Work

• $W=\vec{F}\cdot \vec{d}=Fd\cos (\theta )$

  • $W$ is the work done by the force $\vec{F}$ over the distance $\vec{d}$
  • $\vec{F}$ is the force vector acting on the object
  • $\vec{d}$ is the distance vector
  • $F$ and $d$ are their magnitudes
  • $\theta$ is the angle between the force vector and the distance vector
  • Work is the dot product of the force and distance vectors

• $W={\int }_{x_1}^{x_2}F(x)dx$ (Work = Integral of Force with respect to distance)

  • $F(x)$ is the force acting on the object as a function of distance $x$
  • $dx$ is an infinitesimally small distance.
  • $x_1$ and $x_2$ are the initial and final positions of the object, respectively.
  • $W$ is the work done by the force $F(x)$ over the distance $x_1$ to $x_2$.