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kinetic energy
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K=12mv2
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joule.
SI unit for work and energy
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1N⋅m=1J
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200 |
watt.
SI unit for power
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1W=1Js
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200 |
horsepower.
Unit of power in British engineering system
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1hp=746W
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200 |
kilowatt hour.
Common unit of energy
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1kWh=3.60MJ
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work done by constant force
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W=F⋅d=Fdcosθ
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work done by constant force in direction of displacement
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W=Fd, where θ=0
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work done by constant force in direction opposite displacement
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W=−Fd, where θ=180∘
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work done by force that varies with position.
E.g. conservative forces like gravity or a spring.
Note, Fx is the component of F along the
x-axis and the force at position x???
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Wx=∫xfxiFxdx, where Fx=Fcosθ
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work-kinetic energy theorem
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Wx=∫xfxiFxdx=∫xfximvdv=12mv2f−12mv2i=Tf−Ti=ΔT
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work done by friction
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Wk=−fkd
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net work with friction and other forces
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∑W=Wother−fkd
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work done by a spring
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Ws=∫xfxi−kxdx=12kx2i−12 kx2f=Ki−Kf=−ΔK
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work done by a force applied to a spring (pull or push)
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Wapp,s=−Ws=∫xfxikxdx=12kx2f−12kx2i=Kf−Ki=ΔK
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power
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P=dWdt=F⋅dsdt=F⋅v
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