Thursday, October 31, 2019

The Physics of Elastigirl

Elastigirl Saves the Train!

Elastigirl, or Helen Parr, matriarch of the Incredible Family, is an amazing example of many
different concepts we have learned in physics from springs to momentum to drag. Her ability to stretch
her limbs to extreme lengths allows her to propel herself to the tops of buildings, jump from incredible
(pun intended) distances, and even act as her own parachute.
In “The Incredibles 2” Elastigirl heroically saves a Maglev train that was hacked to travel in the wrong direction, sending it towards the unfinished side of the tracks. 

The producers did not go easy on Elastigirl, and set her up to have to stop a maglev train which mostly avoids friction by hovering over the tracks due to a system of magnetic forces. In this scene, we see Elastigirl (ingeniously) separate the train in the middle, which appears to break the magnetic aspect of the train and introduce friction. She then stretches her body into a parachute to create enough drag to bring the train to a stop before it falls off the unfinished track. In this problem, we will use the dimensions of the Shanghai Maglev train to calculate how much drag (work of a nonconservative force) Elastigirl produces to save the train and its passengers.

The Shanghai Maglev train can travel up to 431 km/hr. Additionally, the mass of a middle car is
about 20,000 kg and the head is about 30,000 kg. From the video, it looks like Elastigirl separated
the train at one head carriage and one middle carriage, so we will assume the total mass of her
section of the car is 50,000 kg. We’ll also assume the evil villain (The screen Slaver, for those who
haven’t seen the movie) set the track to go its fastest speed if he/she was trying to cause a lot of
destruction. The track of a Maglev train is normally made of steel. The bottom of a Maglev train is
covered in electromagnets which is typically made of copper coiled around another metal. We will
assume the friction occuring between the train and the tracks is between steel and copper, which
has a coefficient of friction of 0.36 (while sliding). We assume the track is clean and dry because this
was the opening day of the train. 

We will also assume Elastigirl began parachuting at 1 km (1000 meters) from the end of the tracks
where she stops. 
Initial velocity= 431 km/hr→ 119.72 m/s
mass: 50,000 kg
μ= .36
d= 1000m

ΔKE= -ΔPE + Wnc
½ m(vf2-vi2)= -μgmd + Welastigirl
½(50,000)(0-119.722)= -(.36)(9.8)(50,000)(1000m) + Welastigirl
-358321960= -176400000 + Welastigirl
-181921960 J=  Welastigirl

That’s more than the average US energy consumption for a house in one day! 
Go Elastigirl!

Wednesday, October 30, 2019

Don't Make Me Put My Foot Down

I was walking back to my apartment a couple of days ago, and chose to take the path surrounding Taylor Lake- with its infamous geese. It was a pretty warm day and thus there were an endless number of these loud, messy birds around, but what struck me was that half of them were sleeping standing up on one foot with their head tucked into their body in what seemed like a nearly impossible balancing act. Once I started to research how these birds can possibly maintain this stance, I found that the avian physics research community is especially interested in how the Flamingo, with its long thin legs, maintains this obscure sleeping position shown below.


Its been hypothesized that birds sleep like this to conserve heat. Yet the question still remains- how do they do it!? Two major schools of thought arose on this topic- one proposing that the birds use muscular strength to stabilize themselves and switch legs to conserve energy, and another proposing that the birds are perfectly balanced by gravity without the help of muscular strength. Researchers Young-Hui Chang and Lena H. Ting from the Georgia Institute of Technology went so far to prove the later point that they positioned flamingo cadavers (from flamingos that had undergone natural deaths) in an upright position on one leg to see if the birds could balance without muscular help. And they did!

It turns out that once the leg locks into place, the flamingo’s center of mass shifts forward. Once they tuck their head in, their center of mass rests perfectly above the normal force at the point where their foot touches the ground as shown in parts a and b of the figure below from Chang and Ting’s paper. In the segment free body diagram shown in part c, Mh and Mk represent hip and knee joint movements respectively, and Hy and Ky represent hip and knee reaction forces respectively (equal to mg at that point). The authors argue that these large knee and hip joint movements are necessary to balance the bird since the horizontal femur is not advantageous for muscle contraction in that region. Lastly, the researchers show that as the ideal knee joint angle is about 95 degrees while the ideal hip angle is about 10 degrees in part d. We know from the equation l=rθ that as the hip joint angle increases, the bird will cover a greater linear distance, and thus be more likely to fall as shown in the diagram below. This bird demonstrates that since all forces usually can't be used perfectly by animals, prioritization is necessary. Here, by tucking in its leg, the bird increases its hip joint angle and thus the linear distance that could be covered by its leg due to gravity, throwing it off balance. However, it shifts its center of mass forward and ultimately winds up balancing with out additional support. 


Monday, October 28, 2019

How To Physics Your ACL Tear

I recently started shadowing a doctor at Hamilton Orthopedics.
Although I have seen a large handful of middle aged people with arthritis
in their knees and hips, my greatest field of interest is athletic injuries.
Playing soccer, basketball and running track in high school and sitting
in front of the TV watching UEFA Champions League matches and Knicks
games with my brother and my dad, sports have played a huge role in my
life since a very young age. Fortunately, I haven’t had any injuries requiring
an operation and a long recovery. Although, I’ve still had the typical shin splints
and sprained fingers. In competitive sports, played at a high level, injuries are
inevitable, many of which occur at joints. Our skeletal muscles exert forces through our joints.
The seven forces that act at the knee joint are the tibiofemoral joint force, the patellar tendon force,
the hamstring muscle force, the gastrocnemius muscle force, the anterior shear force,
the posterior shear force and the ground reaction force. 

It’s when there is a force greater than the forces from normal activities
that ligaments, tendons and bones can be injured.
One of the most common knee injuries is an ACL (anterior cruciate ligament) tear.
ACL tears tend to occur when there is a rapid deceleration (velocity and
acceleration in opposite directions) and low velocity in one’s movement,
therefore also decreasing one’s momentum.
An example of this is when one suddenly stops or changes directions in sports.

When one tears their ACL, the forces that break the ligament are greater than the ligament forces. 

The forces that break the ligament include:

1. A large anterior shear force - A large anterior shear force on the ACL tends to occur
when there is hyperextension of the leg. 

2. A ground reaction force (GRF)-The ground reaction force can contribute to the
ACL injury of an athlete when there is ligament dominance. This means that the
quadricep and hamstring muscles are not able to absorb the GRF like they should
and so the knee ligament ends up absorbing the GRF. An example of this is when
an athlete plants their foot or jumps.

3. An internal rotation force - The adduction internal rotation of the hip is a force moving clockwise
along the femur and the tibial rotation is a force moving counterclockwise along the tibia.
Therefore, these rotational forces are moving in opposite directions. 

That’s why strengthening exercises, such as squats and lunges are often critical
in preventing injuries to the ACL. The shorter time given to decelerate results in these
greater impulse forces, and all these forces can work individually or together to place
a large amount of stress on the knee resulting in injury. So if you want to take
some preventative measures, you can start by hitting the gym and improving strength,
flexibility and balance to decrease the likelihood of the ligament breaking forces acting
on the knee. Working on properly executing jumping movements, sudden stopping movements
and changing direction movements is very important for reducing your risk of an ACL tear. 

Saturday, October 26, 2019

The Physics of Swimming: Increasing Efficiency in the Water Using Newton's Third Law of Motion

As a member of the Swim team at Colgate, I spend 20 hours a week swimming laps in the 25 yard pool. My Coach, Ed Pretre, always reminds us that our efficiency is more important than the effort we are putting in (but the effort we are putting in is still very important.) This may sound like he is telling us it is okay to not work hard. However, that is not the case; he is telling us it is more important to swim smart, and swimming smart starts by analyzing Newton’s third law of motion, which can help maximize efficiency in the water, and allow us to excel against our competitors. 

Newton’s third law of motion states that, “whenever one object exerts a force on a second object, the second object exerts an equal force in the opposite direction on the first.” The textbook gives the example of an ice skater pushing against a wall, and the wall pushing back on the skater. The force between these two objects results in the skater accelerating away from the wall.

The same concept can be applied to swimming, when swimmers do flip turns. Flip turns are when the swimmer reaches the wall, does a “somersault,” which orients the swimmer in a way that will allow them to plant their feet on the wall, shoulder-width apart (Figure 1). The swimmer is then ready to “push” off the wall using their legs, and this acceleration from the wall is used to help the swimmer gain speed as they continue their race.                   

In order to push off the wall with the highest acceleration the swimmer can possibly achieve, the swimmer must increase speed as he or she approaches the wall. The more force the swimmer can generate when they push off the wall, the more acceleration the swimmer will be able to attain coming off the wall. The swimmers who swim towards the wall at a higher speed are the ones who have the most acceleration coming off the wall, which will drive the swimmer ahead of his or her competitors who are not using physics to maximize their efficiency in the water. 

The fastest swimmers are the ones who are able to pull the most water, and pull this water at a faster rate than their competitors. The amount of water a swimmer is able to pull is dependent both the strength of the swimmer, and on the angle at which the elbow is bent when it is directly underneath the shoulder. Ideally, this angle should be 90 degrees, as this is the angle at which the surface tension between the water and the swimmers arm is the highest, allowing the swimmer to propel themselves further in the water.

Physics of Pool

The game of pool actually involves a lot of physics! Although they may not know them, good pool players implicitly understand the law of conservation of energy, and the law of conservation of momentum. Because the cue ball does not stick to the ball it hits, all the collisions in pool are elastic, which means that both kinetic energy and momentum are conserved. For example, if you shoot the cue ball horizontally and hit the side of a ball, they will veer off in different directions. If you calculated the y component of momentum for each ball, they would be equal and opposite so that the final momentum in the y direction is equal to the initial y momentum of the shot (which is zero, because you are shooting the cue ball horizontally). This is true because of the law of conservation of momentum. If the head on collision was truly perfectly elastic, the v final (velocity of the second ball) would equal the v initial (velocity of the cue ball), but due to friction and air resistance, the velocity of the second ball is slightly less than the velocity of the cue ball before the collision. Therefore, to be a good pool player, one must first have a solid understanding of the fundamentals of physics!

Friday, October 25, 2019

Flying With Questions

Growing up as an expat kid I was always flying places. Not only did my parents, sisters and I move around all over Asia but our closest family lived in the United States. Therefore, holidays always consisted of 15+ hour flights where little Lara (me) would stick her forehead against the plane window and watch the clouds and night sky.
I always wondered how airplanes worked. Why is it a joke when people say “when pigs fly” and
yet a huge bus-like structure has no problem flying? Despite this curiosity, I never questioned this
out loud as when I looked around, everyone else on the plane seemed calm and unconcerned.
It was not until this fall break, when I was flying home, that I wondered how it really all work.
This is my first ever physics class and right away I was able to connect concepts we have learned
this semester to an aircraft. However, I wanted to look at this even further. How does the air affect
the plane? How does the plane even get off the ground? Therefore, I decided this would be a great
topic to look into for one of my “physics news” blogs.
The Wright brothers were the first to create a successful airplane in 1903. The two wings of their plane had a curved shape. This shape was able to push the air downwards resulting in a reaction force from air to push the wing upwards in an equal magnitude (we can attribute this to Newton’s 3rd Law). Eventually, this results in the lift force and the aircraft will be able to fly off the ground and into the air. Even today, a hundred years later, aircrafts still use the same airfoil technology (cross-sectional shape of a wing) to fly but with the highly aerodynamically optimized airfoil shape.
Simply put, there are four forces acting upon an aircraft. They are:
Weight --> which we know is the measurement of the pull of gravity on the plane and it acts towards the
center of the earth. 
Lift --> which acts perpendicular to the direction of relative motion.
Thrust --> which acts along the direction of motion, generated by engines to move the plane in the forward
Drag --> which acts opposite to the relative motion of the plane, generated by the air resistance.
These forces can account for the actions of a plane:
This course has given me answers to questions I thought of over two decades ago. Now, finally, after 21 years of flying, I have a better understanding of why planes are able to fly and why pigs are not.

Monday, October 21, 2019

"That's so Fetch!"

One of the best parts about going home for fall break was seeing my dog – she’s a Havanese, about a year old, and is always looking to play. Her favorite game is fetch, where I throw her toy and she runs, catches it, and brings it back. The physics is fetch is relatively simple – it involves motion in two dimensions: X (left and right) and Y (up and down).

I throw the toy at an angle Ø. Using trigonometry, we can calculate the initial velocity of the toy in the X direction (VOX). In the diagram below, the toy is thrown to the right so VOX = VO * cos(Ø). The toy’s velocity in the X direction will remain the same throughout the entirety of the throw, as it no other forces interact with the toy in the X direction and Newton’s First Law tells us that every object in uniform motion (constant velocity), such as the toy, will continue in its uniform motion unless acted upon by another force.

The Y velocity is different. While you could calculate the initial Y velocity, once the toy is in the air, it’s acted upon by the force of gravity, which will affect the velocity. The acceleration due to gravity is 9.8m/s2 towards the direction of Earth. For simplicity, we will say the acceleration in the Y direction is 9.8m/s2 downwards for the entirety of the throw. Since the acceleration will affect the velocity in predictable ways, we can conclude some key information about the Y velocity of the toy. After being thrown, the toy will continue to rise upwards but slow down until it reaches its highest point, where VY = 0m/s. After that, the toy will fall and speed up until my dog catches it.

Putting the X and Y velocities together, we know that the toy follows a parabolic movement, as shown in the diagram below. If we had specific values for the initial velocity and angle of the throw, we could use the kinetic equations to calculate other variables such as the time the toy is spent in the air, the distance it travels, and even its final velocity. If I wanted to be an astute physics student, I could find the position of the ball and how long it will take to reach that position in order to catch the ball.

My dog’s never been taught the kinematic equations yet she manages to catch the toy. In her head, she can figure out where to go to catch the ball with only an initial velocity and angle to go off of. In theory, she then calculates the initial X velocity, time, and change in position. Even more, she only a second or two to do this and get in position to catch the toy. The change in position will be how far in the direction the toy will go in the amount of time it takes the toy to rise up then fall to my dog’s height, as she’s not flat on the ground. After all of this I’ve learned she’s a lot smarter than she seems.

One more caveat: Because extensive breeding for different traits, not all dog breeds are great at playing fetch. Here’s a cute video of a dog trying it’s best. Enjoy!