mechanical advantage & efficiency. advantage of machines machines help us do tasks; they give...
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![Page 1: Mechanical Advantage & Efficiency. advantage of machines machines help us do tasks; they give us an advantage example: a lever can be used to lift](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649e355503460f94b23732/html5/thumbnails/1.jpg)
Mechanical Advantage & Efficiency
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advantage of machines
machines help us do tasks; they give us an advantage
example: a lever can be used to lift a load
if the load is 36N and we only apply 12N of force to lift it, then we can figure out the advantage of the lever
ie: (36N/12N = 3 X greater)
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mechanical advantage
there are 2 ways to look at this advantage:
1.actual mechanical advantage (AMA) ratio of load force to effort force (FL/FE)
2.ideal mechanical advantage (IMA) ratio of effort arm to load arm (dE/dL)
most machines involve friction, so AMA<IMA
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typical IMAs
Machine IMA Ratio Equation
wheel & axle ratio of radii rE/rL
set of gears ratio of teeth count NE/NL
set of pulleys count # of support strands
see page 88 fig. 2(count strands that
pull up)
inclined plane ratio of incline length and height
length of incline/height
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practice
In an acrobatic demonstration, one person jumps onto the end of a plank (lever). This creates a large effort force of 920 N at the end of the board at a distance of 1.7 m from the fulcrum. A smaller person (460 N) located 3.1 m from the fulcrum, is launched into the air. Calculate:
(a) the AMA of the board
(b) the IMA of the board
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NOTICE
since AMA and IMA are calculated ratios they have no units!!!
(units cancel out)
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static and moving components
when a machine is in static equilibrium, the law of the lever applies, so:
dE/dL = FL/FE
and the IMA equals the AMA
when the components of the machine move, the effort force increases to account for friction, so:
dE/dL > FL/FE
and the IMA is greater than the AMA
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force advantage (AMA)
can be greater than 1, equal to 1, or less than 1
IF THEN AND
FL/FE = 1 FL = FE dL = dE
FL/FE > 1 FL > FE dL < dE
FL/FE < 1 FL < FE dL > dE
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efficiency
the efficiency of a machine tells us how productive it is
percent efficiency is the ratio of actual mechanical advantage to ideal mechanical advantage as a percentage
% efficiency = AMA x 100 IMA
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practice
Calculate the percent efficiency in each of the following:
(a) the distance ratio of a lever is 3.6 and the force ratio is 3.1
(b) the AMA of a wheel and axle is 6.0 and the IMA is 7.0