Problem 274. Bouncing disk

Created by Nikolai

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A disk is placed in a rectangular room with dimensions a and b in a point with coordinates x0 and y0. The disk is given a startup speed V, m/s, the angle between the speed and the x axis is phi, rad. All coordinates have metric dimensions. (See the figure below, just right-click on it and choose open in new tab). The friction factor is nu (always greater then zero). The energy loss caused by bumping the walls is negligible.

Find the resulting position of the disk. The answer should be given with the tolerance greater than 10^-3.

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Last Solution submitted on Sep 28, 2025

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Franck Dernoncourt on 6 Feb 2012

Image URL: https://lh3.googleusercontent.com/NfbXN6dTVzB7e6hoR68t-zSp7SbSk63R42G5Ep8x41pPlF-_yNjECYgzsY52vY7Xi2Ixjg78nJKIIO4Kbd7DdVtbPRdfuBLCfDw=w1600

@bmtran (Bryant Tran) on 7 Feb 2012

could you define "friction factor"?

Nikolai on 7 Feb 2012

I meant the coefficient of friction

@bmtran (Bryant Tran) on 7 Feb 2012

In that case, what are you using for acceleration due to gravity?

@bmtran (Bryant Tran) on 7 Feb 2012

For those wondering, it's 9.80665

Nikolai on 7 Feb 2012

Thanks to @bmtran, a bug in testing procedures was resolved.

Rafael S.T. Vieira on 14 Jul 2020

For those still wondering, the disk is dimensionless.

Nikolaos Nikolaou on 26 Jul 2021

haha

Diogo Carvalho on 1 Oct 2021

Can't see image.

Dyuman Joshi on 28 Sep 2025 at 8:09

1. The image url has not been working since quite a long time.
2. The last 2 statements seems contradictory - Friction factor is to be considered but then energy loss from bumping the wall is to be considered negligible?
If the bumping is only considered to be with the vertical wall members, it should have been specified clearly.

I have cleaned up some hard-coded solutions.
Best not to spend time on this problem for the time being.

Christian Schröder on 28 Sep 2025 at 20:21

@Dyuman I agree that the problem description could be MUCH improved... see solution 14777825 for a better explanation (and a detailed solution development).

As for friction: friction happens as the "disk" (really dimensionless, as Rafael pointed out) moves about in the rectangular "room". Bounces at any room boundary are frictionless.

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Problem 274. Bouncing disk

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Problem 274. Bouncing disk

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