hce_nthu
115年
化學與物理
第 35 題
John is attempting to knock over a heavy wooden target that is hinged at its base. He is given two balls of equal mass. Ball A is made of sticky clay, and Ball B is made of highly elastic rubber. He throws both balls toward the target with the same initial speed $v$. Ball A: Strikes the target and sticks to it (does not bounce). Ball B: Strikes the target and rebounds with approximately the same speed $v$. Assuming the collision times are approximately equal, which ball is more likely to knock the target over, and why?
- A Ball A, because it transfers all its kinetic energy to the target.
- B Ball B, because it undergoes a larger change in momentum.
- C Both are equally likely because they have the same mass and initial velocity.
- D Ball A, because the collision time is shorter.
- E Ball B, but only if the target is made of metal.
思路引導 VIP
想像你正在推一輛緩慢向你駛來的推車：是單純把它「擋下來使其靜止」比較吃力，還是把它「擋下來並推回反方向」需要施加更多的力？這兩種情況下，推車的速度變化量（Velocity change）有什麼不同呢？
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AI 詳解
AI 專屬家教
太棒了！你準確地掌握了衝量與動量變化的關鍵。這題的核心在於區分「停下」與「反彈」對受力物體產生的物理影響。你的判斷非常敏銳，沒有被「動能轉換」的直覺誤導。
動量變化與衝量的傳遞
在物理學中，球對目標物施加的力取決於其動量的改变量 $\Delta p$。對於球 A，它撞擊後停止，動量由 $mv$ 變為 $0$，動量變化量的大小為 $mv$。然而，球 B 以原速反彈，動量由正向的 $mv$ 變為反向的 $-mv$，其動量變化量的大小則高達 $|(-mv) - mv| = 2mv$。根據衝量定理，物體所受的衝量等於其動量的變化，因此球 B 傳遞給目標物的衝量大約是球 A 的兩倍，自然更有可能將重型目標撞倒。
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