Work

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

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:

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 = Fd \cos{\theta}}

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 ${\vec {a}}\cdot {\vec {b}}$ (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:

$\int {\vec {F}}\cdot \mathrm {d} {\vec {s}}$

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.