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Simple Machines And Efficiency Physics Chapter 10d

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Machine Makes doing work easier by changing direction of applied force or amount of applied force Simple machines have no or few moving parts and no engine Simple machines can be combined to form complex machines Some terms: W o =output work. W o is always less than W i W i =input work W i is always more than W o

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Simple Machines There are six basic simple machines: Lever family: Lever: a long pole or rod that moves around a fixed point (fulcrum) Pulley: grooved wheel with a rope or chain attached to the load Wheel and axle: wheel and axle attached Inclined plane family: Inclined plane: ramp Wedge: 2 inclined planes forming a wedge Screw: inclined plane wound around a cylinder

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InventorsToolbox: The Elements of Machines

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Types of Simple Machines machines/ machines/

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Mechanical Advantage Ratio of the force needed to do the work to the force the machine uses on the load Some terms: Effort force= Fe: The force exerted by the person using the machine Resistance force=Fr: The force exerted by the machine on the load Mechanical advantage (MA) MA= Fr/Fe

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Ideal Mechanical Advantage Uses the definition of Work to describe mechanical advantage Ideal mechanical advantage is equal to the displacement of the effort force divided by the displacement of the load IMA = de/dr

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Efficiency Compares input work to output work Eff = W o /W i x 100 (given as a percent) All real machines have efficiency less than 100% Because W o /W i = F r d r /F e d e And F r /F e =MA and d e /d r =IMA So Eff = MA x 100 IMA

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Sample Problem You examine the rear wheel of a bicycle. It has a radius of 35.6 cm and has a gear with a radius of 4 cm. When the chain is pulled with a force of 155 N, the wheel rim moves 14 cm.The efficiency of this part of the bicycle is 95%. What is the IMA of the wheel and gear? What is the MA of the wheel and gear? What is the reistance force? How far was the chain pulled to move the rim 14 cm?

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What is the IMA of the wheel and gear? What you know: de (for a wheel, this is radius) = 4 cm dr = 35.6 cm What equation will you use? IMA=de/dr Substitute IMA=4 cm/35.6 cm Solve and check for units (no units for MA or IMA)

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What is the MA of the wheel and gear? What you know IMA = Eff = 0.95 Fe = 155 N Write the equation We don't know Fr, so use Eff = MA/IMA Re-write as MA = (Eff)(IMA) Substitute MA = (0.95)(0.112) Solve and check units MA = (no units)

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What is the reistance force? What you know MA = Fe = 155 N Equation MA = Fr/Fe So Fr = (MA)(Fe) Substitute Fr= (0.1067)(155 N) Solve and check units Fr = 16.5 N

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How far was the chain pulled to move the rim 14 cm? What we know dr = 14 cm IMA = What equation IMA = de/dr So de = (IMA)(dr) Substitute de = (0.112)(14 cm) Solve and check units de = cm

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