Difference between revisions of "Work"
(change to magnitudes in second equation) |
(add magnitude signs; perhaps I should texify this paragraph...) |
||
| Line 14: | Line 14: | ||
<br> | <br> | ||
| − | 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". | + | 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". |
When the force is not constant, the correct expression uses [[integration]]: | When the force is not constant, the correct expression uses [[integration]]: | ||
Revision as of 02:39, June 8, 2012
In physics, work refers to the dot product of force and distance vectors [1].
<math>\bold{W} = \bold{F} \cdot \bold{d}</math>
Or:
<math>\bold{W} = Fd \cos\theta</math>
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".
When the force is not constant, the correct expression uses integration:
<math>\int \bold{F} \cdot \mathrm{d}\bold{s}</math>
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.
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