2 MachineMakes doing work easier by changing direction of applied force or amount of applied forceSimple machines have no or few moving parts and no engineSimple machines can be combined to form complex machinesSome terms:Wo=output work.Wo is always less than WiWi=input workWi is always more than Wo
3 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 loadWheel and axle: wheel and axle attachedInclined plane family:Inclined plane: rampWedge: 2 inclined planes forming a wedgeScrew: inclined plane wound around a cylinder
6 Mechanical AdvantageRatio of the force needed to do the work to the force the machine uses on the loadSome terms:Effort force= Fe: The force exerted by the person using the machineResistance force=Fr: The force exerted by the machine on the loadMechanical advantage (MA) MA= Fr/Fe
7 Ideal Mechanical Advantage Uses the definition of Work to describe mechanical advantageIdeal mechanical advantage is equal to the displacement of the effort force divided by the displacement of the loadIMA = de/dr
8 Efficiency Compares input work to output work Eff = Wo/Wi x 100 (given as a percent)All real machines have efficiency less than 100%Because Wo/Wi = Frdr/FedeAnd Fr/Fe=MA and de/dr=IMASo Eff = MA x IMA
9 Sample ProblemYou 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?
10 What is the IMA of the wheel and gear? What you know:de (for a wheel, this is radius) = 4 cmdr = 35.6 cmWhat equation will you use?IMA=de/drSubstituteIMA=4 cm/35.6 cmSolve and check for units0.112 (no units for MA or IMA)
11 What is the MA of the wheel and gear? What you knowIMA = 0.112Eff = 0.95Fe = 155 NWrite the equationWe don't know Fr, so use Eff = MA/IMARe-write as MA = (Eff)(IMA)SubstituteMA = (0.95)(0.112)Solve and check unitsMA = (no units)
12 What is the reistance force? What you knowMA =Fe = 155 NEquationMA = Fr/FeSo Fr = (MA)(Fe)SubstituteFr= (0.1067)(155 N)Solve and check unitsFr = 16.5 N
13 How far was the chain pulled to move the rim 14 cm? What we knowdr = 14 cmIMA = 0.112What equationIMA = de/drSo de = (IMA)(dr)Substitutede = (0.112)(14 cm)Solve and check unitsde = cm
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