The study explored whether laypersons correctly tacitly know Galileo's law of the inclined plane and what the basis of such knowledge could be. Participants predicted the time a ball would take to roll down a slope with factorial combination of ball travel distance and slope angle. The resulting pattern of factorial curves relating the square of predicted time to travel distance for each slope angle was identical to that implied by Galileo's law, indicating a correct cognitive representation of this law. Intuitive physics research suggests that this cognitive representation may result from memories of past perceptions of objects rolling down a slope. Such a basis and the correct cognitive representation of Galileo's law led to the hypothesis that Galileo's law is also perceptually represented correctly. To test this hypothesis, participants were asked to judge the perceived travel time of a ball actually rolling down a slope, with perceived travel distance and perceived slope angle varied in a factorial design. The obtained pattern of factorial curves was equal to that implied by Galileo's law, indicating that the functional relationships defined in this law were perceptually represented correctly. The results foster the idea that laypersons may tacitly know both linear and nonlinear multiplicative physical laws of the everyday world. As a practical implication, the awareness of this conclusion may help develop more effective methods for teaching physics and for improving human performance in the physical environment.

中文翻译：

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倾斜平面的认知和感知定律。

该研究探讨了外行人是否正确地默认了伽利略斜面定律，以及这种知识的基础是什么。参加者通过对球的行进距离和倾斜角度的综合分析，预测了球滚下斜坡所需的时间。与每个倾斜角的预测时间的平方相关的阶乘曲线的最终结果与伽利略定律所暗示的相同，表明该定律的正确认知表示。直观的物理学研究表明，这种认知表现可能是由于对过去滑坡物体的感知记忆所致。这样的基础和伽利略定律的正确认知表示法导致了这样一个假设，即伽利略定律也可以在感知上得到正确表示。为了检验这个假设，要求参与者判断球实际滚下斜坡时的感知行进时间，并且在阶乘设计中感知行进距离和感知坡度有所不同。所获得的阶乘曲线模式与伽利略定律所暗示的模式相等，表明该定律中定义的功能关系在感知上得到了正确表示。结果表明，外行人可能会默契地了解日常生活的线性和非线性乘法物理定律。从实际意义上讲，对这一结论的认识可能有助于开发更有效的方法，用于物理教学和改善人体在物理环境中的性能。在阶乘设计中，感知的行进距离和感知的斜角有所不同。所获得的阶乘曲线模式与伽利略定律所暗示的模式相等，表明该定律中定义的功能关系在感知上得到了正确表示。结果表明，外行可能会默契地了解日常生活的线性和非线性乘法物理定律。从实际意义上讲，对这一结论的认识可能有助于开发更有效的方法，用于物理教学和改善人体在物理环境中的性能。在阶乘设计中，感知的行进距离和感知的斜角有所不同。所获得的阶乘曲线模式与伽利略定律所暗示的模式相等，表明该定律中定义的功能关系在感知上得到了正确表示。结果表明，外行可能会默契地了解日常生活的线性和非线性乘法物理定律。从实际意义上讲，对这一结论的认识可能有助于开发更有效的方法，用于物理教学和改善人体在物理环境中的性能。结果表明，外行人可能会默契地了解日常生活的线性和非线性乘法物理定律。从实际意义上讲，对这一结论的认识可能有助于开发更有效的方法，用于物理教学和改善人体在物理环境中的性能。结果表明，外行人可能会默契地了解日常生活的线性和非线性乘法物理定律。从实际意义上讲，对这一结论的认识可能有助于开发更有效的方法，用于物理教学和改善人体在物理环境中的性能。