • Mechanical energy is conserved (in the absence of friction) • So => initial mechanical energy = final mechanical energy So => MEi = MEf So => KEi + Ptotal,i = KEf + Petotal,f Conservation of Energy This is famed snowboarder Mr. Williams! Notice his ME is constant the entire time. Conservation of Energy • The question is if a 75g egg falls off a 1m counter top what is it’s total ME half way down? • To better understand lets remember a few things. • First Vf = Vi + aΔt • Second Δx = ½ (Vi + Vf)Δt Conservation of Energy • Lets make a chart:75g egg/1m Time 0s .1s .2s .3s .4s Vf KE Δx Height PE ME Law of Conservation of Energy • Energy can neither be created nor destroyed • Energy is always changing from one kind to another. • The total energy of an object never changes. Conservation of Energy • Mechanical energy is not conserved in the presence of Kinetic friction. So what happens to the energy? • Ex rubbing your hands together • Total energy is always conserved, but mechanical energy is lost. • Mechanical energy is converted in to… Conservation of Energy • Now can you answer this basic question: If an object (m=10kg) falls from a height of 10 m, what is it’s: • Potential and kinetic energy at the top • Potential and kinetic energy just before hitting the ground. Practice: • Starting from rest, a child zooms down a frictionless slide from an initial height of 3m. What is her speed at the bottom of the slide? Assume she has a mass of 25kg Practice: • A frog is sitting on a rock. It sees a cat that is trying to eat it. The frog jumps directly up with an initial velocity of .85m/s. What is the total height the frog jumps? • The cat then jumps directly upward 1.2m. What was the initial velocity of the cat’s jump? POWER!!! • What is power!! • Tim “the tool man” Taylor knows what power is, right??? • Not quite POWER!!! • Lets look at: • a rock climber takes 30min. to elevate his body up a few meters along the side of a cliff. POWER!!! • Lets look at: • a trail hiker, who selects the easier path up the mountain, might elevate his body a few meters in 10min. POWER!!! • They both do the same amount of work. • Which one had more power? POWER!!! • is the rate at which work is done • or the rate at which energy is consumed • P = W/t So…. • The more power you have the more work you can do in the same time. • The more power you have you can do the same amount of work in a shorter time. • There is an inverse relationship between work and power How did we get there? Remember: P = W/t Quick review: what is work? • W = Fd Quick review: what is velocity? • v = Δx/Δt or v = d/t • So P = F (d/t) • Or P = F v POWER!!! • P=Fv • This equation shows us that a powerful machine is both strong (big force) and fast (big velocity). • Ex. A powerful car engine is strong and fast. That was a lot to take in • Equations for power are: • • • • P = W/t P = F (d/t) P=Fv P = ΔE/t W E Fd P F av e a t t t What units?? The SI unit of power is the watt. • 1 watt is = 1 joule / second • W=J/s What units?? Horsepower is also a unit. • 1 horsepower = 746 watts • Hp = 746W Examples of power • • • • A dim light bulb 40 W A really bright bulb 500 W Indoor Christmas light .7 W Outdoor Christmas light 7 W Examples situation • A 193kg curtain needs to be raised 7.5m, in 5s. You have 3 motors with power ratings 1.0kW, 3.5kW and 5.5kW. Which motor is best for the job? • How much time would it take for each motor to do the same amount of work? Examples situation • Two horses pull a cart. Each exerts a force of 250.0 N at a speed of 2.0 m/s for 10.0 min. • 1) What is the power delivered by the horses? • 2) How much work is done by the two horses? Practice: • Two physics students, Will N. Andable and Ben Pumpiniron, are in the weightlifting room. Will lifts the 100-pound barbell over his head 10 times in one minute; Ben lifts the 100-pound barbell over his head 10 times in 10 seconds. Which student does the most work? Which student delivers the most power? • During a physics lab, Jack and Jill ran up a hill. Jack is twice as massive as Jill; yet Jill ascends the same distance in half the time. Who did the most work? Who delivered the most power? (plug in fake numbers) • When doing a chin-up, a physics student lifts her 42.0-kg body a distance of 0.25 meters in 2 seconds. What is the power delivered by the student's biceps? • Mr. B gets bored after school one day and decides to play in the hall. He sits in his rolling chair and pushes off the wall with 12N of force producing 30W of power. What was his resulting speed he traveled down the hallway? Answers: A.1