WEBVTT
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This is College Physics Answers
with Shaun Dychko.
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This pulley system is a hoist
for a car engine
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that has a mass of 115 kilograms
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and we can see that the mechanical
advantage is 2
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because the tension force that's
being applied here
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is being exerted twice upwards
on this engine
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and so there's one tension applied and that's
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being multiplied by 2 in the end
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and so that's where the mechanical
advantage comes from.
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Okay!
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So mechanical advantage is defined as
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the output force divided by the input force
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and the input force is the tension in
the rope
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and the output force is the total force
on this bottom pulley
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so this is the output force
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and that's gonna be equal to
the weight of the engine.
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So we substitute *mg* in place of *F o*
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and *T* in place of *F i*
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and then our job is to solve for *T*;
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we want to know the tension in the rope.
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So we multiply both sides by *T* over
mechanical advantage
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so *T* is *mg* over *MA*.
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So that's 115 kilograms times
9.80 newtons per kilogram
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divided by 2 which is 564 newtons.
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In part (b), we are asked, what is the force
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applied by the ceiling upwards
on this whole assembly?
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We can see that there's one force upwards
in total on this assembly
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and there are two forces downwards:
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there's gravity downwards on the engine
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and then there's this applied force...
this tension downwards as well
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and so those two are added together down
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and they have to together equal
the force upwards on the ceiling.
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So that's 563.5 newtonsâ€”tensionâ€”
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plus 115 kilograms times
9.8 newtons per kilogram
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which is 1690 newtons in total exerted by
the ceiling upwards
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on the whole assembly.