Mechanical work from force and displacement (vector)¶

Work is measured result of force applied. Mechanical work is the only reason for the object energy to be changed. Work is a scalar value equal to the dot product of force and displacement vectors.

Notation:

\(\left( \vec a, \vec b \right)\) (dot(a, b)) is the dot product between vectors \(\vec a\) and \(\vec b\).

work¶: Mechanical work done by the force to displace the body.

Symbol:: W
Latex:: \(W\)
Dimension:: energy

force¶: Vector of force exerted on the body.

Symbol:: F
Latex:: \({\vec F}\)
Dimension:: force

displacement¶: Vector denoting the change of the position vector of the body when it moves from one point in space to another. Also see distance.

Symbol:: s
Latex:: \({\vec s}\)
Dimension:: length

law¶

W = dot(F, s)

Latex:: \[W = \left( {\vec F}, {\vec s} \right)\]