Difference between revisions of "Work"
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| − | In [[physics]], '''work''' refers to the [[dot 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> | ||
| − | + | <math>W = \vec{F} \cdot \vec{d}</math> | |
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| − | <math> | ||
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Or: | Or: | ||
| − | <math> | + | <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 | + | 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>. |
When the force is not constant, the correct expression uses [[integration]]: | When the force is not constant, the correct expression uses [[integration]]: | ||
| − | <math>\int \ | + | <math>\int \vec{F} \cdot \mathrm{d}\vec{s}</math> |
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| − | Work is a transfer of [[energy]]; if | + | 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. |
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. | 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:Mechanics]] | [[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]
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 (read "a dot b") can be rewritten as .
When the force is not constant, the correct expression uses integration:
Work is a transfer of energy; if is positive, there is a transfer of energy to the system, and if 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