A Dynamical Model to Analyze the Influence of Sliding Friction on Motion on a Curve—An Analytical Method

Author(s)
Prahlad Kulkarni

ABSTRACT

To demonstrate the influence of sliding friction of motion on a curve, a circular path is considered for simplicity on which a person slides from the highest point to the lowest point. A slide which represents a quadrant of radius 5 m and a person of mass 60 kg are considered for comparison in this paper. A Differential equation for motion considering the fact that the normal force depends both on the sin component of weight and also on the tangential velocity, is established and is solved using integrating factor method, and the motion is analysed for different surface roughness of the slide and is compared using superimposed graphs, also the limiting value of friction coefficient at which the person just exits the slide is determined. The correction factor for exit velocity with friction as compared with the exit velocity for zero friction is determined. The fraction of energy lost to friction at the exit is evaluated. The Variation of normal force with the position of the person on the slide is plotted for different surface roughness of the slide, and the position on the slide where the normal force or the force experienced by the person is maximum, is determined and hence its maximum value is evaluated for different surface roughness. For simplicity, a point contact between the body and the slide is considered.

To demonstrate the influence of sliding friction of motion on a curve, a circular path is considered for simplicity on which a person slides from the highest point to the lowest point. A slide which represents a quadrant of radius 5 m and a person of mass 60 kg are considered for comparison in this paper. A Differential equation for motion considering the fact that the normal force depends both on the sin component of weight and also on the tangential velocity, is established and is solved using integrating factor method, and the motion is analysed for different surface roughness of the slide and is compared using superimposed graphs, also the limiting value of friction coefficient at which the person just exits the slide is determined. The correction factor for exit velocity with friction as compared with the exit velocity for zero friction is determined. The fraction of energy lost to friction at the exit is evaluated. The Variation of normal force with the position of the person on the slide is plotted for different surface roughness of the slide, and the position on the slide where the normal force or the force experienced by the person is maximum, is determined and hence its maximum value is evaluated for different surface roughness. For simplicity, a point contact between the body and the slide is considered.

KEYWORDS

Sliding Friction, Surface Roughness, Integrating Factor Method, Correction Factor, Critical Coefficient of Friction, Exit Velocity

Sliding Friction, Surface Roughness, Integrating Factor Method, Correction Factor, Critical Coefficient of Friction, Exit Velocity

Cite this paper

Kulkarni, P. (2015) A Dynamical Model to Analyze the Influence of Sliding Friction on Motion on a Curve—An Analytical Method.*Open Journal of Applied Sciences*, **5**, 434-442. doi: 10.4236/ojapps.2015.58043.

Kulkarni, P. (2015) A Dynamical Model to Analyze the Influence of Sliding Friction on Motion on a Curve—An Analytical Method.

References

[1] Curnier, A. (1984) A Theory of Friction. International Journal of Solid Structures, 20, 637-647.

[2] Jellet, J.H. (1872) A Treatise on the Theory of Friction. Hodges Foster & Co., Leuven.

[3] Al-Bender, F., Lampaert, V. and Swevers, J. (2002) Modelling of Dry Sliding Friction Dynamics: From Heuristic Models to Physically Motivated Models and Back. Chaos—An Interdisciplinary Journal of Nonlinear Science, 14, 446-460.

[4] Berger, E.J. (2002) Friction Modelling for Dynamic System Simulation. Applied Mechanics Reviews, 55.

[5] Goyal, S. (1989) Planar Sliding of a Rigid Body with Dry Friction: Limit Surfaces and Dynamics of Motion. A Dissertation Presented to the Faculty of Graduate School of Cornell University in Partial Requirements for the Degree of Doctor of Philosophy.

[6] Wu, C.L., Yang, L.F. and He, Y.L. (2013) On the Measurement of Friction Coefficient at the Curved Surface in Metal Forming. Applied Mechanics and Materials, 446-447, 1134-1137.

[1] Curnier, A. (1984) A Theory of Friction. International Journal of Solid Structures, 20, 637-647.

[2] Jellet, J.H. (1872) A Treatise on the Theory of Friction. Hodges Foster & Co., Leuven.

[3] Al-Bender, F., Lampaert, V. and Swevers, J. (2002) Modelling of Dry Sliding Friction Dynamics: From Heuristic Models to Physically Motivated Models and Back. Chaos—An Interdisciplinary Journal of Nonlinear Science, 14, 446-460.

[4] Berger, E.J. (2002) Friction Modelling for Dynamic System Simulation. Applied Mechanics Reviews, 55.

[5] Goyal, S. (1989) Planar Sliding of a Rigid Body with Dry Friction: Limit Surfaces and Dynamics of Motion. A Dissertation Presented to the Faculty of Graduate School of Cornell University in Partial Requirements for the Degree of Doctor of Philosophy.

[6] Wu, C.L., Yang, L.F. and He, Y.L. (2013) On the Measurement of Friction Coefficient at the Curved Surface in Metal Forming. Applied Mechanics and Materials, 446-447, 1134-1137.