In its usual form, the loop-the-loop (LtL) problem involves a uniform solid sphere rolling from rest down a linear ramp that transitions into a circular loop. The task is to find the minimum height from which the ball must be released in order to roll completely around the loop without breaking contact. The answer, found using the conservation of mechanical energy and Newton's second law, is invariably less than the actual measured height. The difference, attributed to non-conservative forces, is consistently larger than the experimental uncertainty. To get a more detailed understanding of the effects of dissipative forces on the loop-the-loop, we made high speed video recordings of balls moving on the commercial LtL apparatus and used video analysis to study their motion in detail. We present our results along with a simple model to predict the motion of the ball on an LtL track taking energy losses into account. Calculations based on the model are in excellent agreement with our measurements.

中文翻译：

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循环中的能量损失和冲击

在通常的形式中，环路问题（LtL）涉及均匀的固体球体，从静止的球体向下滚动到线性的坡道，然后过渡到圆形的环路。任务是找到球必须释放的最小高度，以便在不中断接触的情况下完全绕圈滚动。答案是根据机械能守恒和牛顿第二定律得出的，总是小于实际测得的高度。归因于非保守力的差异始终大于实验不确定性。为了更详细地了解耗散力对环的影响，我们对在商用LtL设备上运动的球进行了高速录像，并使用视频分析来详细研究其运动。我们介绍了我们的结果以及一个简单的模型，该模型可以在考虑到能量损失的情况下预测LtL轨道上球的运动。基于模型的计算与我们的测量非常吻合。