2021 USAYPT Problems

Chatter Ring

The Chatter ring, also Gyro ring or Jitter ring, is a toy with small spinning rings, called beads, around a big hoop, called the ring.  The goal is to keep all of the beads spinning for as long, and as fast, as possible. [1]   Investigate how one works, both experimentally and theoretically.

[1] The Chatter Ring has been marketed also under the names Gyro Ring, Jitter Ring, and Flitter Ring, with a retail price of under US$20.

Lava Lamp

Edward Craven Walker and David George Smith invented the Lava Lamp in 1963[2], and it soon became a fad, remaining popular throughout the 1970s. Investigate, both theoretically and experimentally, the physics of lava lamps.

[2] The figure is from US patent US3387396A, which was filed along with UK patent GB1034255A, on March 18, 1964.

Modeling Impact Craters

What happens when a large rock hits a planet or moon?  Does it matter if it hits the water or land?  How much kinetic energy does it take to produce a crater of a particular diameter?   Where does this energy go during the impact?  What forms the central peaks found in some lunar craters such as Tycho [3] shown.
Conduct experiments designed to reproduce the shape of various terrestrial and lunar craters.  Use your experimental results, and appropriate scaling relations, to estimate the energy needed to produce observed impact craters.  How do your results compare with estimates from the scientific literature?

[3] The top figure is a mosaic of images taken with the Lunar Reconnaissance Orbiter, by scientists at NASA/Goddard and Arizona State University, while the bottom is a view of the central peak by the same team.

Joseph Henry’s Rocking Motor

In 1831 Joseph Henry invented the first electromagnetic motor, or as he put it:  “I have lately succeeded in producing motion in a little machine by a power, which, I believe, has never before been applied in mechanics—by magnetic attraction and repulsion.”[4]  Read Henry’s article and reproduce his experiment.  Clearly explain how it works using Henry’s reasoning, and then using modern electromagnetic field theory.  Next, design and build, a solar powered electromagnetic rocking motor optimized for pumping water in an arid rural area.

[4]Henry, Joseph, On a Reciprocating motion produced by Magnetic Attraction and Repulsion, American Journal of Science and Arts, (1831) Vol. XX, No. 2, Art. XVII, pp. 240-343.

Notes from the Problem Master

Clarification of the term investigate:

All the problems require both a theoretical and an experimental investigation.  To investigate something theoretically, it means that you must start with clearly stated assumptions and derive, or calculate, from those what you expect to measure.  This process is called deductive reasoning.  To investigate something experimentally, it means that you must control variables and test hypotheses.  This is the process of inductive reasoning.  Good science combines inductive and deductive reasoning.  Good physics is both theoretically derivable and experimentally testable.

In practice, however, real things are complicated, so we usually start with grossly simplistic assumptions, called hypotheses, and use deductive reasoning to build a toy model that can predict the results of an experiment.  Through the process of inductive reasoning, we compare our toy model to experimental measurements, and evaluate our assumptions.  By iterating between deductive and inductive reasoning, we learn which assumptions to keep, and which need to be lifted, until the model’s predictions match the experiment.

Academic honesty and sources of information:

When you embark on researching a new topic, often you will refer to a source for information, such as a:  book, journal article, patent claim, data archive, or any other source of information.  In all of these cases, it is important to be clear about where the information came from, which you do by citing each source in context.  You never want to confuse your work with work done by others.  Whenever possible, it is good practice to find, read, and cite primary sources, which were authored by the scientists who did the actual work.  If you took the time to read the literature about a topic, and you make that clear, the jurors will reward you for it.

Understanding where data come from is particularly important in science.  For example, it is acceptable to use public scientific data, so long as you analyze them yourselves and clearly cite where they came from.  Even fundamental constants are measured (or used to define the SI), and need to be appropriately cited.

A PDF of this is also available.