45 research outputs found
Energy in one dimensional linear waves in a string
We consider the energy density and energy transfer in small amplitude,
one-dimensional waves on a string, and find that the common expressions used in
textbooks for the introductory physics with calculus course give wrong results
for some cases, including standing waves. We discuss the origin of the problem,
and how it can be corrected in a way appropriate for the introductory calculus
based physics course.Comment: 5 page
'It Has to Go Down A Little, In Order to Go Around'- Following Feynman on the Gyroscope
In this paper we show that with the help of accessible, teaching quality
equipment, some interesting details of the motion of a gyroscope, typically
overlooked in introductory courses, can be measured and compared to theory. We
begin by deriving a simple relation between the asymptotic dip angle of a
gyroscope released from rest and its precession velocity. We then describe an
experiment which measures these parameters. The data gives excellent agreement
with the model. The idea for this project was suggested by the discussion of
gyroscopic motion in The Feynman Lectures on Physics. Feynman's conclusion
(stated in colloquial terms and quoted in the title) is confirmed and, in
addition, conservation of angular momentum, which underlies this effect, is
quantitatively demonstrated.Comment: 6 pages, 4 figure
Had the planet mars not existed: Kepler's equant model and its physical consequences
We examine the equant model for the motion of planets, which has been the
starting point of Kepler's investigations before he modified it because of Mars
observations. We show that, up to first order in eccentricity, this model
implies for each orbit a velocity which satisfies Kepler's second law and
Hamilton's hodograph, and a centripetal acceleration with an inverse square
dependence on the distance to the sun. If this dependence is assumed to be
universal, Kepler's third law follows immediately. This elementary execice in
kinematics for undergraduates emphasizes the proximity of the equant model
coming from Ancient Greece with our present knowledge. It adds to its
historical interest a didactical relevance concerning, in particular, the
discussion of the Aristotelian or Newtonian conception of motion
Stability boundary approximation of periodic dynamics
We develop here the method for obtaining approximate stability boundaries in
the space of parameters for systems with parametric excitation. The monodromy
(Floquet) matrix of linearized system is found by averaging method. For system
with 2 degrees of freedom (DOF) we derive general approximate stability
conditions. We study domains of stability with the use of fourth order
approximations of monodromy matrix on example of inverted position of a
pendulum with vertically oscillating pivot. Addition of small damping shifts
the stability boundaries upwards, thus resulting to both stabilization and
destabilization effects.Comment: 9 pages, 2 figure
Parametric resonance for vibration energy harvesting with design techniques to passively reduce the initiation threshold amplitude
A vibration energy harvester designed to access parametric resonance can potentially outperform the conventional direct resonant approach in terms of power output achievable given the same drive acceleration. Although linear damping does not limit the resonant growth of parametric resonance, a damping dependent initiation threshold amplitude exists and limits its onset. Design approaches have been explored in this paper to passively overcome this limitation in order to practically realize and exploit the potential advantages. Two distinct design routes have been explored, namely an intrinsically lower threshold through a pendulum-lever configuration and amplification of base excitation fed into the parametric resonator through a cantilever-initial-spring configuration. Experimental results of the parametric resonant harvesters with these additional enabling designs demonstrated an initiation threshold up to an order of magnitude lower than otherwise, while attaining a much higher power peak than direct resonance
The impact of tides on the capillary transition zone
The capillary transition zone, also known as the capillary fringe, is a zone where water saturations decrease with height above the water table/oilâwater contact as a result of capillary action. In some oil reservoirs, this zone may contain a significant proportion of the oil in place. In groundwater assessments, the capillary fringe can profoundly affect contaminant transport. In this study, we investigated the influence of a tidally induced, semi-diurnal, change in water table depth on the water saturation distribution in the capillary fringe/transition zone. The investigation used a mixture of laboratory experiments, in which the change in saturation with depth was monitored over a period of 90 days, and numerical simulation. We show that tidal changes in water table depth can significantly alter the vertical water saturation profile from what would be predicted using capillaryâgravity equilibrium and the drainage or imbibition capillary pressure curves
Using a smartphone acceleration sensor to study uniform and uniformly accelerated circular motions
The acceleration sensor of a smartphone is used for the study of the uniform
and uniformly accelerated circular motions in two experiments. Data collected from both experiments are used for obtaining the angular velocity and the angular acceleration, respectively. Results obtained with the acceleration sensor are shown to be in good agreement with alternative methods, like using video recordings of both experiments and a physical model of the second experiment.Castro-Palacio, JC.; Velazquez, L.; GĂłmez-Tejedor, JA.; ManjĂłn Herrera, FJ.; Monsoriu Serra, JA. (2014). Using a smartphone acceleration sensor to study uniform and uniformly accelerated circular motions. Revista Brasileira de Ensino de Fisica. 36(2):2315-2315. doi:10.1590/S1806-11172014000200015S2315231536