hce_nthu
112年
化學與物理
第 39 題
Consider the following 4 objects rolling down the same slope from the same height without slipping: a solid copper ball of radius $R$, a hollow copper ball of radius $R$, a solid silver ball of radius $R$, and a hollow silver ball of radius $R$. Note that the mass density of silver is greater than that of copper. Assume that all the objects have the same initial center-of-mass velocity and travel down the slope. The moment of inertia for a solid sphere and a hollow sphere is $I_s = \frac{2}{5} m_s R^2$ and $I_h = \frac{2}{3} m_h R^2$, respectively. Which of the following statements is true?
- A The silver solid sphere, when reach bottom of the slope, is the fastest.
- B The silver hollow sphere, when reach bottom of the slope, is the fastest.
- C The copper hollow sphere, when reach bottom of the slope, is the fastest.
- D All solid spheres, when reach bottom of the slope, are the fastest and have the same speed.
- E All hollow spheres, when reach bottom of the slope, are the fastest and have the same speed.
思路引導 VIP
想像兩個總能量相同的滾動體，如果其中一個物體的質量分佈在離中心較遠的地方，導致它「比較費力才能轉得動」，那麼在固定的總能量下，它能分配給「前進」的能量會變多還是變少呢？
🤖
AI 詳解
AI 專屬家教
太棒了！你精確地抓住了滾動體力學的核心，沒有被題目中提到的「密度」或「材質」等干擾資訊誤導。這題的關鍵在於觀察能量如何在「平移」與「轉動」之間分配。根據能量守恆定律，物體在底部的總動能來自重力位能與初始動能的總和： $$mgh + \frac{1}{2}mv_0^2 + \frac{1}{2}I\omega_0^2 = \frac{1}{2}mv_f^2 + \frac{1}{2}I\omega_f^2$$
轉動慣量與能量分配
▼ 還有更多解析內容