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Research Papers

Collision of Two Mass Baton With Massive External Surfaces

[+] Author and Article Information
Ali Tavakoli

 Mechanical Engineering Department, Southern Methodist University, 3101 Dyer Street, Suite 200, Dallas, TX 75275atavakolit@smu.edu

Mohamed Gharib

 Mechanical Engineering Department, Southern Methodist University, 3101 Dyer Street, Suite 200, Dallas, TX 75275mgharib@smu.edu

Yildirim Hurmuzlu1

 Mechanical Engineering Department, Southern Methodist University, 3101 Dyer Street, Suite 200, Dallas, TX 75275hurmuzlu@lyle.smu.edu

1

Corresponding author.

J. Appl. Mech 79(5), 051019 (Jul 02, 2012) (8 pages) doi:10.1115/1.4006456 History: Received December 15, 2010; Revised March 20, 2012; Posted March 29, 2012; Published July 02, 2012; Online July 02, 2012

This paper presents the solution of the impact problem for a sliding/bouncing baton on flat and inclined planes subject to surface friction. The baton is assumed to have unilaterally constrained motion, which means one end slides on the ground while the other end collides with the ground. We use the impulse momentum approach and incorporate the impulse correlation ratio (ICR) hypothesis to solve the ground impact problem when the system has unilaterally constrained dynamics. Parametric investigations were carried out to examine the effect of the baton’s length and the inclined surface slope angle on the impulse correlation ratio. Numerical simulation and experiments were carried out to validate the model.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

System representation; baton on inclined wall

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Figure 2

System at the impact moment; collision with inclined wall

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Figure 3

Baton’s possible impact cases; (a) impulse-velocity diagrams of the colliding mass; (b) rebound directions during the impact

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Figure 4

Level ground experimental setup

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Figure 5

Inclined wall experimental setup

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Figure 6

The post-impact energies at the first ground impact; (a) versus different baton’s lengths (L); γ = 0; (b) versus different slope angles (γ); L = 350 mm. A square point is the mean of five theoretical calculations and an error bar is derived from calculating the mean of the difference between theoretical and experimental results.

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Figure 7

The post-impact velocities at the first ground impact versus different baton’s lengths (L); γ = 0; (a) horizontal velocity of mass m1 ; (b) vertical velocity ratio of mass m1

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Figure 8

ICR versus different baton’s lengths (L); γ = 0

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Figure 9

The post-impact velocities at the first ground impact versus different slope angles (γ); L = 350 mm; (a) tangential velocity of mass m1 ; (b) normal velocity ratio of mass m1

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Figure 10

ICR versus different slope angles (γ); L = 350 mm

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