Some of the content of this guide was modeled after a guide published by OpenStax and has been adapted for the NWP Learning Commons in March 2022. This work is licensed under a Creative Commons BY 4.0 International License.
Work
Work is the change of kinetic energy on a particle by all forces that act on it. In this section, we will review a constant force being exerted on a body and resulting in a displacement of that body as work. The physicist's definition of work is based on these observations.
Consider a body that undergoes a displacement of magnitude \(r\) along a straight line. While the body moves, a constant force \(\vec{\textbf{F}}\) acts on it in the same direction as the displacement \(\vec{\textbf{r}}\). We define the work \(W\) done by this constant force under these circumstances as the dot product of the force \(\vec{\textbf{F}}\) and the displacement \(\vec{\textbf{r}}\). $$dW=\vec{\textbf{F}}\cdot{d}\vec{\textbf{r}}$$ $$\Delta{W}={F_x}\,\Delta{x}+{F_y}\,\Delta{y}+{F_z}\,\Delta{z}$$
How much work was done on the box to move it from point \(A\) to point \(B\)?
$$\vec{\textbf{F}}_a=100N=100N*cos(45)\hat{\textbf{i}}-100N*sin(45)\hat{\textbf{j}}$$
$$\Delta{W}={F_x}\,\Delta{x}+{F_y}\,\Delta{y}$$
$$\Delta{W}=100N*cos(45)\,\Delta{x}-100N*sin(45)\,\Delta{y}$$
$$\Delta{x}={x_2}-{x_1}=10m-0m=10m,\qquad\Delta{y}=0$$
$$\Delta{W}=100N*cos(45)*10m-100N*sin(45)*0$$
$$\Delta{W}=1,000*cos(45)J$$
$$\Delta{W}=707.1J$$
The work done on the box to move it from point \(A\) to point \(B\) is \(707J\).