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| − | In [[physics]], '''work''' refers to the product of [[force]] and [[distance]] vectors | + | In [[physics]], '''work''' refers to the [[scalar product]] of [[force]] and [[distance]] vectors |
| | <ref>Serway and Beichner, ''Physics for Scientists and Engineers'', Fifth Edition</ref>. | | <ref>Serway and Beichner, ''Physics for Scientists and Engineers'', Fifth Edition</ref>. |
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| | <br> | | <br> |
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| − | Or, its integral form: | + | Or: |
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| − | <math>\int \bold{F} \cdot \mathrm{d}\bold{s}</math> | + | <math>\bold{W} = \bold{F} \cdot \bold{d} \cos\theta</math> |
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| | <br> | | <br> |
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| − | Or:
| + | Where θ is the angle that separates the vectors. The second form of the equation is the expanded form of the "dot product" in the first equation. In physics, the dot product "a · b" (read "a dot b") can be rewritten as "a b cos θ". |
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| | + | When the force is not constant, the correct expression uses [[integration]]: |
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| − | <math>\bold{W} = \bold{F} \cdot \bold{d} \cos\theta</math> | + | <math>\int \bold{F} \cdot \mathrm{d}\bold{s}</math> |
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| | <br> | | <br> |
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| − | Where θ is the angle that separates the vectors. The second form of the equation is the expanded form of the "dot product" in the first equation. In physics, the dot product "a · b" (read "a dot b") can be rewritten as "a b cos θ".
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| | Work is a transfer of [[energy]]; if ''W'' is positive, there is a transfer of energy ''to'' the system, and if ''W'' is negative there is a transfer of energy ''from'' the system. | | Work is a transfer of [[energy]]; if ''W'' is positive, there is a transfer of energy ''to'' the system, and if ''W'' is negative there is a transfer of energy ''from'' the system. |
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| − | Its units are that of force multiplied by distance, in SI this is [[newton (unit)|Newton]] · [[Meter]], or [[Joule]] | + | Its units are that of force multiplied by distance, in SI this is [[newton (unit)|Newton]] · [[Meter]], or [[Joule]]. The aberrant unit kWh (kilowatt-hour) is sometimes used; this unit is the product of kilowatt, or 1,000 Watts (Joules per second), and hour, or 3,600 seconds. |
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| | ==References== | | ==References== |