# wkep - and energy have units of Joules The theorem can then...

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Work, kinetic energy and power Suppose the net force that acts on a particle of mass m is F. In general, this force will do work on the particle W net if the particle undergoes a displacement. If the particle has a velocity v 1 when the force begins to act and velocity v 2 when the force stops acting then we will prove in class based on Newton’s second law, W net = ½ m v 2 2 – ½ m v 1 2 . Proof From this proof we see that this equation is derived from the definition of work and Newton’s second law , i.e. it is simply a restatement of Newton’s second law. The above formula goes by the title the work-energy theorem . It is clear that the effect of the net work is to produce a change in the speed of the particle. We call the quantity ½ m v 2 kinetic energy (Greek for motion energy).

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The net work produces motion energy—energy comes from doing work, and later we will show work can come from energy. Work
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Unformatted text preview: and energy have units of Joules. The theorem can then be restated succinctly W net = ∆ K WORK-ENERGY THEOREM Absent from the analysis up to this point is the time it takes for the force to do this work. The force delivers work but it takes time to deliver the work. We say the faster the force delivers the work the more powerful the force. That is, if a force delivers an amount of work, ∆ W, in a time interval, ∆ t, we define the (average) power of this force as P ave ≡ ∆ W/ ∆ t . Taking the limit as ∆ t → 0 converts the average to the instantaneous power, P ≡ dW/dt . Using dW ≡ F ⋅ dr gives another way of finding P, P = F ⋅ v , where the “dot” product appears once again. The units for power are Watts (1Watt ≡ 1Joule/1second). Examples[in class]...
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wkep - and energy have units of Joules The theorem can then...

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