Mechanical work is force times distance¶
Work is measured result of force applied. Mechanical work is the only reason for the object energy to be changed. Work is scalar value equal to force multiplied by distance.
Notes:
This law works even when the force vector \(\vec F\) and the displacement vector \(\vec s\) are not collinear or codirectional. In that case one should use the projection of \(\vec F\) onto \(\vec s\) as the force or the projection of \(\vec s\) on \(\vec F\) as the distance, due to the projection law. See the second note for reference.
\[ \begin{align}\begin{aligned}W = \left( \vec F, \vec s \right) = \left( \vec F, \frac{\vec s}{\left \Vert \vec s \right \Vert} \right) \left \Vert \vec s \right \Vert = F_s s\\W = \left( \vec F, \vec s \right) = \left( \frac{\vec F}{\left \Vert \vec F \right \Vert}, \vec s \right) \left \Vert \vec F \right \Vert = F s_F\end{aligned}\end{align} \]
Use the vector form of this law for non-collinear vectors of force and movement.
Conditions:
The force and displacement vectors are collinear and codirectional.
Links:
- Symbol:
W- Latex:
\(W\)
- Dimension:
energy
- Symbol:
F- Latex:
\(F\)
- Dimension:
force
- Symbol:
s- Latex:
\(s\)
- Dimension:
length
- law¶
W = F * s- Latex:
- \[W = F s\]