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Chapter 4: Machines, Work, and Energy “Reserve your right to think, for even to think wrongly is better than not to think at all.” HYPATIA, Natural Philosopher (355? - 415 CE) She taught mathematics and natural philosophy. She is credited with the authorship of three major treatises on geometry and algebra and one on astronomy. 2 4.1 Work and Power • Define work in terms of force and distance and in terms of energy. • Calculate the work done when moving an object. • Explain the relationship between work and power. 3 Reviewing the Definition of Work • We say work is done on an object when a force acts to move that object in the direction of the force. • Work done on an object transfers energy to that object. • An object (or system) with energy has the ability to do work. • Work, like energy, is measured in Joules (J). 4 Work and Energy • When a force does work on an object, it could: – Increase the kinetic energy of the object (make it speed up) – Increase the potential energy of the object (so the object gains the ability to do work on something else later – Or, if friction is involved, perhaps just heat up the surroundings. • Remember only forces acting in the direction of motion will do work. Force A does no work Force B does some work Force C does the most work 5 Work Done Against Gravity • The work done while lifting an object against gravity is equal to its change in potential energy of the object. • This is true whether you lift the object straight up or use a (frictionless) ramp and lift it diagonally. 6 Power • Power is the rate at which work is done. • The quicker work is being done (or energy transferred) the more power used. • The metric unit for power is the Watt which is equal to one joule per second (1 horsepower = 746 watts). Michael and Jim do the same amount of work but Michael is more powerful! 7 Power • How much energy does a typical light bulb give off in 1 second? 10 seconds? 1 minute? • The maximum power output of a person is typically around a few hundred watts. • Highly trained athletes can keep up a power of 350 watts for about an hour. 60 Joules in 1 second 600 Joules in 10 seconds 3600 Joules in 1 minute Calculate this amount of energy and compare to lifting an average person in the air! 8 4.2 Simple Machines • Describe how a machine works in terms of input and output. • Define simple machines and name some examples. • Calculate the mechanical advantage of a simple machine given the input and output force. 9 Simple Machines • Below are some examples of simple machines. Most of these machines were known in ancient times. • Simple machines are “force multipliers” – they allow you to exert a small “input” force and get a larger “output” force? For free? • Many modern machines are combinations of simple machines – the textbook cites bicycles and VCRs. 10 Mechanical Advantage • The ratio of the “output” force to the “input” force is called the mechanical advantage. • Generally simple machines have a MA > 1; that’s why we use them, we can exert a smaller “input” force and get a larger “output” force! • Usually the “output” force is just the weight of the object we are trying to move. 11 Work and Machines • A simple machine has no source of energy except the immediate forces you apply. That means the only way to get output work from a simple machine is to do input work on the machine. • The output work of a machine can never be greater than the input work. So how do we get a larger output force? What is the trade off? 12 Work and Machines • The force and distance are related by the amount of work done. Remember W = Fd. • You can exert less force only if you do so over a longer distance. That is the trade off! • This pulley ideally has a Mechanical Advantage of 2. 13 Mechanical Advantage of Pulleys The Mechanical Advantage of a pulley will simply be the number of strands of rope directly supporting the weight (load). 14 Block and Tackle • A block and tackle is a system of two or more pulleys with a rope threaded between them. • What is the mechanical advantage of the block and tackle shown to the right? • If you wanted to lift a 600 lbs crate onto the boat, how much force would you need to exert? • If you needed to lift the crate 5 feet off the ground, how much rope would you have to pull in? MA = 6, 100 lbs, 30 feet Count the number of strands 15 Mechanical Advantage of Ramps • If the mechanical advantage is 10, how much input force do you have to exert to pull the 500 N cart up the ramp? • Instead of just lifting the cart 1 meter off the ground (this is want you want to accomplish after all), what distance do you have to exert the input force? 1/10th of the force: 50 N, but… 10 times the distance, 10 m! Less force, but… More distance – that is the tradeoff 16 Levers • • • Levers rotate about a pivot point called a fulcrum. There are three classes of levers discussed in the textbook. An example of each diagram below would be: (1) a see-saw, (2) a wheelbarrow, (3) the human arm. What class of lever is Archimedes using? “Give me a place to stand and with a lever I will move the whole world.” - Archimedes (c. 287 BC – c. 212 BC) 17 Mechanical Advantage of Levers • What is the mechanical advantage of the lever shown if the input force “effect” is applied 5 feet from the fulcrum, while the load is 1 foot from the fulcrum? • How much work, in ftlbs, do you input into the machine? • How much work does the machine output? 18 Screws and Gears • Gears: When you force a larger “input” gear, the smaller “output” gear’s speed will be increased, but not it’s force. • Archimedes' screw is a machine historically used for transferring water from a low-lying body of water into irrigation ditches. 19 4.3 Work, Energy, and Efficiency • Describe the relationship between work and energy in a simple machine. • Use energy conservation to calculate input or output force or distance. • Explain why a machine’s input and output work can differ. 20 Efficiency • No machine is 100% perfectly efficient. Some of the input work is lost to useless energy, such as heat, or wear & tear on the parts. • Bicycles may be up to 95% efficient, but automobiles are about 15% - most of the chemical energy stored in the gasoline goes into overcoming frictional forces of all kinds! 21 Efficiency • If the input work = the output work, the machine is 100% efficient, but generally which is greater? The input work • The efficiency can be calculated using the following equation: Output _ Work Efficiency 100% Input _ Work How efficient is the 8 foot long ramp, if the man pushes the 200 lbs dresser 2 feet off the ground with 62.5 lbs of force? 22 Time’s Arrow • Systems tend to go from a more organized state to a less organized state. • For example the Kinetic Energy of a moving bullet is more “organized” than the random motion and heat generated after the bullet hits an apple. • An irreversible process, one that is less than 100% efficient, is what we encounter in nature. Nature seems to have a direction in time! • What do some say is the ultimate fate of the universe? A heat death! 23 How a sandcastle reveals the end of all things http://www.youtube.com/watch?v=uQSoaiubuA0 24 Chapter 4 Review 1) What is the usual purpose of a simple machine? 2) What is the tradeoff to using less force? 3) In what way is a machine subject to the law of energy conservation? Is it possible for a machine to produce more output work compared to the the input work? 25 26