kinetic friction

Question

Kinetic friction does negative work because it:

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Work done $W$ by a force $\vec{F}$ is $W = \vec{F} \cdot \vec{d} = F d \cos \phi$, where $\phi$ 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 $\phi = 180^\circ$, 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.

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