Work (physics)

In physics, mechanical work is the amount of energy transferred by a force acting through a distance in the direction of the force. Like energy, it is a scalar quantity, with SI units of joules. The term work was first coined in 1826 by the French mathematician Gaspard-Gustave Coriolis.^[1][2]
According to the work-energy theorem, if one or more external forces act upon a rigid object, causing its kinetic energy to change from E_k1 to E_k2, then the mechanical work (W) done by the net force is equal to the change in kinetic energy. For translational motion, the theorem can be specified as:^[3]

where m is the mass of the object and v is the object's velocity.
If a force F that is constant with respect to time acts on an object while the object is displaced in a straight line along the length and direction of a vector d, the mechanical work done by the force on the object is the dot product of the vectors F and d:^[4]

If the force and the displacement are parallel and in the same direction (θ = 0), the mechanical work is positive. If the force and the displacement are parallel but in opposite directions (i.e. antiparallel, θ = 180⁰), the mechanical work is negative. If a force F is applied at an angle θ, only the component of the force in the same direction as the displacement (Fcosθ) does work. Thus, if the force acts perpendicular to the displacement (θ = 90⁰ or 270⁰), zero work is done by the force.^[4]