Trouble on the loop-the-loop

Tea, Peter L.

doi:10.1119/1.14997

Cited by 5 publications

(4 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It can be concluded that when the velocity v 0 is below the threshold value in equation ( 27), the sphere cannot complete the vertical loop rolling without slipping in all points of the path. Following another formulation, Tea [7] also concludes that according to the conventional solution of the classical problem (h = 2.7R), the static friction coefficient must tend to infinity.…”

Section: Modifying the Usual Problemmentioning

confidence: 99%

“…It is proved that the conventional solution found in many text books has several flaws, which are discussed and compared with the solution presented in this paper. A similar problem has already been studied in the literature [7]; however, in that work, Tea analyzes different particular cases focusing the attention around a reference initial condition h/R = 2.7, h being the initial height of the sphere and R the radius of the vertical loop, but searching for a general solution of this problem is not the focus of Tea's paper. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A revised solution for a sphere rolling in a vertical loop

Bertrán¹,

Riba²

2020

Eur. J. Phys.

View full text Add to dashboard Cite

show abstract

Section: Modifying the Usual Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A revised solution for a sphere rolling in a vertical loop

Bertrán¹,

Riba²

2020

Eur. J. Phys.

View full text Add to dashboard Cite

show abstract

“…Este problema ha sido ampliamente estudiado en la literatura y se han propuesto soluciones alternativas a partir de consideraciones geométricas, utilizando los conceptos de serie de Taylor y radio de curvatura, así como las nociones de límite de una función continua y funciones trigonométricas, además de elementos de geometría euclidiana y la congruencia deángulos en triángulos isósceles [3,4]. La complejidad se incrementa cuando se considera la presencia de fricción, por ello, este problema y sus variantes pocas veces se abordan en cursos de licenciatura, sin embargo, dicho problema también ha sido ampliamente estudiado en la literatura [5][6][7][8]. A pesar de esto, el tema sigue siendo de interés desde el punto de vista teórico, experimental y educativo [9][10][11][12][13].…”

Section: Introductionunclassified

Estudio teórico-experimental de la dinámica del movimiento circular con fricción

et al. 2021

View full text Add to dashboard Cite

En este trabajo se presenta un estudio teórico-experimental de la dinámica del movimiento de una esfera que se mueve en una trayectoria circular vertical con fricción. En el estudio teórico se resuelve una ecuación diferencial de Bernoulli que permite calcular la rapidez en cualquier posición angular y la rapidez mínima necesaria para que la esfera complete una vuelta en la trayectoria circular. En el estudio experimental se utilizan fotopuertas para medir la posición angular de la esfera como función del tiempo; a partir de esto, se obtienen de manera indirecta la rapidez y fuerza normal en cualquier posición angular. Al comparar los resultados teóricos y experimentales obtenidos de forma indirecta para la rapidez y fuerza normal se observa que el modelo teórico describe de forma cualitativa el comportamiento experimental cuando µ = 0.12. Finalmente, se analiza el comportamiento teórico de la rapidez y fuerza normal para distintos valores del coeficiente de fricción cinética, donde se observa que para µ ≥ 0.2 la rapidez y fuerza normal final decaen de manera abrupta.Descriptores: Rapidez; fuerza normal; fricción; ecuación de Bernoulli. This work presents a theoretical and experimental study of the dynamics of the motion of a sphere that moves in a vertical circular trajectory with friction. In the theoretical study, a Bernoulli differential equation is solved to calculate the velocity at any angular position and the minimum velocity necessary for the sphere to complete one turn in the circular track. In the experimental study, photogates are used to measure the angular position of the sphere as a function of time, from which the velocity and normal force are indirectly obtained in any angular position. When comparing the theoretical and experimental results obtained indirectly for the velocity and the normal force, it is observed that the theoretical model qualitatively describes the experimental behavior when µ = 0.12. Finally, the theoretical behavior of the speed and normal force is analyzed for different values of the coefficient of friction kinetic, where it is observed that for µ ≥ 0.2 the final normal speed and force decline abruptly.

show abstract

“…In a real "loop-the-loop "system, where the rolling of a solid sphere is combined with occasional sliding, relying on this equation leads to a discrepancy between the expected and experimental results [18]. As Tea Jr points out [19], in real systems, the ratio between the initial height and the loop's radius has to be at least 2.7 to ensure that the ball completes the loop.…”

Section: Introductionmentioning

confidence: 99%

Loop-the-Loop as a Real Tribomechanical System Applicable in Engineering Education

Miljojković¹,

Kocovic²,

Košarac³

et al. 2021

Tribol. Ind.

View full text Add to dashboard Cite

Using a "loop-the-loop" system, the authors developed a double-track apparatus and based their experimental research on theoretical foundations related to the motion on an inclined plane laid by Leonhard Euler. The method enabled the quantification of very small "energy losses". The paper presents the results of experimental research and the analysis of the changes in friction force and other causes of energy dissipation. In engineering education, the method contributes to a deep understanding of the concept of energy transformation -the appearance of "energy losses" in real tribomechanical systems.

show abstract

Trouble on the loop-the-loop

Cited by 5 publications

References 0 publications

A revised solution for a sphere rolling in a vertical loop

A revised solution for a sphere rolling in a vertical loop

Estudio teórico-experimental de la dinámica del movimiento circular con fricción

Loop-the-Loop as a Real Tribomechanical System Applicable in Engineering Education

Contact Info

Product

Resources

About