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Modeling a falling slinky

机译:模拟掉落的紧身衣

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A slinky is an example of a tension spring: in an unstretched state a slinky is collapsed, with turns touchinga finite tension is required to separate the turns from this state. If a slinky is suspended from its top and stretched under gravity and then released, the bottom of the slinky does not begin to fall until the top section of the slinky, which collapses turn by turn from the top, collides with the bottom. The total collapse time t c (typically ~0.3 s for real slinkies) corresponds to the time required for a wave front to propagate down the slinky to communicate the release of the top end. We present a modification to an existing model for a falling tension spring [Calkin, Am. J. Phys. 61, 261-264 (1993)] and apply it to data from filmed drops of two real slinkies. The modification of the model is the inclusion of a finite time for collapse of the turns of the slinky behind the collapse front propagating down the slinky during the fall. The new finite-collapse time model achieves a good qualitative fit to the observed positions of the top of the real slinkies during the measured drops. The spring constant k for each slinky is taken to be a free parameter in the model. The best-fit model values for k for each slinky are approximately consistent with values obtained from measured periods of oscillation of the slinkies.
机译:紧身裤是拉力弹簧的一个例子:在未拉伸状态下,紧身裤塌陷,接触匝数时,需要有限的拉力才能使匝数与该状态分开。如果紧身衣从其顶部悬垂并在重力作用下拉伸然后释放,则紧身衣的底部直到开始逐渐从顶部塌陷并与底部碰撞的紧身衣的顶部开始下降。总的塌陷时间t c(对于实际紧身来说通常约为0.3 s)对应于波前向下传播到紧身以传达顶端释放所需的时间。我们提出了一种用于下降拉力弹簧[Calkin,Am。 J.物理61,261-264(1993)]并将其应用于来自两个真实紧身衣的拍摄滴的数据。该模型的修改是包含了一个有限的时间,用于使塌陷前部后面的弯曲的塌陷部塌陷,并在秋季跌落时将其向下传播。新的有限塌陷时间模型在实测滴落过程中,对实实链顶顶部的观测位置实现了良好的定性拟合。每个紧身衣的弹簧常数k被视为模型中的自由参数。对于每个link骨,k的最佳拟合模型值与从所测oscillation骨的振动周期获得的值大致一致。

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