Kinetic to Potential Energy Transformation Using a Spring as an Intermediary: Application to the Pole Vault Problem

2019 ◽  
Vol 86 (5) ◽  
Author(s):  
Sheryl Chau ◽  
Ranjan Mukherjee
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Point Mass ◽  
External Torque ◽  
Nonconservative Force ◽  
Muscle Work ◽  
Simplifying Assumptions ◽  
Linear Spring ◽  
Pole Vault ◽  
Work Done

The kinetic energy of a mass moving horizontally can be completely converted into potential energy using a spring as an intermediary. The spring can be used to temporarily store some of the energy of the mass and change the direction of motion of the mass from horizontal to vertical. A nondimensional framework is used to study this problem for a point mass, first with a linear spring and then with a nonlinear spring that is an elastica. Solutions to the problems with the linear spring and elastica show many similarities and some dissimilarities. The dynamics of the point mass and elastica resemble the mechanics of a pole-vault; and therefore, a nonconservative external torque is introduced to parallel the muscle work done by vaulters. For the nonconservative system, the problem is solved for complete transformation of the kinetic energy of the mass and the work done by the external torque into potential energy of the mass. The initial velocities for the two cases, with and without the nonconservative force, are quite similar; and therefore, the maximum potential energy of the mass is higher in the presence of the nonconservative force. A realistic dimensional example is considered; the solution to the problem, despite several simplifying assumptions, is found to be similar to data of elite pole vaulters presented in the literature.

Tracker-assisted modelling: simultaneous validation of the conservation law of energy and the work-energy theorem

2021 ◽  
Vol 57 (1) ◽  
pp. 015012
Author(s):  
Unofre B Pili ◽  
Renante R Violanda
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Conservation Law ◽  
Gravitational Potential Energy ◽  
Time Data ◽  
Home Based ◽  
Basic Physics ◽  
Free Falling ◽  
Work Done

Abstract The video of a free-falling object was analysed in Tracker in order to extract the position and time data. On the basis of these data, the velocity, gravitational potential energy, kinetic energy, and the work done by gravity were obtained. These led to a rather simultaneous validation of the conservation law of energy and the work–energy theorem. The superimposed plots of the kinetic energy, gravitational potential energy, and the total energy as respective functions of time and position demonstrate energy conservation quite well. The same results were observed from the plots of the potential energy against the kinetic energy. On the other hand, the work–energy theorem has emerged from the plot of the total work-done against the change in kinetic energy. Because of the accessibility of the setup, the current work is seen as suitable for a home-based activity, during these times of the pandemic in particular in which online learning has remained to be the format in some countries. With the guidance of a teacher, online or face-to-face, students in their junior or senior high school—as well as for those who are enrolled in basic physics in college—will be able to benefit from this work.

scholarly journals The Generalized Hamilton Principle and Non-Hermitian Quantum Theory

2021 ◽  
Author(s):  
Xiang-Yao Wu ◽  
Ben-Shan Wu ◽  
Xiao-Jing Liu ◽  
Ming-Li Ren ◽  
Meng Han ◽  
...  
Keyword(s):  
Quantum Theory ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Path Integration ◽  
Lagrange Function ◽  
Energy Potential ◽  
Feynman Path ◽  
Hamilton Principle ◽  
Nonconservative Force ◽  
Force Systems

Abstract The Hamilton principle is a variation principle describing the isolated and conservative systems, its Lagrange function is the difference between kinetic energy and potential energy. By Feynman path integration, we can obtain the Hermitian quantum theory, i.e., the standard Schrodinger equation. In this paper, we have generalized the Hamilton principle to the generalized Hamilton principle, which can describe the open system (mass or energy exchange systems) and nonconservative force systems or dissipative systems, and given the generalized Lagrange function, it has to do with the kinetic energy, potential energy and the work of nonconservative forces to do. With the Feynman path integration, we have given the non-Hermitian quantum theory of the nonconservative force systems. Otherwise, with the generalized Hamilton principle, we have given the generalized Hamiltonian for the particle exchanging heat with the outside world, which is the sum of kinetic energy, potential energy and thermal energy, and further given the equation of quantum thermodynamics. PACS: 03.65.-w, 05.70.Ce, 05.30.Rt

scholarly journals Ocean Convective Available Potential Energy. Part II: Energetics of Thermobaric Convection and Thermobaric Cabbeling

2016 ◽  
Vol 46 (4) ◽  
pp. 1097-1115 ◽  
Author(s):  
Zhan Su ◽  
Andrew P. Ingersoll ◽  
Andrew L. Stewart ◽  
Andrew F. Thompson
Keyword(s):  
Potential Energy ◽  
Deep Convection ◽  
Center Of Mass ◽  
Convective Available Potential Energy ◽  
Vertical Mixing ◽  
Available Potential Energy ◽  
Energy Part ◽  
Different Temperatures ◽  
Simplifying Assumptions ◽  
Diabatic Processes

AbstractThe energetics of thermobaricity- and cabbeling-powered deep convection occurring in oceans with cold freshwater overlying warm salty water are investigated here. These quasi-two-layer profiles are widely observed in wintertime polar oceans. The key diagnostic is the ocean convective available potential energy (OCAPE), a concept introduced in a companion piece to this paper (Part I). For an isolated ocean column, OCAPE arises from thermobaricity and is the maximum potential energy (PE) that can be converted into kinetic energy (KE) under adiabatic vertical parcel rearrangements. This study explores the KE budget of convection using two-dimensional numerical simulations and analytical estimates. The authors find that OCAPE is a principal source for KE. However, the complete conversion of OCAPE to KE is inhibited by diabatic processes. Further, this study finds that diabatic processes produce three other distinct contributions to the KE budget: (i) a sink of KE due to the reduction of stratification by vertical mixing, which raises water column’s center of mass and thus acts to convert KE to PE; (ii) a source of KE due to cabbeling-induced shrinking of the water column’s volume when water masses with different temperatures are mixed, which lowers the water column’s center of mass and thus acts to convert PE into KE; and (iii) a reduced production of KE due to diabatic energy conversion of the KE convertible part of the PE to the KE inconvertible part of the PE. Under some simplifying assumptions, the authors also propose a theory to estimate the maximum depth of convection from an energetic perspective. This study provides a potential basis for improving the convection parameterization in ocean models.

MULTI–INERT OSCILLATORY MECHANISM

2020 ◽  
Vol 2 ◽  
pp. 19-25
Author(s):  
I.P. POPOV
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Oscillation Frequency ◽  
Free Oscillation ◽  
Initial Conditions ◽  
Oscillatory System ◽  
Harmonic Oscillations ◽  
Oscillatory Systems ◽  
Oscillatory Mechanism ◽  
Mutual Conversion

A mechanical oscillatory system with homogeneous elements, namely, with n massive loads (multi– inert oscillator), is considered. The possibility of the appearance of free harmonic oscillations of loads in such a system is shown. Unlike the classical spring pendulum, the oscillations of which are due to the mutual conversion of the kinetic energy of the load into the potential energy of the spring, in a multi–inert oscillator, the oscillations are due to the mutual conversion of only the kinetic energies of the goods. In this case, the acceleration of some loads occurs due to the braking of others. A feature of the multi–inert oscillator is that its free oscillation frequency is not fixed and is determined mainly by the initial conditions. This feature can be very useful for technical applications, for example, for self–neutralization of mechanical reactive (inertial) power in oscillatory systems.

Study of the Mechanisms of Vortex Variability in the Lofoten Basin Based on the Energy Analysis

2021 ◽  
Vol 37 (3) ◽  
Author(s):  
V. S. Travkin ◽  
◽  
T. V. Belonenko ◽  
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Baroclinic Instability ◽  
Positive Trend ◽  
Barotropic Instability ◽  
Available Potential Energy ◽  
Conversion Rates ◽  
Order Of Magnitude ◽  
The Mean ◽  
Mean Kinetic Energy

Purpose. The Lofoten Basin is one of the most energetic zones of the World Ocean characterized by high activity of mesoscale eddies. The study is aimed at analyzing different components of general energy in the basin, namely the mean kinetic and vortex kinetic energy calculated using the integral of the volume of available potential and kinetic energy of the Lofoten Vortex, as well as variability of these characteristics. Methods and Results. GLORYS12V1 reanalysis data for the period 2010–2018 were used. The mean kinetic energy and the eddy kinetic one were analyzed; and as for the Lofoten Vortex, its volume available potential and kinetic energy were studied. The mesoscale activity of eddies in winter is higher than in summer. Evolution of the available potential energy and kinetic energy of the Lofoten Vortex up to the 1000 m horizon was studied. It is shown that the vortex available potential energy exceeds the kinetic one by an order of magnitude, and there is a positive trend with the coefficient 0,23⋅1015 J/year. It was found that in the Lofoten Basin, the intermediate layer from 600 to 900 m made the largest contribution to the potential energy, whereas the 0–400 m layer – to kinetic energy. The conversion rates of the mean kinetic energy into the vortex kinetic one and the mean available potential energy into the vortex available potential one (barotropic and baroclinic instability) were analyzed. It is shown that the first type of transformation dominates in summer, while the second one is characterized by its increase in winter. Conclusions. The vertical profile shows that the kinetic energy of eddies in winter is higher than in summer. The available potential energy of a vortex is by an order of magnitude greater than the kinetic energy. An increase in the available potential energy is confirmed by a significant positive trend and by a decrease in the vortex Burger number. The graphs of the barotropic instability conversion rate demonstrate the multidirectional flows in the vortex zone with the dipole structure observed in a winter period, and the tripole one – in summer. The barotropic instability highest intensity is observed in summer. The baroclinic instability is characterized by intensification of the regime in winter that is associated with weakening of stratification in this period owing to winter convection.

scholarly journals Walking in simulated reduced gravity: mechanical energy fluctuations and exchange

1999 ◽  
Vol 86 (1) ◽  
pp. 383-390 ◽  
Author(s):  
Timothy M. Griffin ◽  
Neil A. Tolani ◽  
Rodger Kram
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Inverted Pendulum ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Metabolic Cost ◽  
Metabolic Energy ◽  
Gravitational Potential Energy ◽  
Reduced Gravity

Walking humans conserve mechanical and, presumably, metabolic energy with an inverted pendulum-like exchange of gravitational potential energy and horizontal kinetic energy. Walking in simulated reduced gravity involves a relatively high metabolic cost, suggesting that the inverted-pendulum mechanism is disrupted because of a mismatch of potential and kinetic energy. We tested this hypothesis by measuring the fluctuations and exchange of mechanical energy of the center of mass at different combinations of velocity and simulated reduced gravity. Subjects walked with smaller fluctuations in horizontal velocity in lower gravity, such that the ratio of horizontal kinetic to gravitational potential energy fluctuations remained constant over a fourfold change in gravity. The amount of exchange, or percent recovery, at 1.00 m/s was not significantly different at 1.00, 0.75, and 0.50 G (average 64.4%), although it decreased to 48% at 0.25 G. As a result, the amount of work performed on the center of mass does not explain the relatively high metabolic cost of walking in simulated reduced gravity.

scholarly journals An Analysis of the Energetics of Tropical and Extra-Tropical Regions for Warm ENSO Composite Episodes

2017 ◽  
Vol 32 (1) ◽  
pp. 39-51
Author(s):  
Zayra Christine Sátyro ◽  
José Veiga
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
El Niño ◽  
Energy Production ◽  
El Nino ◽  
Southern Oscillation ◽  
Stable Condition ◽  
The Other ◽  
Tropical Regions ◽  
Using Data

Abstract This study focuses on the quantification and evaluation of the effects of ENSO (El Niño Southern Oscillation) warm phases, using a composite of five intense El Niño episodes between 1979 – 2011 on the Energetic Lorenz Cycle for four distinct regions around the globe: 80° S – 5° N (region 1), 50° S – 5° N (region 2), 30° S – 5° N (region 3), and 30° S – 30° N (region 4), using Data from NCEP reanalysis-II. Briefly, the results showed that zonal terms of potential energy and kinetic energy were intensified, except for region 1, where zonal kinetic energy weakened. Through the analysis of the period in which higher energy production is observed, a strong communication between the available zonal potential and the zonal kinetic energy reservoirs can be identified. This communication weakened the modes linked to eddies of potential energy and kinetic energy, as well as in the other two baroclinic conversions terms. Furthermore, the results indicate that for all the regions, the system itself works to regain its stable condition.

scholarly journals The theory of the chain fountain revisited

2021 ◽  
Vol 2090 (1) ◽  
pp. 012166
Author(s):  
Dragos-Victor Anghel
Keyword(s):  
Energy Transfer ◽  
Kinetic Energy ◽  
Significant Role ◽  
Mechanical Work ◽  
Scientific Consensus ◽  
Energy And Momentum ◽  
Work Done

Abstract We analyze the chain fountain effect-the chain siphoning when falling from a container onto the floor. We argue that the main reason for this effect is the inertia of the chain, whereas the momentum received by the beads of the chain from the bottom of the container (typically called “kicks”) plays no significant role. The inertia of the chain leads to an effect similar to pulling the chain over a pulley placed up in the air, above the container. In another model (the so called “scientific consensus”), it was assumed that up to half of the mechanical work done by the tension in the chain may be wasted when transformed into kinetic energy during the pickup process. This prevented the chain to rise unless the energy transfer in the pickup process is improved by the “kicks” from the bottom of the container. Here we show that the “kicks” are unnecessary and both, energy and momentum are conserved-as they should be, in the absence of dissipation-if one properly considers the tension and the movement of the chain. By doing so, we conclude that the velocity acquired by the chain is high enough to produce the fountain effect. Simple experiments validate our model and certain configurations produce the highest chain fountain, although “kicks” are impossible.

scholarly journals Is the Ocean Speeding Up? Ocean Surface Energy Trends

2020 ◽  
Vol 50 (11) ◽  
pp. 3205-3217
Author(s):  
Carl Wunsch
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Ocean Circulation ◽  
State Estimate ◽  
Monotonic Trend ◽  
Energy Inputs ◽  
Oceanic Surface ◽  
Data Density ◽  
Power Inputs ◽  
Noisy Background

AbstractA recent paper by Hu et al. (https://doi.org/10.1126/sciadv.aax7727) has raised the interesting question of whether the ocean circulation has been “speeding up” in the last decades. Their result contrasts with some estimates of the lack of major trends in oceanic surface gravity waves and wind stress. In general, both the increased energy and implied power inputs of the calculated circulation correspond to a small fraction of the very noisy background values. An example is the implied power increase of about 3 × 108 W, as compared to wind energy inputs of order 1012 W. Here the problem is reexamined using a state estimate that has the virtue of being energy, mass, etc. conserving. Because it is an estimate over an entire recent 26-yr interval, it is less sensitive to the strong changes in observational data density and distribution, and it does not rely upon nonconservative “reanalyses.” The focus is on the energy lying in the surface layers of the ocean. A potential energy increase is found, but it is almost completely unavailable—arising from the increase in mean sea level. A weak increase in kinetic energy in the top layer (10 m) is confirmed, corresponding to an increase of order 1 cm s−1 yr−1 over 26 years. An estimate of kinetic energy in the full water column shows no monotonic trend, but the changes in the corresponding available potential energy are not calculated here.

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