The Physics of Pool/Billiards

When I was growing up, I had a pool (billiards) table in my basement (I will refer to it at pool in this post). Although I was not a very dedicated player, I would always go down and occasionally play either by myself or with my brothers. Even at Colgate, I still sometimes go to the SRS house (100 Hamilton) and play pool there with some of my friends. When I think about how pool works, I realized that we can essentially boil it down to momentum and collision (mostly elastic). 

Because we are assuming that the collisions are mostly elastic, we have conservation of momentum and conservation of kinetic energy. When hitting the cue ball into another ball, we can use the equation mAvA = mAvA’ + mBvB’ with A being the cue ball and B being the ball it hit (at rest). Because the masses of the cue ball are the same as the other balls on the table, we can say that mA and mB are the same. Therefore, we have vA = vA’ + vB’.

Because we are assuming it is an elastic collision, kinetic energy is conserved, meaning that we have KEi = KEf . We can rewrite as ½ mA(vA)2 = ½ mA(vA’)2 + ½ mB(vB)2 . Again, because mA and mB are the same, we have (vA)2 = (vA’)2 + (vB’)2 .

Therefore, using the two equations above, we can draw the velocity vectors to form a triangle as shown below, except V1A is vA and V2A is vA’ and V2B is vB’.

As a result, ball A moves in a direction perpendicular to that of ball B after the collision, assuming that the collision is not head-on. 

Dr. Gaurav Arya

I researched Dr. Gaurav Arya, who is currently an associate Professor of Mechanical Engineering and Materials science at Duke University. He received his Bachelor's in Technology at the Indian Institute of Technology (India) in 1998, earned his PhD at the University of Notre Dame in 2003, and completed his Postdoc at Princeton University from 2003-2005. He was then an Assistant Research Scientist at New York University from 2005-2007. From there, he ended up at Duke University being appointed not only as an associate Professor of Mechanical Engineering and Materials Science, but also an Associate Professor of Biomedical Engineering and an Associate Professor of Chemistry. He heads a research lab which combines technology, physics, biology, biostatistics, and chemistry to help students gain a "molecular-level understanding of  biological and soft-material systems, with the aim of discovering new phenomena and developing new technologies". He divides his current research interests into four categories: genome organization and regulation, polymer-nanoparticle composites, viral-DNA-packaging, and DNA nanotechnology. 

One paper that was published pretty recently (on October 30 by Dr. Arya and Brian Hyun-Jong Lee (a student at Duke pursuing his PhD) was titled "Analytical van der Waals interaction potential for faceted nanoparticles". Using calculus, physics, and technology, they were able to come up with an analytical model for van der Waals forces between faceted nanoparticles. They were able to compute exact atomistic calculations and compared them to the model and they ended up yielding only insignificant errors in predicted energies across all relevant particle configurations. In addition, they also developed a user-friendly interface application for implementing the model. Furthermore, this model is useful in the sense that it will help reduce the amount of work in future faceted nanoparticle investigations that require the calculation of interparticle interactions. This paper is representative of the type of work that Dr. Arya does in his lab, where he works with other students to produce other publications and papers, such as "Kinetically assembled binary nanoparticle networks" and "Orientational phase behavior of polymer-grafted nanocubes".

The work that Dr. Arya publishes shows that there are not only a lot we still can learn when it comes to the realm of biophysics, but also that there are many useful applications the result from his research. For example, in a basic chemistry class, you would learn about Van Der Waals forces but not actually understand the mechanics behind them. Not only did Dr. Arya and Brian Hyun-Jong Lee explore that, but they were able to come up with a model that predicts the interactions between those nanoparticles and the Van Der Waals forces. 

Sources: 

https://www.researchgate.net/profile/Gaurav_Arya3

https://mems.duke.edu/faculty/gaurav-arya

Dr. Leslie Yeo

            Dr. Leslie Yeo is both a professor of chemical engineering and the director of the Micro/Nanomedical Research Centre at the Royal Melbourne Institute of Technology in Australia. In 1998, Dr. Leslie Yeo graduated with a master of chemical engineering from the Imperial College of London and received a PhD in chemical engineering in 2002 from the same institution. Today, Dr. Leslie focuses his research upon microfluidics driven by acoustics and electrokinetics with special attention to the engineering and biomedical fields. 

Dr. Yeo is also the Editor-in-Chief of the Biomicrofluidics journal from the American Institute of Physics and is an Editorial Board Member for the Scientific Reports and Interfacial Phenomena & Heat Transfer journals. His recent research on high frequency sound waves has shown for the first time new possibilities for the application of sound waves in medicine and manufacturing of smart materials. These applications include drug and vaccination delivery through the lungs rather than the current use of injections, nano-coatings that could protect drugs, sustainable smart materials, and nanosheets. 

This current research being led by Dr. Yeo shows the little we currently know about high frequency sound waves and opens a variety of useful applications as the study continues. The team has patented new methods of drug delivery that could eliminate the need for needle vaccinations. Further, they have discovered a use of these sound waves which produces metal-organic frameworks much more sustainably than in the current moment. This research is incredibly important and may alter the practice of medicine and development of smart materials in a world that is increasingly reliant upon sustainable practices. Dr. Yeo’s research shows opposition to classic theories of physics and demonstrates the opportunity for their development as knowledge advances.

Sources:

https://www.rmit.edu.au/contact/staff-contacts/academic-staff/y/yeo-distinguished-professor-leslie

https://www.sciencedaily.com/releases/2020/11/201124101029.htm

Dr. Bing Zhang

 

Dr. Bing Zhang is a theoretical astrophysicist conducting research at the University of Nevada, Las Vegas (UNLV), where he is currently serving as a Distinguished Professor in the Department of Physics and Astronomy and as an Associate Dean for Research in UNLV’s College of Sciences.  He also became a Fellow of the American Physics Society in 2015.  His research is focused on high-energy astrophysics, involving the study of some of the universe’s most powerful energetic phenomena, such as gamma-ray bursts, radio pulsars, and the bodies that produce them, such as black holes, neutron stars, and magnetars.

Dr. Zhang’s passion for astronomy began while he was a young student living in China.  He was fascinated by the concepts of space, time, and infinity, and he decided to pursue these interests by enrolling at Peking University.  Though originally a geophysics major, he later entered Peking University’s graduate school for astrophysics and obtained his PhD in 1997.  After serving as a research associate for NASA’s Goddard Space Flight Center and completing his postdoctoral work at Penn State, Dr. Zhang joined UNLV in 2004, where he still conducts research today.

Currently, Dr. Zhang is studying the phenomena of fast-radio bursts (FRB’s), mysterious radio wave emissions that emanate from the far reaches of outer space.  Recently, Zhang and his international research team’s work on determining the source of FRB’s was published in the journal Nature.  Using his team’s own radio telescope and those of two other collaborators, the researchers provided evidence that FRB’s can originate from magnetars, which are a class of dense neutron stars that are known as some of the most magnetized bodies in the universe.  The team also showed that FRB’s can emanate very close to home, with one radio burst being detected from within the Milky Way.  Though Zhang agrees that his work is not exactly done for a practical purpose, he wishes to stoke curiosities with his research and hopes that the work of astrophysicists today may be used for good in the future.

References

1. http://www.physics.unlv.edu/~bzhang/

2. https://www.unlv.edu/news-story/astrophysicist-bing-zhang-elected-aps-fellow

3. https://phys.org/news/2020-11-astronomers-clues-unveil-mystery-fast.html

The Physics of the Greenland Ice Sheet

I researched Dr. Aurélien Mordret after reading the article “Monitoring southwest Greenland’s ice sheet melt with ambient seismic noise.” Dr. Mordret is a French geophysicist. He got an undergraduate degree in Seismology from Strasbourg University and PhD from Institut de Physique du Globe de Paris, France. He is interested in many aspects of seismology, including volcano seismology and industrial seismology. 

The paper of his that I read is about using seismic noise to quantify the changes in the Greenland Ice Sheet volume. Increases and decreases in the snow pack impacts the subsidence and uplift of the crust under the ice sheet, which creates variations in the seismic wave velocity of the ice sheet. The differences in the seismic wave velocity can be seen particularly when examining different seasons; there is a decrease in seismic velocity during the summer when the ice melts and an increase in winter when more ice forms.

Using ambient seismic noise to measure the variations in seismic wave velocity, Dr. Mordret can gain data on the short-term fluctuations of the ice sheet, which is helpful for predicting the volume of ice that will melt in the future. Using the physics concept of looking at sound waves was not a method of gathering data on ice sheets that I had encountered before, and I thought that it was a really interesting paper and concept. Dr. Mordret’s work is an example of how researchers can use physics to understand anthropogenic climate change.

The Physics of a Viral Video

For those that remember and were fans of Vine, there was a viral video in 2014 of an 11 year old boy screaming with happy enthusiasm while being hit in the head with a basketball. I wondered, how does this kid not have any brain damage or a concussion from getting hit so hard? Well, I was able to find the answer with physics!

The basketball bouncing off the kid’s head was an elastic collision: thus, energy and momentum had to be conserved. First, I analyzed the momentum of the system:

Δpsys= 0kgms → p’ = p

mcvc’+mbvb’=mcvc+mbvb

In the video, the boy does not have an initial velocity, and the basketball only comes in contact with his head. According to GW Osteopathy (https://www.gwosteopathy.co.uk/much-head-weigh/), the average human head has a mass of about 5kg. Because this is a child, I used 4.5 kg as the mass of his head. A standard NBA basketball (as in the video) has a mass of 0.62 kg. To find the initial velocity of the basketball, I used Tracker software that is used in the lab. Thus, the initial velocity of the basketball was found to be -5.52 m/s. I was able to substitute these values into the equation above:

mcvc’+mbvb’=mcvc+mbvb

(4.5 kg)vc’+(0.62 kg)vb’=(36 kg)(0 m/s)+(0.62 kg)(-5.52 m/s)

Because this was an elastic collision, energy was also conserved. Thus, the following equation could also be used:

vc+vc’=vb+vb’

0+vc’=(-5.52 m/s)+vb’

vc’=(-5.52 m/s)+vb’

This was then substituted into the equation for conservation of momentum, and both final velocities were calculated:

(4.5 kg)(-5.52 m/s+vb’)+(0.62 kg)vb’=(36 kg)(0 m/s)+(0.62 kg)(-5.52 m/s)

vb’= 4.18 m/s

vc’=(-5.52 m/s)+vb’

vc’=-5.52 m/s+4.18 m/s

vc’=-1.34 m/s

With the initial and final velocities of both the child and the basketball, the force on the child’s head could be calculated using impulse. Tracker software also showed that the collision occurred over 0.05 seconds:

ΣFΔt=Δp

F(0.05 s)=(4.5 kg)(-1.34 m/s - 0 m/s)

F=-120.6 N

It is known that the human head can withstand about 90 g’s before sustaining a concussion. Thus, this force was converted into an acceleration in g’s:

F=ma

-120.6 N=(4.5 kg) a

a=26.8 m/s2=2.73 g

The 2.73 g’s that the boy experiences in this video is much less than the 90 g’s needed to get a concussion! If you’re curious about the viral video, it can be found in this Buzzfeed article.

Unmasking COVID-19: Exhalation Valves DO NOT Slow the Spread

National Institute of Standards and Technology (NIST) research engineer, Matthew Staymates, has recently examined the effectiveness of exhalation valves in stopping the spread of COVID-19. 

Using a schlieren imaging system, Staymates was able to show airflow dynamics of a person wearing an N95 mask with an exhalation valve and without an exhalation valve. With a schlieren imaging system, exhaled breath becomes visible because it is warmer, and therefore less dense, than the surrounding air. Valves are typically placed on masks to allow for easier breathing and allow air to escape unfiltered. However, Staymates' videos show that N95 masks allow air to pass right through.

Staymates also wanted to examine the movement of exhaled droplets since droplets are one major source of spreading COVID. He decided to build an apparatus that emits air the same as a resting human does and connected the device to a mannequin to best simulate actual human breath. An LED light placed behind the mannequin then illuminated the airborne droplets, which scattered the light and allowed them to appear brightly on the camera. He discovered that droplets escaped unfiltered through the valve of an N95 mask. Overall, Staymates' research shows that masks with valves do not slow the spread of COVID and should not be worn for the purpose of stopping the spread.

Staymates was quoted as saying: "I don't wear a mask to protect myself. I wear it to protect my neighbor, because I might be asymptomatic and spread the virus without even knowing it," Staymates said. "But if I'm wearing a mask with a valve on it, I'm not helping."

Matthew received his Bachelor's of Science and Master's of Science degrees in Mechanical Engineering at Penn State University and has had over 25 published research projects. His research interests focus on improved metrology technologies for evaluating trace explosives and narcotics detection technology. He also has great interest in fluid dynamics and particle release mechanisms. He decided to temporarily shift his interests towards mask design to help slow the spread of COVID. He is currently the Explosives Safety Officer for NIST and oversees the safe handling of high explosives and energetic materials. SUPER COOL!

Sources:

https://phys.org/news/2020-11-valves-n95-masks-filter-exhaled.html

https://www.nist.gov/people/matthew-e-staymates