Difference between revisions of "Work"
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| − | In [[physics]], the | + | 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> |
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| + | <math>W = \vec{F} \cdot \vec{d}</math> | ||
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| + | Or: | ||
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| + | <math>W = Fd \cos{\theta}</math> | ||
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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 <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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| + | When the force is not constant, the correct expression uses [[integration]]: | ||
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| + | <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. | ||
==References== | ==References== | ||
<references/> | <references/> | ||
| − | [[ | + | [[Category:Physics]] |
| + | [[Category:Mechanics]] | ||
Latest revision as of 10:51, October 23, 2026
In physics, work refers to the dot product of force and distance vectors.[1]
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle W = \vec{F} \cdot \vec{d}}
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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{a} \cdot \vec{b}} (read "a dot b") can be rewritten as Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |\vec{a}| |\vec{b}| \cos{\theta}} .
When the force is not constant, the correct expression uses integration:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int \vec{F} \cdot \mathrm{d}\vec{s}}
Work is a transfer of energy; if Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle W} is positive, there is a transfer of energy to the system, and if Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle W} is negative there is a transfer of energy from the system.
Its units are that of force multiplied by distance, in SI this is 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.
References
- ↑ Serway and Beichner, Physics for Scientists and Engineers, Fifth Edition