Problems from USIYPT
2020 Problems
The Astronomical Unit: By 1700 AD all observable sizes and distances in the solar system could be measured, but only in ratio to the semi-major axis of Earth’s orbit. This led to odd results. Ole Roemer, for example, measured the speed of light in ratio to the orbital velocity of Earth, and Newton calculated the mass of the Sun in ratio to Jupiter’s mass. However, neither the speed of light, nor the mass of the sun, could be found in standard units until the mid nineteenth century. In fact, this was such a problem that scientists traveled the world in order to observe the 1761 and 1769 transits of Venus in hopes of measuring the distance between the Sun and the Earth. Measure the length of one Astronomical Unit. If your result depends on other physical or astronomical quantities, you should measure as many of these that you can.
The Archimedes Death Ray: The great Sicilian engineer Archimedes (c. 287-212 BC) famously fought off the Roman invasion of Syracuse using his many high-tech inventions. While most of his booby-traps relied on mechanical advantage, such a pulleys and levers, the most famous invention was a giant heliostat that sunk Roman warships. As legend has it, Archimedes instructed each soldier to highly polish his shield and reflect the morning sun to light each Roman ship ablaze. The television show Mythbusters devoted three episodes to testing the physical feasibility of the “Archimedes Death Ray” (29-September-2004, 25-January-2006, 8-December-2010), and declared the story implausible in all three episodes. However, a group at the Massachusetts Institute of Technology (MIT) came to the opposite conclusion after performing a successful experiment in 2005. Investigate, experimentally, theoretically, and historically, the story’s feasibility.
Spherical Magnets: Sets of 216 strong spherical magnets are sold in 6x6x6 cubes, which make wonderful toys for anyone old enough to know not to eat one. According to neocubes.com: “The magnetic balls will almost mystically guide your hands to build complex fractal patters and other symmetric designs found everywhere in nature and space.” Investigate, both experimentally and theoretically, the stable configurations that these can make.
The Apparent Weight of an Hourglass: As the sand flows from the top to the bottom of an hourglass, does it appear to weigh more, or less, than it does after the sand stops? On the one hand, some of the sand is in free fall so it is not in contact with the scale, but, on the other hand, an additional upward force is needed to stop the sand when it hits the bottom pile. In their 2017 paper, Achim Sack and Thorsten Pöschel answered this question for one particular hourglass using one particular line of reasoning.[1] Investigate the apparent weight of multiple hourglasses, using more than one line of physical reasoning. [1] See: A. Sack and T. Pöschel, “Weight of an hourglass - Theory and experiment in quantitative comparison,” American Journal of Physics, 85, 98 (2017). Photo from justhourglasses.com.
2019 Problems
Extraterrestrial Rainbows: When it is both sunny and rainy, we see rainbows. What if, rather than water, it rained some other clear liquid, as it does on Saturn’s moon Titan? If, someday, future astronomers took a picture of a non-water rainbow, could they determine the chemical composition of the raindrops from the image? Investigate, both experimentally and theoretically, the physics of rainbows caused by a variety of clear liquids.
Faraday's Homopolar Generator: Michael Faraday set up a round copper plate in a magnetic field and used it to generate current, which he measured using a galvanometer. Reproduce Faraday’s experiment. Investigate how it works both experimentally and theoretically.
Juggling Hammers: Hold a typical carpenter’s hammer with the claw up. Throw it in the air, catching it by the handle after a single rotation. The claw will still be up. Paradoxically, if you turn it 90 degrees and throw the hammer again, the claw will now be on the opposite side. Investigate this both experimentally and theoretically.
Pneumatic Tube Mail System: Up until the mid 20th century, pneumatic mail systems were installed to quickly transport small items over short distances but they sometimes exploded when scaled up over longer distances. Design, and build, a working pneumatic tube mail system. Investigate the feasibility of using such a system for high-speed travel.
2018 Problems
The Moon’s Orbit: Measure the moon’s three main orbital elements: (1) the period of its orbit, (2) the eccentricity of its orbit, and (3) the semi-major axis of its orbit.
Electromagnetically Coupled Mechanical Oscillators: Set up a system of coupled mechanical oscillators, but rather than coupling them using a mechanical device, such as a rod, they must be coupled electromagnetically without any external power source. How does your system work fundamentally?
rojectile Motion through Air: For this problem, you are to investigate the motion of a spinning ball theoretically and experimentally. How, and under what circumstances, does the Galilean model need to be adapted?
Incandescent Light Bulbs and Blackbody Radiation: Use common incandescent light bulbs to verify the proportionality laws of both Stefan and Wien.
2017 Problems
Granular Materials: Build an apparatus that performs the following procedure: a rectangular container is placed on a vibrating base. The container is split into two equal parts by a vertical wall that is shorter than the outer walls of the container. An equal number of beads are placed in both containers at a level slightly less than half the height of the middle wall. As the base oscillates up and down at a constant frequency the beads jump above the middle wall from side to side; eventually they will all be in one side of the container. Explain this phenomenon and estimate how long the process takes for your apparatus.
Blowpipe: Investigate the motion of a projectile inside a blowpipe. Determine the conditions for maximum exit velocity when blown by the mouth.
Geyser 3: Support a long, vertical tube containing water. Heat the tube directly from the bottom and you will observe that the water erupts. Arrange for the water to drain back into the tube to allow repeated eruptions. Investigate the parameters that determine the eruption frequency.
Planck's Constant: Use LEDs to measure Planck’s constant, and explain the theoretical basis for your experiment. Measure the wavelength of the LED light directly, without relying on the manufacturer's data. Describe the precision of your experiment and discuss if your margin of error covers the currently accepted value of the constant. You must build the experiment yourself from standard electronic parts, without relying on a commercially available Planck's constant apparatus.
2016 Problems
Domino Toppling: On 6 August 2014, in Charlotte, North Carolina, a team from Prudential Financial broke the Guinness World Record for toppling the largest domino stone, measuring roughly 30 ft x 15 ft x 3 ft. Each domino in the chain had the same aspect ratio of 10:5:1. Study this phenomenon, then design and construct a domino chain whose overall lateral length before toppling is 3 meters, that starts with a domino stone that you can hold in your hand, and will topple the tallest possible stone. You may change the aspect ratio of your domino stone chain, however all stones must have the same aspect ratio, and all stones must be constructed of the same materials and in the same manner. You must launch the initial, smallest stone with a gentle finger push that topples that stone.
Blender Lift: If you hold an immersion hand blender's blades under water in a beaker or pot or pail, under certain circumstances you can lift the beaker and the water by lifting only the hand blender as shown in the picture below. Study this phenomenon for a wide range of the relevant parameters comparing your theory that explains the effect to the experimental results. Predict the maximum weight of water and container that your blender can lift and verify this prediction by experiment.
Transformer Impedance Reflection: A YouTube video titled "Transformers – Experiments and Demos" shows a demo at the 4 minute mark. The demo purports to show that removing a light bulb in the secondary circuit of a transformer will cause a light bulb in series with the primary to turn off, i.e., "a impedance reflection. " Analyze this demo and the published explanation of this effect (W. Layton Transformer Impedance Reflection, The Physics Teacher 52 (7), Oct 2014, p. 426-427). Provide theoretical and experimental evidence to explain or refute this effect.
Bouncing Laser Beam: A laser will curve and even bounce in a medium whose index of refraction decreases with height. Although there are several ways to produce this medium, the photo below was created by pouring thick, transparent Karo syrup into a tank and then pouring water on top of the syrup. Approximately 12 hours later, the bouncing laser beam can be observed. Create this apparatus or a similar one, study the theory of this effect, and use your results to measure the index of refraction of the medium as a function of height from the bottom of the tank.
More can be found at http://physics.randolphcollege.edu/usaypt/past/