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Understanding Work and Machines in Physics

Learn about work, machines, mechanical advantage, and efficiency in physics. Calculate mechanical advantage and efficiency. Explore real and ideal machines, as well as compound machines.

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Understanding Work and Machines in Physics

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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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