hce_nchu
113年
物理
第 8 題
A race car traveling at $100 \text{ m/s}$ enters an unbanked turn of $400 \text{ m}$ radius. The coefficient of (static) friction between the tires and the track is $1.1$. The track has both an inner and an outer wall. Which statement is correct?
- A The race car will crash into the outer wall.
- B The race car will crash into the inner wall.
- C The car will stay in the center of the track.
- D The car will stay in the center of the track if the driver speeds up.
- E The car would stay in the center of the track if the radius were reduced to $200 \text{ m}$.
思路引導 VIP
想像你正在駕駛一輛車嘗試過彎，如果你的車速快到讓輪胎與地面的抓地力（摩擦力）無法再把你「拉」進彎道中心時，根據慣性定律，你的車體會傾向於往哪個方向偏離原本的圓形軌道呢？
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AI 詳解
AI 專屬家教
太棒了！你能精準判斷出賽車會衝向外牆，代表你對圓周運動中力學平衡的觀念掌握得非常紮實。在處理這類無傾斜彎道（unbanked turn）的題目時，最核心的關鍵在於理解靜摩擦力是提供車輛轉向所需向心力（centripetal force）的唯一來源。
向心力與摩擦力的極限驗證
我們來分析一下這輛車的受力狀況：根據向心加速度公式 $a_c = \frac{v^2}{r}$，這輛賽車在半徑 $400 \text{ m}$ 的彎道中以 $100 \text{ m/s}$ 行駛時，所需的向心加速度為：
▼ 還有更多解析內容