论文标题
在两球反弹问题中延迟篮板
Delayed Rebounds in the Two-Ball Bounce Problem
论文作者
论文摘要
在教室的演示中，一个网球落在篮球顶部的表演中，通常使用动量保护进行弹性碰撞的弹力来解释出令人惊讶的高弹跳网球，而篮球层碰撞被视为独立于两个球之间的碰撞。该教科书的解释扩展到了非弹性碰撞，包括恢复系数。本文综述，这种独立的接触模型（ICM）对于多种情况是准确的，即使碰撞并非真正独立。但是，很容易探索ICM无法解释的情况，例如将网球换成乒乓球。在本文中，我们研究了导致“延迟反弹效应”的条件，这是一个小的第一次反弹，然后使用本科生可以使用的技术进行了更高的第二反弹。动力学模型基于阻尼谐波振荡器的熟悉解。我们专注于使运动方程无量纲以进行数值模拟，并减少参数和初始条件的数量，以强调普遍行为。在一系列参数中发现了延迟的反弹效应，最常见的是，在第一个反弹低于ICM预测的情况下。
In the classroom demonstration of a tennis ball dropped on top of a basketball, the surprisingly high bounce of the tennis ball is typically explained using momentum conservation for elastic collisions, with the basketball-floor collision treated as independent from the collision between the two balls. This textbook explanation is extended to inelastic collisions by including a coefficient of restitution. This independent contact model (ICM), as reviewed in this paper, is accurate for a wide variety of cases, even when the collisions are not truly independent. However, it is easy to explore situations that are not explained by the ICM, such as swapping the tennis ball for a ping-pong ball. In this paper, we study the conditions that lead to a "delayed rebound effect," a small first bounce followed by a higher second bounce, using techniques accessible to an undergraduate student. The dynamical model is based on the familiar solution of the damped harmonic oscillator. We focus on making the equations of motion dimensionless for numerical simulation, and reducing the number of parameters and initial conditions to emphasize universal behavior. The delayed rebound effect is found for a range of parameters, most commonly in cases where the first bounce is lower than the ICM prediction.
