Work

Work is when energy is applied or expended to move an object. To change an object’s velocity, (and therefore it’s acceleration), Newton’s First Law states that a force must be applied to that object. Hence work is done when a force acts on an object and makes it move. Work done and energy are interrelated, work done can be thought of as movement energy.

Definition §

Formula - 1 §

Work from Force

W = \vec{F} \cdot \vec{x} = Fx \cos(\theta)

Formula - 2 §

Work from Energy in a System

$$W_{body}=\Delta K_{body}=-\Delta U_{sys}$$

$$\sum W_{body}=W_{net}=\Delta K_{sys}=-\Delta U_{sys}$$

Terms §

• $W$ = Work Done (in Joules, $J$)
  • $W_{body}$ = Work applied onto a body in a system
  • $W_{sys}$ = Work applied onto the system as a whole
• $F$ = Force (in Newtons, $N$)
• $x$ = Displacement vector (in metres, $m$)
• $\theta$ = Angle between direction and force

I.e. if the force is parallel to the distance, the work done is just the product. ($W=Fx$)