= Load dependence of kinetic friction
{title2=$|f_k|=\mu_kN$}
Changing the added <mass> while retaining the same contact pair and sliding <speed> tests whether a constant <coefficient of kinetic friction> is a useful model. Compute $N=(m_{\mathrm{block}}+m_{\mathrm{added}})g$ for each level horizontal run, and plot the mean sliding <force> vertically against <normal force> horizontally. The constant-coefficient prediction is a straight line through the origin; its <slope> is $\mu_k$. This extracts a ratio from several loads rather than relying on one reading.
\Image[/kinetic-friction-load-model-and-apparatus.png]
{title=Horizontal wooden-block force-probe apparatus and original load model: 19.6 N and 39.2 N normal loads predict 5.88 N and 11.76 N sliding forces}
The apparatus sketch identifies the contact pair and horizontal pull used by the cited laboratory procedure. The plotted line and points are the original stipulated $\mu_k=0.30$ model from <coefficient of kinetic friction>, not laboratory data. The two model points give
$$
\frac{\Delta |f_k|}{\Delta N}=\frac{11.76-5.88}{39.2-19.6}=0.30.
$$
In actual measurements, a <linear regression> $\overline F=b+\mu_kN$ can expose an unexplained <intercept> $b$. A nonzero <intercept> calls for checking the gauge zero, other resisting <forces> and the contact model; forcing the line through zero can hide those problems. Conversely, constant ratios within <measurement error> support the approximation only over the loads, <speeds> and surface conditions tested. A load sweep alone cannot establish independence from contact <area> or sliding <speed>; those require separate controlled variations.
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