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| − | In [[physics]], work refers to the product of [[force]] and [[distance]] vectors | + | In [[physics]], '''work''' refers to the [[dot 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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| − | ''W'' = F · d
| + | <math>W = \vec{F} \cdot \vec{d}</math> |
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| | Or: | | Or: |
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| − | ''W'' = F d Cosθ
| + | <math>W = Fd \cos{\theta}</math> |
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| − | Where θ is the angle that separates the vectors. | + | 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 <math>\vec{a} \cdot \vec{b}</math> (read "a dot b") can be rewritten as <math>|\vec{a}| |\vec{b}| \cos{\theta}</math>. |
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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.
| + | When the force is not constant, the correct expression uses [[integration]]: |
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| − | Its units are that of force multiplied by distance, in SI this is [[newton (unit)|Newton]] · [[Meter]], or [[Joule]] | + | <math>\int \vec{F} \cdot \mathrm{d}\vec{s}</math> |
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| | + | Work is a transfer of [[energy]]; if <math>W</math> is positive, there is a transfer of energy ''to'' the system, and if <math>W</math> 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]]. 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== |
| | <references/> | | <references/> |
| − | [[category:physics]] | + | [[Category:Physics]] |
| | + | [[Category:Mechanics]] |