Work

#teaching #physics #energywork

Summary

Work is a measurement of the amount of energy transferred when a force moves an object

Key Equations:

General work equation:
$W = \int_{r}^{r_{f}} F (r) \cdot d x$

If force is non-constant:
$W = F \cdot Δ x$

Read Time

⏱ 2 mins

Definition

Work is a scalar and measures the amount of energy transferred when a force moves an object a distance. Mathematically, it's defined as the integral of force dotted with displacement.

\begin{matrix} W = \int_{a}^{b} \vec{F} \cdot \vec{d x} \\ If force is constant: \\ W = \vec{F} \cdot Δ x = \vec{F} Δ x \cos (θ) \end{matrix}

Note

There is a dot product between the force and displacement because only the component in the direction of displacement contributes to the work done.

Physically, this makes. Imagine pushing a box at an upward angle, the force done upward won't contribute to pushing the box forward (in the direction of displacement)

Work Diagram

!wor_1.png
^[1]
Only the force in the same direction of displacement contributes to work. The perpendicular force will not contribute to a change in motion in the direct of displacement.

Taken from https://tikz.net/energy_work/ by Izaak Neutelings (September 2020) ↩︎