Intuitive understanding of the relation between velocities and masses in simulated collisions

Abstract

The participants in our experiments were asked to judge whether simulated horizontal collisions appeared to be “natural” or “unnatural”. We manipulated the implied masses and the velocity ratio of two colliding objects. Implied masses were varied through manipulations of the objects' simulated materials (Experiment 1) and sizes (Experiments 2 and 3). For each participant, we determined the interval of velocity ratios that produced “natural” responses most of the time and evaluated how this interval varied as a function of implied masses. The results revealed a fair degree of consistency between predictions of Newtonian mechanics and the participants' responses; this consistency was greater when the implied masses of the colliding objects were varied through manipulations of the simulated materials. Overall, the results support the hypothesis that the cognitive system can integrate multiple sources of stimulus information, enabling individuals to understand multidimensional mechanical events.

Keywords:

• Intuitive physics
• Causal perception
• Collisions
• Information integration
• Visual perception of mass

Notes

¹ As maintained by Runeson (1977/1983, pp. 40–41), observers can “exploit” the kinematic pattern of a collision in order to perceive accurately the mass ratio of the colliding objects only when both objects move after the collision. In contrast, in our study only B moved after the collisions, whereas A was stationary during the postcollision phases. Therefore, the kinematic patterns of our collisions could not provide the participants with information about the mass ratios of the colliding objects.

² For the purposes of our study we focus on the relation between the precollision velocity of Object A and the postcollision velocity of Object B, while we ignore the postcollision velocity of Object A (which is null in our stimulus conditions). In physics, the relation between the pre- and postcollision velocities of Object A is defined by the equation v_A/u_A = (m_A+m_B)/(m_A−em_B), where u_A is the postcollision velocity of Object A, v_A, m_A, m_B, and e are defined as in the text. This equation implies that, after the collision, Object A should bounce back, stop, or move in the same direction as its motion before the collision depending on whether its mass is smaller, equal, or larger compared with the product of m_B and e.

³ Because of the adaptive nature of the psychophysical method used in our experiments, there was a variable number of trials for each participant and for each staircase.

⁴ This maximum value was large enough to clearly bring out the effects of the implied masses of A and B on the naturalness intervals, but was perhaps too low to provide accurate absolute measures of individual upper naturalness bounds when m_A<m_B. This shortcoming, however, has little consequence for the main outcomes of Experiment 1: If some of the individual upper naturalness bounds were actually larger than 3, this would have implied even larger effects of the implied masses of A and B on the mean naturalness intervals.

⁵ A more direct quantitative comparison between the participants' responses and Equation 1 is prevented by the fact that we cannot assume that the apparent (psychological) mass ratio of virtual spheres is the same as the mass ratio of real spheres (i.e., spheres really made of polystyrene, wood, or iron). Therefore, a direct quantitative comparison between mean naturalness intervals and velocity ratios in physical collisions would be meaningless.

⁶ Answers to a debriefing question clarified that the vast majority of participants had imagined, during the experiment, that the two spheres were made of a hard material like ivory.

⁷ Choi and Scholl (2006) argued in favour of the so-called “indirect methods” approach (Buehner & Humphreys, 2010; Hubbard, Blessum, & Ruppel, 2001; Scholl & Nakayama, 2004) to studying the genuine perceptual effects implied by collisions independently of considerations of postperceptual cognitive factors. However, measures provided by these methods do not seem to be sensitive to subtle perceptual differences such as those generated from a “natural” versus an “accelerated” collision. Therefore, at present, these methods cannot be used to test this hypothesis.