American Journal of Physics

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American Journal of Physics

June 2021 Issue,

Volume 89, No. 6

Why does water shoot higher if we partially block the garden hose outlet?

It is a common experience that water shoots higher when we block a garden hose outlet by our thumb. But what causes this? How high does the water go? Does water from our neighbor's garden hose reach the same height? Is there an optimum outlet blockage that results in the greatest height that water can reach? Here, we show that a competition between viscous friction along the hose and the viscous dissipation at the thumb-generated constriction results in a variable water shooting height. Through systematic analysis, we demonstrate that depending on the municipal water main pressure, and length and diameter of the hose, the maximum water height may increase, decrease, or gain an optimum as the blockage ratio of the outlet varies.

Journal TOC Archive

EDITORIAL

In this issue: June 2021 by Beth Parks. DOI: /10.1119/10.0004797

Statistics, updates, and changes at AJP by Beth Parks. DOI: 10.1119/10.0004963

PAPERS

Interception and rendezvous: An intuition-building approach to orbital dynamics by Eric M. Edlund. DOI: 10.1119/10.0003489
The analysis of intercept and rendezvous of two spacecraft is mathematically challenging and is typically tackled by solving multiple differential equations. In this article, the author sidesteps these complications by choosing a geometry-based approach, making the topic suitable for the junior level mechanics course. An HTML JavaScript orbit calculator is also provided so that students (and their instructors!) can easily test their calculated solutions and strengthen physical intuition.

Why does water shoot higher if we partially block the garden hose outlet? by Mohammad-Reza Alam. DOI: 10.1119/10.0003512
You may have idly wondered why partially blocking a hose outlet makes the water shoot out faster, and then carelessly assumed that it had something to do with keeping the mass flow rate constant. But, of course, there’s no law of conservation of mass flow rate. Read this paper to find a better explanation. You’ll find not only a simple physical intuition and use of dimensional analysis, but also a treatment of fluid dynamics at a level appropriate for upper-level undergraduates in physics or engineering.

Not the garden hose instability: Wavelength selection in a buckling garden hose by Tianyi Guo, Xiaoyu Zheng and Peter Palffy-Muhoray. DOI: 10.1119/10.0003819
Imagine this. On a nice summer day, you have just watered your plants with a garden hose. You close the water inlet valve and then, before coiling up the hose, you release the water pressure by opening the outlet valve. As you watch, the garden hose spontaneously curves into a sinusoidal shape. This paper shows how the helical angle of the hose’s reinforcing mesh causes it to elongate upon pressure release. When it elongates, the hose will then spontaneously exhibit a buckling instability, which is responsible for its undulating shape. This effect has interesting consequences for the rigidity of hydroskeletons–fluid-filled tubes reinforced by helical filaments–in nature. This article provides a fun application of Euler’s self-buckling instability for undergraduate mechanics lectures or labs.

Energy loss and jerk on the loop-the-loop Video Abstract Icon by Karl C. Mamola and William A. (Toby) Dittrich. DOI: 10.1119/10.0003877
In a paper well suited to a first semester college physics course, analysis (without calculus) and video are used in a discussion of the loss of mechanical energy of a ball as it follows the loop-the-loop motion of a frequently used mechanics demonstration. Readers may be surprised to see the large effect of jerk, that is, the sudden change in the acceleration, even though the track is smooth. The above link will also take the reader to the article’s video abstract.

On viewing the Himalayas from the plains by Vijay A. Singh and Arnav Singh. DOI: 10.1119/10.0003920
Clearer skies due to the pandemic-induced lock-down inspired a fresh look at reported sightings of Himalayan peaks in the historical record. This pedagogical article can inspire problems for undergraduate students.

ArduinoTM microprocessors as a platform for modeling framework labs by Matthew J. Farrar. DOI: 10.1119/10.0004856
This paper shows how Arduino™ microprocessors can be used within a modeling lab framework to eliminate the “black box” aspect of data collection in the introductory lab.

Fréedericksz transition on air Video Abstract Icon by Juliette Plo, Dihya Sadi, Elio Thellier, Pawel Pieranski, Mehdi Zeghal and Patrick Judeinstein. DOI: 10.1119/10.0003350
An experiment is described in which the Fréedericksz transition, a phase transition involving liquid crystals, can be seen as well as heard in a classroom setting. The experiment uses a twisted nematic display as the capacitor in an RC oscillator circuit. Changes in the oscillator frequency are induced by applying magnetic and electric fields and detected using a software-defined radio. Extensive supplementary materials show how to re-create the experiment. The above link will also take the reader to the article’s video abstract.

Algorithm to visualize a 3D normal surface in anisotropic crystals and the polarization states of the o- and e-waves in uniaxial crystals by Luis Oscar González-Siu, Martha Rosete-Aguilar and Neil C. Bruce. DOI: 10.1119/10.0003427
An algorithm is presented to help students and teachers visualize the propagating electromagnetic field in uniaxial and biaxial crystals. This algorithm is implemented with Mathematica and can be useful in electrodynamics and optics courses at the undergraduate and graduate level.

Searching a quantum database with Grover's search algorithm by Ben Kain. DOI: 10.1119/10.0004835
This illustration of a useful quantum computing algorithm can be presented to undergraduate students who have not yet completed a quantum mechanics course, and includes code that can be run on IBM’s quantum computers. The demonstration uses Grover’s search algorithm, which searches an unsorted database faster than a classical algorithm. The standard presentation is expanded to produce a more satisfying and useful solution.

A new look at quantal time evolution by Aparajita Bhattacharyya, Jayanta K. Bhattacharjee and Debabrata Sinha. DOI: 10.1119/10.0003397
The time evolution of a Gaussian wave packet is evaluated in three potentials using the Heisenberg approach instead of the normal Schrödinger approach. Instructors of quantum mechanics will gain insight from this paper and may choose to develop problems to help their students better understand time evolution of wave functions.

Gravitational time dilation, free fall, and matter waves by Anna P. Czarnecka and Andrzej Czarnecki. DOI: 10.1119/10.0003448
Free fall in a gravitational field is explained as the effect of refraction of the quantum mechanical wave function due to time dilation. Read that sentence again. Then read the article.

BACK OF THE ENVELOPE

Naïve Bohr-type quantization for power-law potentials by Jacob Katriel. DOI: 10.1119/10.0004956
Since the number of quantum-mechanical potentials that can be solved exactly is limited, approximation methods are important. In this paper inspired by Sanjoy Mahajan’s “Back of the Envelope” treatment of power-law potentials (June 2020), the author shows how the Bohr quantization condition mvr=nℏ can be used to determine the dependence of energy levels on the quantum number n for spherically symmetric potentials. Results are exact for the hydrogen atom, harmonic oscillator, and the infinite square well, and asymptotically correct for the linear potential. This treatment is suitable for both beginning and more advanced students.

INSTRUCTIONAL LABORATORIES AND DEMONSTRATIONS

Soil analysis using a 2″ NaI gamma detector by Rebekah Aguilar, Patrick Powers, Nina Abramzon and P. B. Siegel. DOI: 10.1119/10.0003490
This paper shows how students can use a 2-in. NaI detector to measure the main sources of terrestrial gamma radiation in their environment, i.e., the 40K, 238U and 232Th decay series, and learn how to calibrate the detector for efficiency and sample self-absorption. This apparatus allows the experiments to be performed over two three-hour laboratory sessions so that even students in lower-level courses can learn about natural radiation in the environment.