A particle sliding down a movable incline: An experiment

Vermillion, Robert Everett; Cook, Gilbert

doi:10.1119/1.15573

Cited by 2 publications

(2 citation statements)

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“…However, sometimes there are variations on this class of problems by allowing the inclined plane to be affected by the reaction force between the object and the inclined plane (see problem 15-98 of [3]). In the literature, similar problems have been addressed with different approaches like the use of Lagrangian mechanics [4], including friction [5][6][7], or the experimental demonstration [8].…”

Section: Introductionmentioning

confidence: 99%

Sliding down over a horizontally moving semi-sphere

Lineros¹

2022

Eur. J. Phys.

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We studied the dynamics of an object sliding down on a semi-sphere with radius $R$. We consider the physical setup where the semi-sphere is free to move over a flat surface. For simplicity, we assume that all surfaces are friction-less. We analyze the values for the last contact angle $\theta^\star$, corresponding to the angle when the object and the semi-sphere detach one of each other. We consider all possible scenarios with different combination of mass values: $m_A$ and $m_B$. We found that the last contact angle only depends on the ratio between the masses, and it is independent of the acceleration of gravity and semi-sphere's radius. In addition, we found that the largest possible value of $\theta^\star$ is $48.19^{\circ}$ that coincides with the case of a fixed semi-sphere. On the opposite case, the minimum value of $\theta^\star$ is $0^\circ$ and it occurs then the object on the semi-sphere is extremely heavy, occurring the detachment as soon as the sliding body touches the semi-sphere.

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Section: Introductionmentioning

confidence: 99%

Sliding down over a horizontally moving semi-sphere

Lineros¹

2022

Eur. J. Phys.

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“…The problem of a object sliding down on a circular path is an academic example to teach such concepts [1][2][3]. Similar problems have been addressed with different approaches like the use of lagrangian mechanics [4], the case with friction [5][6][7], or the experimental demonstration [8].…”

Section: Introductionmentioning

confidence: 99%

Sliding down over a horizontally moving semi-sphere

Lineros

2021

Preprint

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We studied the dynamics of an object sliding down on a semi-sphere with radius R. We consider the physical situation where the semi-sphere is free to move over a horizontal surface. Also, we consider that all surfaces in contact are friction-less. We analyze the values for the last contact angle θ , corresponding to the angle when the object and the semi-sphere detach one of each other, considering all possible scenarios with different values of mA and mB. We found that the last contact angle only depends on the ratio between the masses, and it is independent of the acceleration of gravity and semi-sphere radius. In addition, we found that the largest possible value of θ occurs for the case when the semi-sphere does not move. On the opposite case, the minimum value of the angle occurs for mA mB occurring at the top of the semi-sphere.

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A particle sliding down a movable incline: An experiment

Cited by 2 publications

References 0 publications

Sliding down over a horizontally moving semi-sphere

Sliding down over a horizontally moving semi-sphere

Sliding down over a horizontally moving semi-sphere

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