What is the fastest articulated motion a human can execute?

Us humans are unique among animals in our ability to throw projectiles at great speeds, with very high accuracy. This motion, facilitated by muscles and tendons in the shoulder, creates the fasted articulated motion a human can execute.

Neil Roach, a researcher at George Washington University, explains that the ability for the muscles and tendons in the shoulder to store energy is the result of three main evolutionary changes in humans' upper bodies. "The expansion of the waist, a lower positioning of the shoulders on the torso, and the twisting of the humerus," were the three changes that appeared at the same time as our ancestors' shift toward more hunting, and less gathering/scavenging. Roach argues that throwing was incredibly important in our ancestors' development of hunting behavior.

Roach has used 3-D motion capture system, similar to our use of iPhone cameras and motion analytics in phys 111L, to track the motion of collegiate baseball players' arms as they throw. They analyzed the data using kinetics and attributing forces, and were able to estimate forces needed to create each certain motion at each certain joint. Roach and his colleagues found that humans store elastic energy in their shoulder as they "cock" their arms back to throw.

Assuming that energy is conserved among a human, his arm, and the ball he or she is throwing...

△KE=-△PE

KEf+ PEf = KE0 + PE0

Therefore...

the chemical potential energy in the humans' body is converted into kinetic energy, as he/she cocks back the ball in their hand. This kinetic energy is converted into spring potential energy, which is quickly converted into kinetic energy again, propelling the ball forward. All of the chemical energy used at the beginning of the process has been converted into kinetic energy of the ball (again, assuming that there are no non-conservative forces). 

The velocity at which the ball with a known mass is thrown can be determined if that quantity of transferred energy is known, by plugging △KE and m, and letting V0 be 0 m/s, and solving for Vf  in the equation...

△KE=(1/2)m(Vf^2 - V0^2)

Roach was the first research of his kind to link this throwing ability to evolutionary changes at the time of increased hunting in our ancestors. 

http://phys.org/news/2013-06-fastest-articulated-motion-human.html

A Very Blustery Day

As the wind picks up in Hamilton this fall, our Physics 111 class has moved on from kinematics to the study of Energy and Work. While helping my roommate (an environmental studies major) with a project, I came across many articles on the harnessing of eco-friendly energy. The inner workings of wind turbines caught my attention.

The purpose of a wind turbine is to take kinetic energy (wind energy) and change it into electrical energy. To determine kinetic energy from the wind, we start with the basic formula:

KE = 1/2 * mass * velocity^2

In our equation, velocity is equal to wind speed. But what about mass? At first, I was puzzled, but mass in this case has to be related to the volume and density of the air hitting the rotors of the wind turbine, so:

KE(wind) = 1/2 * air volume * air density * velocity^2

The above equation would allow you to find the kinetic energy of the wind, which (theoretically, some is lost) is transferred into electrical energy. Generally when measuring wind energy, a more useful equation tells us the power of the wind. Power is essentially energy divided by time. Obviously, determining the wind energy over time helps us see where best to place wind turbines and whether they are being effective. The equation for wind power is:

P(wind) = (KE wind)/(change in time)

Wind turbines change wind energy into electrical energy, but really this is only one form of kinetic energy into another. There is much ongoing research about using wind turbines to change the kinetic energy of the wind into a stored potential energy. Particularly, there is interest in integrating energy storage with energy generation. 

After wind turbines convert wind energy into electrical energy, this electrical energy needs to further be converted into an energy that can be stored. When it is time to harness this energy, it is then converted back into electrical energy. Each of these conversions causes a loss of energy and is also fairly expensive. Integrating energy storage inside a wind turbine could give access to a more constant flow of electrical energy when it is needed and eliminate some energy conversions. 

For example, wind turbines (as windmills used to do) could pump water up a hill and then whenever people choose to release the water they could harness that energy and convert it to electrical energy. The author of my article suggests using gas compression as a means to store potential energy converted from wind energy inside the wind turbine.

I think it's neat that energy is all around us and that by being a little more inventive we can find all sorts of harmless ways to create usable energy.

http://spectrum.ieee.org/energywise/energy/renewables/an-energystoring-wind-turbine-would-provide-power-247

http://www.energy-fundamentals.eu/15.htm

JT's Dance Moves Coming to the Big Screen (Kinda)

http://time.com/4510426/justin-timberlake-documentary-netflix/

As we all know, Justin Timberlake is a multitalented sensation who has graced our TVs and radios with his comeback in recent years. So great is his entertainment value that Netflix has deemed him worthy of a documentary following his most recent tour, the 20/20 Experience. While most artists have a vast wardrobe that they rotate through for shows, ever-classy JT's perpetual suit-and-tie look services him beyond just making the ladies swoon. He is able to harness the power of the smooth-soled dress shoe in ways that many of us at various weddings, bar mitzvahs, etc. have fallen prey to on the dance floor. Anyway, there's some science involved.

Lee et al. document the coefficient of kinetic friction of dress shoes on a treadmill to be 0.20 (surprisingly, there aren't many resources documenting shoe friction. Go figure.) Since treadmills are theoretically made to aid  running, let's assume that this coefficient is 0.05 higher than that of dress shoes on a stage. Let's also assume that our superstar doesn't have custom-made shoes specifically for dancing (he totally does). Most of Justin's moves involve sliding in some capacity. As he slides forward on one foot (see picture below. Ok enough staring, we have physics to do), his initial acceleration is in the forward direction from the push off his other foot, and friction is resisting the movement. If we google his weight, we find it is 76kg, which we can use to find the normal force.

The only force acting on his movement after his pushing foot leaves the ground is the force of friction. His acceleration is negative since he is slowing down. We see the frictional force (76*9.81*.15) is equal to 110 N. Therefore, using kinematics equations, he can calculate the force he needs to push off with in order to travel a certain distance in a certain amount of beats. He also does some really cool spins and jumps and moves on his toes but that's physics for another day.

https://www.ncbi.nlm.nih.gov/pubmed/22098188
http://healthyceleb.com/justin-timberlake-height-weight-body-statistics/5427
http://www.dailymail.co.uk/tvshowbiz/article-2297186/Justin-Timberlake-The-20-20-Experience-review-Justin-strutting-new-beat.html

Bend It Like Beckham

Throughout almost every type of sport, the ability to purposely curve the ball's trajectory is absolutely vital. Mariano Rivera became the greatest closer of all time thanks to his devastating usage of a pitch called the cutter, while across the pond, David Beckham shocked the world enough to create the saying "Bend It like Beckham". With one kick of the ball in the World Cup qualifying, David Beckham scored the "Goal that Shook the World", knocked Greece out of the qualification, and sent England to the 2002 World Cup. Apart from the hours and hours of physical preparation, training, ball work, and shooting practice, the physics that impacted the ball and made the event possible exist in every day activities and occurrences.

http://www.real-world-physics-problems.com/physics-of-soccer.html

The striking of the ball involves an elastic collision between the ball and the players foot. The kinetic energy of the moving foot is conserved and transferred into the ball, resulting in the ball picking up speed and moving forward. Beckham's unique free kick involves an incredible amount of spin and bend on the ball which allows him to move the ball around the wall and away from the goalie. This involves the Magnus Effect and the force of friction.

Once airborne, the ball acts like a projectile and follows kinematic behavior. Therefore, the initial work done by the player, the force applied over a distance to move the foot, the conservation of kinetic energy in the strike of the ball, the various forces acting on the ball to give it direction and spin, and the kinematics of the ball all lead to an incredible entertaining spectacle that transcends country lines and bonds cultures.

Smashing Pumpkins, anyone?

http://www.cbc.ca/news/canada/new-brunswick/pumpkin-fling-miramichi-1.3776150

The above article, written by Jordan Gill from CBS News, discusses an annual event that occurs in New Brunswick, Canada on the Miramichi River. While many are welcoming the new season through apple picking, drinking homemade apple cider, or purchasing their first ripe pumpkin, there are handfuls of people in New Brunswick that opt to welcome Fall by smashing pumpkins -- and no, not for baking pumpkin pie.

Image of the pumpkin launcher.  
url: http://www.cbc.ca/news/canada/new-brunswick/pumpkin-fling-miramichi-1.3776150

The leaders of this event, which is rightly called the Fall Harvest Pumpkin Fling, are from the Association of Professional Engineers and Geoscientists of New Brunswick. With the goal to educate the group about science, the masterminds behind the event encourage the attendees (mostly children) to load up the pumpkin launcher and estimate where the pumpkin will land in the water or on the land. While this might be quite the challenge for an elementary child or an adult that hasn't taken a physics course recently, this would be second-nature to the Physics 111 students (hopefully!). 

Here's what I would do if I were in this scenario. According to the article, the pumpkin launcher is more than 4-meters in length. I would need a meter-stick (to determine the launcher's height above the water), a protractor (to calculate the angle that I launch the pumpkin), a radar gun (to determine the velocity), and a stopwatch (to determine the total time it takes the pumpkin to 1) reach its maximum height and 2) land in the water). Using this information as the basis for my projectile motion-like problem, I would use the kinematic equations to solve for Δx.  Alternatively, given the time it took for the pumpkin to land in the water and the landing distance, I could determine the velocity of the launcher. 
The Fall Harvest Pumpkin Fling, which recently occurred on 9/24/16, would have been a fun supplementary field-trip for Physics 111, had it happened a few weeks back in the midst of the kinematic lessons. In the meantime, if you or your friends have an urge to smash some pumpkins, maybe take the time to think about the physics side of your Fall-time hobby and determine the velocity or displacement of your free-flying pumpkin!

Bend it Like Ligety

http://www.nytimes.com/newsgraphics/2014/sochi-olympics/giant-slalom.html

A few years ago, the International Ski Federation (FIS) changed the regulations for giant slalom (GS) skis to make them longer, straighter, stiffer, and generally harder to bend. The New York Times published an interactive article during the Sochi Olympics that highlighted American ski racer Ted Ligety’s unmatched ability to adapt to the new GS ski regulations. Most skiers were unable to adapt to the new regulation, and resorted to skidding the tops of their turns, but not Ted Ligety. As described by the New York Times, “the trace of his path is smoother and more serpentine than that of his foes, who ski in somewhat violent fits and starts, sliding into the turns and making adjustments that spray snow.”           

The first panel of the news-graphic says “through each turn, Ligety is so low that he is nearly sitting on the snow, and the edges of his skis for a nearly 90-degree angle with the snow.” This “nearly 90-degree angle” is crucial to the explanation of why he is so good at GS. So why does having a higher edge angle lead to a more bend ski? It has to do with the horizontal component of force applied to the middle of the ski by the skier’s legs.

If a skier is standing straight up, they have a 0^o edge angle and the skis do not bend at all. On a standard coordinate system, this downward vector would be at -90^o, and Cos(-90^o)=0. There is no horizontal component to the force on the ski when they are flat on the snow and the skier’s legs are straight beneath them. However, as the edge angle approaches 90^o, and the skier’s legs move from -90^o to 0^o on the standard coordinate plane, the horizontal component of their force approaches the total force that the skier is applying on their skis. Ted Ligety gets the best angles out of anyone, which explains why he can carve tighter arcs on the new equipment than anyone else can.

 

Self-Driving Cars Become a Reality

Yesterday, the New York Times announced that self-driving cars have received backing from the federal government.

According to the article, last year, nearly 40,000 people died in automobile accidents in the US. In theory, self-driving cars have the potential to change that. If all cars on the road are self-driving, no one can have accidents, right?

Unfortunately, it's not quite that simple. In fact, self-driving cars have created some of the most difficult ethical puzzles for our generation. Programmers must now determine whether cars should attempt to minimize a loss of life in general, or prioritize the life of the car's passengers. For instance, if an autonomous car is heading toward a crowd of people, should it continue forward, risking many lives, or spin off the road, risking its passengers' safety?

This problem has recently become much more relevant. According to the New York Times article, the first fatal self-driving car collision occurred this past May, when an automated Tesla crashed into a tractor-trailer in Florida.

Based on the results of the crash report from the National Transportation Safety Board, I calculated the speed at which the car was traveling when it crashed into a utility pole on May 7, 2016. At the time of impact, the car was traveling at 74 mph (33 m/s), nine mph above the posted speed limit on the Florida highway. After the collision, the car coasted off the road for approx. 297 feet (90.5 m) before colliding with a utility pole. The car then broke the pole and continued for an additional 50 feet while rotating counterclockwise, but I only calculated the speed at the time of impact with the utility pole.

During this 297-foot journey post-collision, the only force acting on the car in the x-direction (disregarding drag) was the force of friction. The weather conditions were dry, so the coefficient of kinetic friction was approximately 0.7. Since ∑F = m*a = force of friction = μ*normal force, and normal force is equal in magnitude to m*g, a = μ*g, or about -7 m/(s^2). (Final velocity^2) = (initial velocity^2) + 2*a*(distance traveled).Therefore, after traveling 90.5 m, the car had slowed to a stop by the time it collided with the utility pole. (Note: I ignored the effect of the collision with the truck itself on the car's initial velocity. I also ignored the fact that the car did not travel in a perfectly straight line after the collision, but veered off the road in a curved path according to the diagram above.)

Should we be glad that the government is supporting self-driving cars? Like most things in science, it depends. Perhaps, with more research, we can reduce the number of automobile accidents in the US. Ethicists, physicists, public health experts, and programmers will have to come together to make this pipe dream a reality. For now, though, we are a long way from a highway dominated by autonomous cars.

*Note: All sources are linked in text.

Juno Spacecraft

http://www.cbsnews.com/news/nasas-juno-spacecraft-unveils-jupiters-poles/

The above article details how NASA’s spacecraft Juno made it’s first run over Jupiter’s poles on August 27^th.  This is the first exploration of Jupiter that involves instruments to examine the planet’s core to determine if it is solid and how the magnetic field is generated.  According to Jet Propulsion Laboratory, in order to accomplish this feat Juno will reach speeds of over 250,000 km/hr, which means it will be one of the fastest man made objects ever.

Having recently learned about kinematics, I did some research to approximate the average velocity of Juno.  It was launched on August 5^th, 2011 and entered orbit around Jupiter on July 5^th 2016, which means a total of 1796 days.  If there are about 24 hours in every day, then 1796 days means 43,104 hours were spent traveling to Jupiter.  NASA scientists have calculated that the distance traveled by Juno is about 2,800,000,000 km.  Although it is infinitely more complicated like everything in the real world, the approximate average velocity of the Juno spacecraft would be 64959 km/hr, which becomes 65000 km/hr due to significant figures.

http://www.jpl.nasa.gov/news/press_kits/juno/facts/