Work

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In physics, work refers to the dot product of force and distance vectors [1].


W = \bold{F} \cdot \bold{d}


Or:

W = Fdcosθ


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:

\int \bold{F} \cdot \mathrm{d}\bold{s}


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

  1. Serway and Beichner, Physics for Scientists and Engineers, Fifth Edition
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