Work done $W$ by a force $\vec{F}$ is $W=\vec{F}\cdot \vec{d}=Fd\cos \varphi$, where $\varphi$ is the angle between force and displacement.

• Kinetic friction $f_k$ always acts in a direction opposite to the relative motion (slipping) of the surfaces.
• Therefore, the angle $\varphi =180^{\circ }$, and $\cos 180^{\circ }=-1$.
• $W=f_{k}d(-1)=-f_{k}d$, which is negative. Negative work means energy is being removed from the system, typically appearing as heat.