Inelastic collapse in one-dimensional driven systems under gravity

Wakou, J.; Kitagishi, Hiroaki; Sakaue, Takahiro; Nakanishi, Hiizu

doi:10.1103/physreve.87.042201

Cited by 4 publications

(5 citation statements)

References 21 publications

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“…These results suggest that models of collisions of multiple spheres should account for impact velocity dependence when the lower ball is in contact with the floor and gravity is present [9,[22][23][24]. These results may also be relevant for modeling granular materials under gravity or another driving force [25], while gas models typically lack such a driving force [26] and can neglect this effect.…”

Section: Discussionmentioning

confidence: 81%

Gravity effects in mass-spring-damper models of inelastic collisions

Bartz¹

2023

Eur. J. Phys.

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A ball bouncing on a rigid surface is modeled as a mass-spring-damper system. We consider the effect of including or neglecting the force of gravity, extending previous work that shows that including gravity yields a velocity-dependent coefficient of restitution. This velocity dependence is most pronounced at low impact velocities and high damping. Previously-published models differ in defining the termination of the collision, with some referencing the ball's position and others noting when the contact force becomes zero. We propose a new model that combines aspects of these approaches. The various models are compared in their predictions for the coefficient of restitution and collision duration, and are compared to experimental data from a cart on an inclined track bouncing repeatedly on a spring. While the new model shows some improvement over the prior collision termination conditions, the inclusion of gravity is the more important consideration in modeling repeated bouncing.

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Section: Discussionmentioning

confidence: 81%

Gravity effects in mass-spring-damper models of inelastic collisions

Bartz¹

2023

Eur. J. Phys.

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“…These results suggest that models of collisions of multiple spheres should account for impact velocity dependence when the lower ball is in contact with the floor and gravity is present [3,14,15,16]. These results may also be relevant for modeling granular materials under gravity or another driving force, [17] while gas models typically lack such a driving force [18] and can neglect this effect.…”

Section: Discussionmentioning

confidence: 83%

Coefficient of restitution of a linear dashpot on a rigid surface

Bartz¹

2022

Preprint

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The linear dashpot model is applied to a single ball bouncing on a rigid surface. It is shown that when gravity is included the coefficient of restitution depends on impact velocity, in contrast to previous work that ignored the effects of gravity. This velocity dependence is most pronounced at low impact velocities and high damping. Previous work has considered the ball to be in contact with the floor when the compression is nonzero, while other analysis terminates the collision earlier, to prevent an attractive force. We compare these models and propose a hybrid between the two. The hybrid model is successful in reproducing experimental results for a cart bouncing repeatedly on a spring.

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“…This toy model can serve as a student's introduction to impact mechanics, which is relevant in a variety of fields including engineering, granular materials, and molecular dynamics. The results of this model may be relevant to study of inelastic collapse and clumping in granular flows [23][24][25][26][27], particularly in the presence of gravity or another driving force [28]. Inelastic collapse involves an infinite number of collisions in finite time, which presents challenges to event-driven modeling [29], so understanding when the ICM is accurate can help improve simulation efficiency.…”

Section: Discussionmentioning

confidence: 99%

Delayed rebounds in the two-ball bounce problem

Bartz¹

2022

Eur. J. Phys.

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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.

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Inelastic collapse in one-dimensional driven systems under gravity

Cited by 4 publications

References 21 publications

Gravity effects in mass-spring-damper models of inelastic collisions

Gravity effects in mass-spring-damper models of inelastic collisions

Coefficient of restitution of a linear dashpot on a rigid surface

Delayed rebounds in the two-ball bounce problem

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