When experiment and energy conservation
collide: video analysis of an unrolling mat
Carl E Mungan
1,3
and Trevor C Lipscombe
2
1
Physics Department, US Naval Academy, Annapolis, MD 21402-1363, United States
of America
2
Catholic University of America Press, Washington, DC 20064, United States of
America
E-mail: mungan@usna.edu and lipscombe@cua.edu
Received 11 October 2017, revised 15 November 2017
Accepted for publication 23 November 2017
Published 8 February 2018
Abstract
A mat consisting of round bamboo rods connected by strings perpendicular to
their axes unrolls without slipping on a horizontal table. Video analysis is used
to measure the position of the centre of the remaining roll as a function of time.
It is found to accelerate with time due to the ‘rocket effect’ of the roll ejecting
rods backward relative to itself. Mechanical energy is not conserved because
of the inelastic collisions of the rods with the table. The fitted coefficient of
restitution (COR) is 0.59±0.04 which is consistent with known values for
wood on wood. In support of this explanation, progressively smaller values of
the COR are found when the mat is unrolled on a flat woven rug and on a
shock-absorbing pad. The level of analysis is appropriate to an undergraduate
course in physical mechanics.
Keywords: rolling without slipping, rocket problem, video analysis, mechan-
ical energy, coefficient of restitution
(Some figures may appear in colour only in the online journal)
1. Introduction
In 1946, Freeman modelled the motion of a flexible ribbon with nonzero mass density that is
initially rolled up tightly on itself and then unrolls without slipping along a surface [1]. The
dynamics of this system is pedagogically interesting because it simultaneously encompasses
two important topics that often confuse students of introductory physics. The first topic is the
motion of an object that rolls without slipping. In the absence of any deformation of the object
European Journal of Physics
Eur. J. Phys. 39 (2018) 025004 (8pp) https://doi.org/10.1088/1361-6404/aa9cb7
3
Author to whom any correspondence should be addressed.
0143-0807/18/025004+08$33.00 © 2018 European Physical Society Printed in the UK 1