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Work & Energy 2

Work & Energy 2. Chapter 8. Review. Work is the amount of energy transferred by mechanical means. W = Fd Work is measured in Joules. Machines. A machine is something that eases the load by either changing the magnitude or the direction of the force.

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Work & Energy 2

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  1. Work & Energy 2 Chapter 8

  2. Review • Work is the amount of energy transferred by mechanical means. • W = Fd • Work is measured in Joules

  3. Machines • A machine is something that eases the load by either changing the magnitude or the direction of the force. • It does not change the amount of work done.

  4. Machines • The force you exert on a machine is called the effort force.

  5. Machines • The force exerted by the machine is called the resistance force.

  6. Machines • The ratio of resistance force to effort force: Fr / Fe is called the mechanical advantage. MA = Fr / Fe

  7. Machines • When the mechanical advantage is greater than one, the machine increases the force you apply.

  8. Mechanical Advantage • We can calculate the mechanical advantage of a machine using the definition of work. • The input work is the product of the effort force you exert (Fe) and the displacement of your hand (de). • The output work is the product of the resistance force (Fr) and the displacement caused by the machine (dr).

  9. Mechanical Advantage • Therefore : • Wo = Wi • Or Frdr = Fede

  10. Mechanical Advantage • In a real machine, not all of the input work is available as output work. • The efficiency of a machine is defined as the ratio of output work to input work.

  11. Mechanical Advantage • MA = Fr/Fe

  12. Efficiency • Efficiency = (Wo / Wi ) x 100% • An ideal machine has equal output and input work and the efficiency is 100% • All real machines have efficiencies of less than 100%

  13. Ideal Mechanical Advantage • The ideal mechanical advantage of most machines is fixed by the machine’s design. • An efficient machine has an mechanical advantage almost equal to the ideal.

  14. Efficiency • A less efficient machine has a smaller mechanical advantage. • Lower efficiency means that a greater effort force is needed to exert the same resistance force.

  15. Ideal Mechanical Advantage • IMA = de/dr

  16. Example • A student uses a bicycle wheel with gear radius 4.00cm and wheel radius 35.6cm. When a force of 155N is exerted on the chain, the wheel rim moves 14.0cm. • Due to friction, its efficiency is 95%.

  17. Example • What is the IMA of the wheel and gear? • What is the MA of the wheel and gear? • What force does a scale attached to the the wheel read? • How far did the student pull the chain?

  18. Example • What is the IMA of the wheel and gear? • IMA = de/dr • de = gear radius • dr = wheel radius • IMA = 4/35.6 = 0.112

  19. Example • What is the MA of the wheel and gear? • Since efficiency = MA/IMA x 100% • MA = eff x IMA/100% • MA = (95% x 0.112)/100% • MA = 0.107

  20. Example • What force does a scale attached to the wheel read? • MA = Fr/Fe • Fr = (MA)(Fe) • Fr = (0.107)(155) = 16.6N

  21. Example • How far did the student pull the chain? • IMA = de/dr • de = (IMA)(dr) • de = (0.112)(14.0) • de = 1.57cm

  22. Simple Machines • Lever • Pulley • Wheel and axle • Inclined plane • Wedge • Screw

  23. Compound Machines • A compound machine consists of two or more simple machines linked so that the resistance force of one machine becomes the effort force of the second.

  24. Machines • What does a machine do for us? • A machine can change the direction of the force required. • It can increase the amount of force required or the velocity, but not both at once.

  25. Machines • What does a machine NOT do for us? • A machine does not put out more energy than we put into it. • In fact, the amount of energy put out is always less than the amount of energy put in.

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