一台150吨(公制)的机车能够牵引大约100节每节约100吨的车厢(约10,000吨总重)是因为牵引力由摩擦决定,不仅仅是总质量。静摩擦 \(F_s\) 满足 \(F_s\le \mu_s N\):在物体静止时,摩擦力会随着外力增大而增大,直到达到上限。动摩擦 \(F_k\) 更小(\(\mu_k<\mu_s\)),并且在滑动过程中近似恒定。文章给出的例子包括:橡胶–沥青 \(\mu_s=0.9\)、橡胶–冰面 \(\mu_s=0.15\)、钢–钢 \(\mu_s=0.74\)、\(\mu_k=0.57\)。由于 \(N=mg\),法向力越大可产生的牵引力越大。
在两台相同机车相向拖拽的玩具式对拉中,质量相等意味着法向力 \(N\) 相等、静摩擦上限相同,因此不会产生相对位移。如果一台更重,它更大的 \(N\) 和更高的静摩擦上限占优,较轻的一台会打滑。尽管如此,动力要求机车质量必须大于整列车这一表面规则并不成立,因为当运动状态由滑动转为静接触时,轮轨界面的静摩擦可提供比滑移接触更强的牵引。
滚动是核心机制。被拖运行的车轮主要在滚动,因此与钢轨的滑动摩擦很小,而车轮轴与车体/轴箱界面仍需摩擦以实现转动。通过滚柱轴承和润滑,这些内摩擦的 \(\mu_k\) 可从约0.56(干摩擦钢对钢)降至约0.002。重达10,000吨的列车会产生约 \(10^8\) N 的法向力,因此可获得很高的静态牵引,但起步仍最困难,因为 \(F_s\) 是限制阈值。故列车使用“松弛动作”:逐渐缩短车钩间隙,让车厢分批被带动启动,并且钢轮滚阻很小,有利于能效。
The article resolves why a 150‑metric‑ton locomotive can pull about 100 freight cars of roughly 100 metric tons each, about 10,000 tons total, by attributing traction to friction rather than mass alone. Static friction \(F_s\) follows \(F_s\le \mu_s N\): it rises with applied force while the body remains still until a maximum is reached. Kinetic friction \(F_k\) is lower (\(\mu_k<\mu_s\)) and roughly constant during sliding. Given examples include coefficients for rubber on asphalt \((\mu_s=0.9)\), rubber on ice \((\mu_s=0.15)\), and steel on steel \((\mu_s=0.74,\ \mu_k=0.57)\). Since \(N=mg\), larger normal force means greater available traction.
In a two-locomotive tug-of-war setup, equal masses imply equal \(N\) and equal static-friction limits, so neither can pull the other. If one unit is heavier, it has a larger \(N\) and higher static ceiling, and the lighter unit loses adhesion first and skids. This makes it seem a locomotive must outweigh the train, but that conclusion ignores regimes: static contact at the wheel–rail interface can generate stronger effective pull than sliding contact.
Rolling is the decisive mechanism. Towed wheelsets roll rather than slide on the rail, so rail sliding losses are minimal, while axle interfaces still need friction for wheel rotation. Roller bearings and lubrication reduce internal kinetic coefficients from about 0.56 (dry steel-on-steel) to around 0.002. A 10,000-ton train creates about \(10^8\) N normal force, enabling very high static pull, yet starting is still the hardest stage because \(F_s\) sets the threshold. Therefore trains use slack action, closing coupler gaps gradually to bring cars into motion sequentially, and steel-wheel low rolling resistance supports energy efficiency.