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Work, Power and Machines Warm Up • How would you define work and energy? Do these words have the same meaning in science and in everyday speech? • What different types of energy do you know about? PSc. 3.1.3 • Explain scenarios in which work is done, identifying the force, displacement, and energy transfer. • Compare scenarios in which work is done and conceptually explain the differences in magnitude of work done using the relationship W=f x d Energy THERMAL The ability to cause change. internal motion of particles MECHANICAL NUCLEAR ENERGY motion of objects changes in the nucleus ELECTRICAL CHEMICAL bonding of atoms joules (J) motion of electric charges Energy • Kinetic Energy (KE) • energy in the form of motion • depends on mass and velocity • Which has the most KE? 80 km/h truck • Which has the least KE? 50 km/h motorcycle 80 km/h 50 km/h 80 km/h Energy • Potential Energy (PE) • stored energy • depends on position or configuration of an object • Which boulder has greater gravitational PE? • What other ways can an object store energy? Work It’s not what you think! Work is a transfer of energy to a body by the application of a force that causes the body to move in the direction of the force. Huh? Work is using a force to change the position of an object. Work Work is Force times distance where Force is the force acting on the object (could be applied force, could be gravitational force) and distance is how far the object moved. W = F•d Units of work are Joules (J). Examples • A crane operator uses an average force of 5200N to lift a girder 25m. How much work does the crane do on the girder? • Given: F = 5200N d = 25m W=? W = F•d W = 5200N x 25m W = 130,000J Examples • An apple weighing 1N falls a distance of 1m. How much work is done on the apple by the force of gravity? Given: Fg = 1N d = 1m W=? W = Fg•d W = 1N x 1m W = 1J Examples • The brakes of a bicycle apply 125N of frictional force to the wheels as the bicycle travels 14m. How much work have the brakes done on the bike? Given: F = 125N d = 14m W = F•d W = 125N x 14m W = 1750J Examples • A mechanic uses a hydraulic lift to raise a 1200kg car 0.5m off the ground. How much work does the lift do on the car? Given: m = 1200kg d = 0.5m W=? W = F•d but… we have a mass, not a force. So, we go back to Fg = mg (g = 9.8m/s/s) F = 1200kg x 9.8m/s/s = 11,760N Now, W = 11,760N x 0.5m = 5880J Warm up • A father is playing with his baby by lifting her into the air repeatedly. How much work does he do with each lift, assuming he lifts her 2m and exerts an average force of 190N? How much work does he do when he holds her and walks her to her crib? PSc.3.1.4 • Infer the Work-Power relationship: P = W = FΔd = F x vave Power • You have to mow 30 lawns in a month. You can mow 6 lawns per day and be done in 5 days or you can mow one lawn per day and take all 30 days to finish. What is analogous to the total number of lawns mowed? Work What is analogous to the rate of mowing? Power Power • Power is the rate at which work is done. QuickLab: What is your power output when climbing the stairs? Question: Running up a flight of stairs takes the same amount of work as slowly walking up a flight of stairs. Why is it more tiring? Power • Power = Work = W time t Units: Watts (W) or commonly kW (1kW = 1000W) 1W is the amount of power required to do 1J of work in 1 second. Example • It takes 100kJ of work to lift an elevator 18m. If this is done in 20s, what is the average power of the elevator during this process? Given: W = 100kJ d = 18 m t = 20s 100kJ x 1000J = 100,000J 1kJ P = Work = 100,000J = 5000W time 20s 5000W x 1kW = 5kW 1000W Power • You may be familiar with horsepower as a measure of power. This originally referred to the average output of a draft horse. 1hp = 746W Power • While rowing across the lake in a race, John does 3960J of work on the oars in 60s. What is the power output in watts? Given: W = 3960J t = 60s P = W = 3960 = 66W t 60s Problems • Suppose you are moving a 300N box of books. Calculate your power output if… a. You exert a force of 60N to push the box across the floor 12m in 20s. b. You lift the box 1m onto a truck in 3s. For a. W = Fxd = 60N x 12m = 720J P = W/t = 720J/20s = 36W For b. W = Fxd = 300N x 1m = 300J P = W/t = 300J x 3s = 900W Problems • A student lifts a 12N textbook 1.5m on 1.5s and carries the book 5m across the room in 7s. a. How much work does the student do on the book? W = Fxd = 12N x 1.5m = 18J to lift the book Note: No work is done to carry the book across the room because the force on the book (vertical) is in a different direction than the applied force (horizontal). b. What is the power output of the student? P = W/t = 18J/1.5s = 12W Problems • Compare the work and power used in the following situations: a. A 43N force is exerted through a distance of 2.0m over a time of 3s. b. A 43N force is exerted through a distance of 3m over a time of 2s. Problems (cont.) a. Given: F = 43N d = 2m t = 3s W = F x d = 43N x 2m = 86J P = W/t = 86J/3s = 29W b. Given: F = 43N d = 3m t = 2s W = F x d = 43N x 3m = 129J P = W/t = 129J/2s = 65W Energy transformation • http://youtu.be/i6e-KrNCe_E C. Conservation of Energy • Law of Conservation of Energy • Energy may change forms, but it cannot be created or destroyed under ordinary conditions. • EX: • PE KE • mechanical thermal • chemical thermal C. Conservation of Energy PE KE Conservation of Energy Check Your Understanding Energy Includes includes Is the ability to do can be a. which measures b. Kinetic energy transformed c. Which is energy Associated with which is energy of but never acting over a e. distance position d. or destroyed Warm Up 1. A force of 15N is used to push a box along the floor a distance of 3m. How much work was done? 2. What is the power of a kitchen blender if it can perform 3,750J of work in 15s? Warm Up Answers 1. Given: F = 15N d = 3m W = F x d W = 15N x 3m = 45J 2. Given: W = 3,750J t = 15s P = W/t P = 3,750J/15s = 250W PSc. 3.1.4 • Determine the component simple machines present in complex machines • Define and determine Ideal Mechanical Advantage • Define and determine the efficiency of machines • Explain why no machine can be 100% efficient Machines and Mechanical Advantage • Changing a car tire – the jack lets you lift a car you otherwise couldn’t lift • Machines redistribute work – they can change the direction of the input force or they can increase or decrease a force by changing the distance. (W = F x d) Machines and Mechanical Advantage • Work with and without a machine: You lift a 225N box 1m onto the back of a truck. W = F x d = 225N x 1m = 225J You push the box up a 3m ramp with 75N of force. W = F x d = 75N x 3m = 225J Same amount of work, but the machine (inclined plane) lets you exert much less force. Machines and Mechanical Advantage • Mechanical advantage tells how much the machine multiplies the force or increases the distance traveled. • Mechanical advantage is the ratio between the output force and the input force or the input distance and the output distance. • AMA = output force IMA = input distance input force output distance Machines & Mechanical Advantage In the example of lifting a 225N box 1m on to the back of a truck by itself and with a 3m ramp using 75N of force, determine the input and output distances and forces. With ramp: Without ramp: Input F = 75N Input F = 225N Input d = 3m Input d = 1m Output F = 225N Output F = 225N Output d = 1m Output d = 1m Machines and Mechanical Advantage • No machine can increase force and distance at the same time: W=fxd if one increases the other must decrease. (See example above) • Said another way, you can’t get more work out of a machine than you put into it. • Machines don’t increase the amount of work being done; they make the work easier to do. Problems • A mover uses a pulley system with a mechanical advantage of 10.0 to lift a piano 3.5m. Disregarding friction, how far must the mover pull the rope? MA = input dist output dist 10.0 = input dist/3.5m Input dist = 10.0 x 3.5m = 35m Problems • A person pushes a 950N box up an incline. If the person exerts a force of 350N along the incline, what is the mechanical advantage of the incline? • MA = output force = 950N = 2.7 input force 350N What are the units of mechanical advantage? None, it is a ratio. The units cancel out. Problems 1. Calculate the MA of a ramp that is 6m long and 1.5m high. 2. A sailor uses a rope and pulley to lift a 140N sail. The sailor pulls down with a force of 140N on the rope. What is the MA of the pulley? 3. Alex pulls on the handle of a claw hammer with a force of 15N. If the hammer has a MA of 5.2, how much force is exerted on the nail in the claw? 4. A rower pulls an oar back a distance of 0.8m on each stroke. If the oar has a MA of 1.5, how far does the blade of the oar move through the water on each stroke? 1. MA = input dist/output dist = 6.0m/1.5m = 4.0 2. MA = output force/input force = 140N/140N = 1 3. Output force = MA x input force = 5.2 x 15N = 78N 4. Output dist = input dist/MA = 0.8m/1.5 = 0.53m Warm Up 1. Put your phones in your backpacks and get out your notes and a pencil. 2. Write the term with its correct definition. Then write its equation and its units. 1. Work 2. Power 3. Mechanical advantage a. The amount that a machine multiplies a force or a distance b. The rate at which work is done c. What is done when a force makes an object move Simple Machines 6 types of simple machines classified in 2 groups: The Lever Family The Inclined Plane Family Simple lever Simple inclined plane Wheel & Axle Wedge Pulley Screw The Lever Family 1st Class Lever Fulcrum is between points of application of input and output forces. Fulcrum – point on which the lever balances Input Force – the force you apply to the lever (effort) Output Force – the force the lever exerts on the object (load) Ex: claw hammer, teeter totter The Lever Family 2nd Class Lever Fulcrum is at one end of the arm and input force is applied to the other end. Ex: wheelbarrow – wheel is fulcrum nutcrackers hinged doors The Lever Family 3rd Class Levers Multiply distance rather than force. Ex: many in human body – bicep contracts a small distance and the hand moves a large distance Which is the bicep? Which is the hand? Which is the fulcrum? The Lever Family • 1st Class Levers – can either multiply force OR increase distance (not both) claw hammer • 2nd Class Lever – always multiplies force hinged door • 3rd Class Lever – always increases distance broom The Lever Family Pulleys Ex: flag pole, sail on boat Can have different set ups of fixed and free pulleys that change the input force required. Pulleys Lifting a 150N weight with a single fixed pulley, the weight must be fully supported by the rope on each side of the pulley. (MA=1) Mechanical Advantage in pulley systems is found by counting the number of weight supporting ropes. Input Force = 150N Output Force = 150N Pulleys Output force = 150N Input force = 75N The 150N force is shared by two sections of rope both pulling upward. (MA=2) Pulleys All of the sections of rope pull up against the downward force of the weight. This gives it an even larger mechanical advantage. (MA=3) Input force = 50N Output force = 150N The Inclined Plane Family Simple Inclined Plane – multiplies and redirects the force. Output force Input force The output force is the force needed to lift the box straight up to the top of the ramp. The inclined plane spreads that force out over a longer distance so it takes less input force to do the same amount of work. The Inclined Plane Family Wedge • modified inclined plane • acts like two inclined planes back-to-back Input Force • takes 1 downward force and turns it into 2 forces directed out and towards the sides Output Forces The Inclined Plane Family Screw • Inclined plane wrapped around a cylinder • Small force acting over large distance • Ex: jar lids, spiral staircase The Inclined Plane Family Ex: The Great Pyramid at Giza was built by ancient Egyptians as tombs for their royalty. It is made up of over 2 million blocks of stone. The largest is 15 tons. The average stone weighs 2.5 tons. The pyramid is 140M high. Q: How did they get these stones onto the pyramid? (2.5 tons = 22,000N) Giza Problem cont’d Given: ave. Weight = 2.5 tons = 22,000N height = 140m W = F•d W = 22,000N x 140m W = 3,100,000J (3.1MJ) so it takes 3.1MJ of work to lift one block of stone to the top of the pyramid. The Inclined Plane Family If they used ramps with MA = 3, the average block could be lifted by 7300N. If one person can pull with an input force of 525N, how many people did it take to pull an average block up a ramp? Given: MA = 3 Input force = 525N/1 person Output force = 7300N output force/input force 7300N = 14 people 525N/1person Compound Machines • A machine made of more than one simple machine • Ex: scissors = 2 1st class levers joined at a fulcrum • Ex: car jack = lever and screw • Q: ID all of the simple machines on a bicycle that you can. • A: brake = lever pedal = wheel & axle Efficiency of Machines Just like us, machine can be more or less efficient at what they do. The amount of work obtained from a machine is always less than the amount of work put into it. Machines can lose work to friction. Efficiency is calculated as: Work output x 100% Work input Engineers’ jobs are to design machines that are as close to 100% efficient as possible. Efficiency of Machines Try this: A man expends 100J of work to move a box up an inclined plane. The amount of work produced is 80J. What is the efficiency of the inclined plane? Eff = work output/work input x 100% Eff = 80J/100J x 100% Eff = 0.8 x 100% Eff = 80% Note that efficiency does not have units. The units cancel out in the calculation and you wind up with just a percent. Review List the 2 families of simple machines and the types of simple machines that belong in each family. Then describe what a compound machine is. Quiz 1. List 6 types of simple machines. 2. Identify the kind of simple machine: 1. A drill bit 2. Skateboard ramp 3. Boat oar 3. Describe how a lever can increase force without changing the amount of work being done. 4. Choose a compound machine you use everyday and identify the simple machines it contains. Draw a sketch.