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As a Physics C student during the 2016-2017 school year at Irondequoit High School, I am interested in discovering how I can relate what I learn in the classroom to the world around me. This blog will include how I see physics in action in my everyday life.

## Physics of College

Hey y'all,

Chris, a student at Cornell, wakes up at 8:59am for his 9:05 class. If the class is 1.5 km away, at what constant velocity does he need to travel in order to make it to class at 9:05? Neglect air resistance.

## The World's First Quad Cork 1800

A couple days ago, a Swiss skier named Andri Ragettli landed the first ever 'Quad Cork 1800', in which he flew 38 yards off of a jump in Italy, making five full rotations and four head-under-body spins. The video of the jump is attached below. The true difficulty of landing such a trick is very clear when considering the physics behind it. First, in order to be in the air long enough to perform such a trick, a skier needs to gain a great amount of kinetic energy as he descends from the top of the hill. In order to do this, the height of the top of the hill should be maximized so as to maximize gravitational potential energy, which is then converted into kinetic energy as the skier descends. Additionally, once Ragettli is in the air, you may notice that he crouches down low, which minimizes the rotational inertia of his body, allowing him to experience a more rapid angular acceleration. After Ragettli rotates multiple times in mid air, just before landing, he straightens his body, which increases his rotational inertia. Since angular momentum is conserved, an increasing rotational inertia causes a decreasing angular speed. Therefore, by straightening his body, his angular speed decreases, making it easier to stick the landing.

## Physics of the Saxophone

I have played the saxophone for a very long time and really enjoy it. Although I have played it for so long, I have never learned the physics behind how blowing on a little piece of wood generates sound. In making a sound on the saxophone, one blows air at a high pressure through the mouthpiece. The reed controls the air flow through the instrument and acts like an oscillating valve. The reed, in cooperation with the resonances in the air in the instrument, produces an oscillating component of both flow and pressure. Once the air vibrates, some of the energy is radiated as sound out of the bell and any open holes. A much greater amount of energy is lost as a sort of friction with the wall. The column of air in the saxophone vibrates much more easily at some frequencies than at others. These resonances largely determine the playing frequency and thus the pitch, and the player in effect chooses the desired resonances by suitable combinations of keys. Also, the saxophone acts as a closed end resonator, and, more simply, a conical pipe. The natural vibrations in the saxophone that cause it to play notes are standing waves. The standing waves in a cone of length L have wavelengths of 2L, L, 2L/3, L/2, 2L/5... in other words 2L/n, where n is a whole number. The wave with wavelength 2L is the fundamental, that with 2L/2 is called the second harmonic, and that with 2L/n the nth harmonic. The frequency equals the wave speed divided by the wavelength, so this longest wave corresponds to the lowest note on the instrument: Ab on a Bb saxophone, Db on an Eb saxophone.

For a more complete overview, visit the University of South Wales website on acoustics: https://newt.phys.unsw.edu.au/jw/saxacoustics.html#overview

## The Leaning Tower of Lire

Recently in my BC Calc class, we've been talking about series and in some cases the application of them. The harmonic series is especially applicable to music: in music, strings of the same material, diameter, and tension whose lengths form a harmonic series produce harmonic tones. Another application of the harmonic series is the Leaning Tire of Lire, a theoretical structure. Suppose that an unlimited identical books are stacked on the edge of a table in such a way that the maximize the overhang. In order to maximize overhang but prevent the structure from collapsing, we can apply the formula for calculating center of mass: c= (x1M+ x2M2) / (M1+M2). In order to maximize the overhang, we need to stack the books in a way such that their center of gravity remains at x=0. This prevents the weight of the stack from applying a torque to the stack, which would result in an angular acceleration and the toppling of our structure. If we consider the center of mass of the stack with n+1 books, we get the following:

The length of the overhang, therefore, can be modeled by the harmonic series, Theoretically, the harmonic series will balance with an infinite number of books. It takes 31 books for the overhang to be two books long, 227 books for the overhand to be 3 books long, and over 272 million books for the overhang to be 10 books long. Crazy stuff.

## Physics of Magnetism

Mr. Fullerton recently gave us a hand out explaining electromagnetism and how it directly relates to Einstein's Theory of Special Relativity.  According to the theory, length and time are not absolute measures, but can be perceived differently based on the motion of the observer. This can be applied to current in a wire. Take a wire with no current flowing in it. As a whole, the wire is neutral as there are equal numbers of protons and electrons. When current flows through the wire, the electrons flow in a specific direction. The density of positive and negative charges in any section of the wire is the same, however, making the wire still neutral. Imagine a charged observer object moving outside the wire. The charges within the wire experience different motion relative to the charged object, so the separations of protons and electrons differ slightly from the observer's perspective, creating a difference in charge density, leading to a non zero net electrical charge, and therefore a net electric field. The charged observer sees the wire as having a net electric charge; therefore, it experience a magnetic force. It is crazy to think that the charged observer would experience a force simply because of what it perceives in the wire; even though the wire is neutral, it is not neutral to the charged observer. Crazy stuff.

## Recent Planetary Discovery

Recently, astronomers discovered a solar system much like ours that could potentially support life. Seven earth-sized planets orbiting nearby star Trappist-1 were found this past week. The solar system is 40 light years away from the Earth. At least three of the seven planets are the right temperature to sustain life. They're rocky and could have oceans. Their orbital periods range from 1 to nearly 13 Earth days. All of the planets are located within a distance from Trappist-1 that is 1/5 the distance from Mercury to our sun. However, Trappist-1 is a relatively cool star, making the temperatures on these 7 planets not too hot despite their close proximity to their sun. This discovery indicates an increased possibility of extraterrestrial life, which is pretty cool. We are still millions of years away from ever being able to travel to this planet, but nevertheless its discovery is exciting.

## Physics of Bowling

Last week, I went bowling for the first time in a long time. I noticed that there is a lot of physics in the sport. When rolling the ball, the bowler applies a force to the ball causing it to accelerate and travel with a relatively constant velocity down the lane. The reason that the ball does not decelerate very much at all is because a substance with a very very low coefficient of friction is applied to the surface of the lane, making the force of friction on the ball small, but nonzero. If the force of friction were zero, the ball would not rotate at all. Bowlers also commonly apply a torque to the ball when throwing it down the lane. This causes the ball to gain rotational kinetic energy. The friction of the ball on the lane also causes the ball to move outside-in.

## Physics of the Compound Bow

Last week, we began the archery unit in gym class. One thing that was especially interesting was when Mr Carrick brought in his compound bow. The compound bow, unlike the longbow and recurve bows, utilizes a system of cams and cables, which is a basically a Pully system, redistributing the tension in the string of the bow. This allows the archer to hold the bow at full drawn length with less force than the maximum draw force. This is especially useful for hunters, where bows may need to be held at full draw length for long periods of time. Mr Carrick would shoot alongside us, where most of us were using recurve bows. His arrows would be released from the bow at a higher initial velocity and would penetrate the target further than our arrows would, demonstrating the superiority of the compound bow. By applying a compounded force on the arrow, the arrow experiences a greater impulse, causes it to accelerate more rapidly, giving it a greater initial velocity upon its release. A greater velocity indicates a greater kinetic energy. When the arrow hit the target, the target had to do a significant amount of work by applying a normal force to the arrow, causing a deceleration of the arrow.

## Physics of the African gourd drum

This past week, a group called the Saakumu dance troop featuring Bernard Woma came to IHS. Their performance featured multiple instruments that are atypical in the United States. For example, they brought with them an African gourd drum, which looked a lot like a curved marimba. However, a marimba's resonators are hollow pipes, whereas this gourd drum's resonators were gourds, the vegetable. This instrument is played by striking wooden bars with mallets. The work done by hitting the wooden bars with the mallet adds energy to the system at one of its natural frequencies. Tones are caused by vibrating columns of air contained within the gourd. The gourd is a closed end resonator, much like the pipes of a pipe organ, or a bottle. Another thing that I noticed is that the smaller the gourd beneath the wooden bar and the smaller the wooden bar, the higher the frequency of the sound produced.  This makes sense, when considering the fundamental frequency of a closed end resonator. There is one node and one antinode for the whole length of the resonator, meaning that the length of the resonator contains 1/4 of a wavelenth. Frequency is v / lamba, and lamba in this case equals 4L. Therefore, when L decreases, the frequency increases.

## Physics of Intervals in Music

As a saxophone player, I have always wondered how exactly sound waves work and why some notes sound good together while others don't. For example, when notes that are a half step apart are played simultaneously, "wobbles" are produced. If two sound waves interfere when they have frequencies that are not identical but very close, there is a resulting modulation in amplitude. When the waves interfere constructively, we say that there is a beat. The number of beats per second is known as the beat frequency, which is simply the absolute value of the difference in the frequencies of the two pitches. From a music theory standpoint, intervals can be referred to as consonances or dissonances. Consonances occur when tones of different frequencies are played simultaneously and sound pleasing together. Dissonances occur when tones of different frequencies are played simultaneously and sound displeasing together. According to a lecture by Professor Steven Errede from the University of Illinois, the Greek scholar Pythagoras studied consonance and dissonance using a device known as a monochord, a one stringed instrument with a movable bridge, which divides, "the string of length L into two segments, x and L–x. Thus, the two string segments can have any desired ratio, R = x/(L–x). When the monochord is played, both string segments vibrate simultaneously. Since the two segments of the string have a common tension, T, and the mass per unit length, mu = M/L is the same on both sides of the string, then the speed of propagation of waves on each of the two segments of the string is the same..." Basically, the ratio of the lengths of the two string segments is also the ratio of the two frequencies. Consonance occurs when the lengths of the string segments are in unique integer ratios. To learn more about the physics of consonances and dissonances, read his lecture here: https://courses.physics.illinois.edu/phys406/lecture_notes/p406pom_lecture_notes/p406pom_lect8.pdf.

## Physics of Transistors

Recently in AP Chemistry, we talked about modern materials, like transistors, and how exactly they work. Transistors are a type of semiconductor. Semiconductors correspond with the metalloids on the periodic table. In Physics C, we typically refer to objects as either conducting or non-conducting, and have learned how to deal with electric fields, electric potential, electric potential energy, and capacitance for either of the two objects. The physics becomes more involved when considering semiconductors. Semiconductors have conductivities that are intermediate between conductors and insulators. The conductivity of a nonconductor can be increased by increasing its temperature because increasing the temperature increases the average kinetic energy of the nonconductor's electrons, making them able to be freed and flow to produce electrical current. One can also increase the conductivity of a semiconductor by chemical doping, which involves the presence of small amounts of other atoms. The following video explains how transistors work, and refers to n-type and p-type doping.

## Physics of Equilibrium

I recently saw this picture on one of my friend's Snapchat stories. How is this water bottle able to balance on its side? The bottle is positioned so that its net torque is equal to zero. On the left side of the bottle, the force of gravity due to all of the infinitesimally small pieces of its mass on one side of the system's center of mass multiplied by the distance that their weight vectors are from the center of mass (AKA the counter clockwise torque) has some definite magnitude. On the right side of the bottle, the forces of gravity due to all of the tiny pieces of mass multiplied by their distances from the center of mass equals a net clockwise torque on the bottle. The counter clockwise torque and clockwise torques applied to the bottle are equal in magnitude and opposite in direction, causing the bottle to remain in rotational equilibrium. The calculus behind this situation is quite complicated, as you can probably tell.

## Physics of Hip Checking

This past weekend, I went to an IHS hockey game, and noticed that @SJamison was able to completely send his opponents off of their feet without even applying too great a force to the opponent. Skylor continually used the hip check, which seemed effortless compared to body checking and a lot less painful for the defender. What is the physics behind hip checking? By applying a force further from a player's center of gravity, a defender applies a torque to the other player, causing that player to experience a rotational acceleration which makes it easy for that player to lose his/her balance. The defender's hip does not need to apply a force other than letting the offender skate into their hip basically. By causing a rotational acceleration of any magnitude, an offender can easily lose their balance. Body checking is much more difficult, however, because in order to stop a player's momentum, the defender needs to have a momentum at least equal in magnitude and opposite in direction.

## Gauss's Law - for both Electricity and Gravity?

This past week in physics, we learned about Gauss's Law for electricity. It states that the electric flux, or the amount of electric field penetrating a surface, is proportional to the charge enclosed within the surface. Interestingly, Gauss's Law does not only apply to electricity: it also applies to gravity. According to Wikipedia, gravitational flux is a surface integral of the gravitational field over a closed surface. This is analogous to electric flux, equivalent to the surface integral of the electric field over a closed surface. Gauss's Law for gravity is mathematically represented by this equation:  {\displaystyle \scriptstyle \partial V} {\displaystyle \mathbf {g} \cdot d\mathbf {A} =-4\pi GM} , where  represents a surface integral over a closed surface. Gauss's Law for electric fields states that:

= {\displaystyle \scriptstyle _{S}} {\displaystyle \mathbf {E} \cdot \mathrm {d} \mathbf {A} } . Electric flux can also be represented by 4 pi k Q. Since G is the gravitational constant analogous to k for electricity, and since M is analogous to charge, it makes sense that total gravitational flux is equivalent to -4 pi GM. Gravitational flux is negative because gravitation fields always attract, where electric flux can be positive or negative depending on the enclosed charge.

## Electricity and Magnetism

This past week in Physics C, we started the electricity and magnetism course. It has proven to be very difficult so far, especially when talking about electric fields and finding electric fields at a point by integrating across an object where its charge is uniformly distributed. I am even more scared to start learning about Gauss' Law. Since I do not entirely understand the hard stuff yet, I'll talk about simple electrostatics which can be seen in everyday circumstances. Charging by conduction, for example, occurs when materials become electrically charged by contact. This can be seen by rubbing a balloon against your hair. The atoms in your hair lose their valence electrons, which are transferred to the balloon, leaving your hair positively charged and the balloon negatively charged. If you place the charged balloon to the wall, it will stick because the wall is more positively charged than the balloon, and since opposite charges attract, the balloon sticks to the wall.

## Physics of Arm Wrestling

Today was an unfortunate day in Physics class. After some bickering over some physics problem between my brother Jason and I, we decided that the only way to properly settle our dispute was to arm wrestle. Unfortunately, he beat me. Although I did not get the victory I deserved, I noticed that arm wrestling has quite a lot of physics to it. When arm wrestling, both people are trying to apply a greater torque than applied by the other person. Since torque equals the force applied times the distance from the point of rotation, the greater the arm length, the greater the applied torque. However, arm length plays a very small factor in terms of who has the advantage in an arm wrestle. According to Zidbits.com, "Stance, muscle density, stabilizer muscles, shoulder muscles, as well as where the specific tendons and muscle fibers attach to the bone are more important, and play a much larger role in arm wrestling. These same attributes are the reason why primates are generally much stronger than humans despite their smaller stature and size." In my opinion, Jason is not the true arm wrestling champion until he beats a primate. You've got a lot of work ahead of you @jcstack6

## Physics of Trampolines

This coming Friday, I'm going to Skyzone with a bunch of my friends. If you've never been to Skyzone, an indoor trampoline park, you definitely should go. I've been thinking about the ways that trampolines work, and notice that they demonstrate an important physical concept: conservation of mechanical energy. When jumping on a trampoline, your weight and work done by your legs causes the elastic surface of the trampoline to stretch and it causes the springs attached to the trampoline to stretch.  The springs and surface of the trampoline eventually stretch until the velocity of the person is 0 m/s. This is the point at which the springs and surface are at their amplitude. Since spring potential energy equals 1/2 k x^2, the greater the amplitude or maximum displacement from equilibrium, the greater the spring potential energy in the system. Since mechanical energy is conserved, the spring potential energy when the springs and surface of the trampoline are at their amplitude must equal the gravitational potential energy when the person jumping is at their maximum height. Therefore, the more work that your legs do in stretching the surface and springs of the trampolines, the greater their amplitude will be, causing the spring potential energy to be greater, causing the maximum height that you reach to be greater.

## Physics in The Simpsons

The other day, I was watching The Simpsons, one of my favorite TV shows, and noticed that in a particular scene, one of the characters, Mr. Burns, experienced multiple laws of physics in action. He was on a camping trip with his millionaire friends, and, with a shotgun, attempted to shoot a stationary pigeon. Mr Burns, who is unrealistically underweight, shot backwards dramatically after firing the gun. This occurrence demonstrates conservation of linear momentum. Originally, both him and the gun were stationary. After firing the gun, the bullet of relatively little mass travelled at an extremely high velocity in the positive direction. Since linear momentum is conserved, Mr. Burns' body was propelled in the negative direction at a high velocity because of how small the mass of his body is. Therefore, the mass of the bullet times its velocity minus the mass of Mr. Burns times his velocity is equal to 0. Mr Burns was, unfortunately, standing next to a lake, and was propelled into it. However, he did not sink in the lake. This occurred because of the surface tension of the water. The force of gravity on Mr burns is relatively small, considering how little he weighs. When he came in contact with the water, the surface tension of the water was greater than his weight, causing him not to accelerate into the water.

## Physics of Golf

One of my favorite sports to play is golf. I have played the game since I was about 8 years old, and have played on the golf team at school since 7th grade. I also play with friends over the summer pretty frequently. However, the game can be really frustrating due to the complexity of hitting a perfect golf shot. Hitting a golf ball well is much more complicated than simply keeping your eye on the ball and hitting it as hard as you can. Some people view a golf swing much like a baseball swing. However, they are very different. In a golf swing, there are two main components that result in the best possible shot. The first is having a good swing speed of the arms and shoulders. The second is letting the wrists rotate freely while still holding onto the club. On the downswing, when a golfer's hands are parallel to the ground, he/she must drop their wrists and allow them to move centripetally until after the ball has been hit. This maximizes the speed at which the club head strikes the ball because of the centripetal acceleration of the club. This is unlike a baseball swing, where the baseball player relies on strong forearms and wrists to exert a great force. The golfer's wrists, however, are passive in swinging through a golf ball. Also, by contacting the ball when the player's club is perpendicular to the ground provides the greatest acceleration of the ball because the applied force of the club of the ball is in the direction of the fairway, causing the ball to accelerate in that direction.

## Physics of Ice Skating

This past weekend, I went ice skating for the first time in a couple years. I was not as good as I remembered, but I still had a lot of fun. When I was ice skating, a noticed a group of girls who looked like they were on a figure skating team. At one point, one of them went out on the ice. She did some fancy spins, like triple axles and stuff (I don't know very much about figure skating sorry), and I paid particular attention when she would spin. She began her spin with her arms and one of her legs out, and when she brought them in, her rotational velocity increased dramatically. This is a perfect example of the conservation of angular momentum. Angular momentum equals moment of inertia multiplied by angular velocity. When bringing her arms and legs in closer to her body, she decreased her moment of inertia by decreasing her radius (moment of inertia is proportional to mr^2 for any object). Since her initial angular momentum must equal her final angular momentum, the decrease in her moment of inertia causes an increase in her rotational velocity. Watch this cool figure skating video from the 2010 Vancouver Olympics to see for yourself.

## Physics of Snow Plows

Last week Rochester experienced a pretty heavy snow storm. Sadly, irondequoit was one of the only schools that didn't get a snow day. During the snow storm, I noticed a lot of snow plows hit the streets. Particularly, I noticed how the snow plows effectively get the snow off of the road. They have to angle their snow plows away from the center of the road in order to apply a force to the snow that has a component towards the sidewalks.  If instead they did not angle their plows, the snow would simply be pushed forward and not off of the streets because the force that the plow applies to the snow has no component towards the sidewalk. By exerting a force towards the sidewalk, the snow accelerates off of the road because of Newton's second law.

## Physics of Jumping into a Pile of Leaves

When I was younger, I liked to rake all of the many leaves in my yard into one big pile. Then, I would jump into the big pile along with my siblings. Why did I, like many young kids, love to jump into a big leaf pile? Let's consider the physics behind the scenario in terms of momentum and impulse. When in the air, the instant before I have come in contact with the leaves, I have a downward and rightward (assuming that I jump in the rightward direction) velocity, meaning that I have a non zero initial momentum. When my body hits the ground again, my velocity becomes 0. Therefore, my momentum has changed, meaning that I experienced an impulse. If the same jump is repeated, but the leaves are removed, my momentum changes by exactly the same amount as in the previous scenario, meaning that the impulse that I experienced was exactly the same, but I feel a greater force than I did in the previous scenario. That is because impulse is equivalent to the average force multiplied the time during which it is exerted. The leaves lengthen the amount of time during which the impulse is applied, meaning that the force that I experience is lesser when I jump into a pile of leaves.

## Physics of Speed Bumps

Have you ever driven too fast over a speed bump and felt an uncomfortable jolt? Have you ever wondered why the feeling is so much less uncomfortable when you travel over the speed bump at a slower speed? This discomfort can be explained when considering the physics of speed bumps. When going over the speed bump, you experience an impulse, equivalent to the average force applied to you multiplied by the time during which it is applied. Let's say that you are approaching the speed bump at a relatively high speed, and that you roll over the speed bump in 0.001 seconds. The speed bump applies an impulse to you which stays constant no matter how fast you go over the speed bump. Since the impulse remains the same, the smaller the time interval during which you pass over the speed bump, the greater the force applied to you, which causes discomfort. Conversely, the greater the time interval during which you pass over the bump, the smaller the force you experience. When traveling at a slower velocity, you are passing over the speed bump for a longer time, making the force smaller. Therefore, speed bumps should be travelled over slowly in order to avoid a discomfortably large force.

## Physics of Playground Swings

When I was younger, I loved swinging on the playground swings. I always tried to go as high as possible because it made me go faster when at my lowest point, which was an exhilarating feeling. What I didn't understand then I understand now when considering the physics behind it. If you set your reference level at the lowest point of the swing, then when you first get on the swing, you have no mechanical energy. Then, when someone applies a force to you, they do work on you, causing you to accelerate and travel to a higher level. The work that they do in pushing you increases the mechanical energy of the system. The more work that they do to you, the more mechanical energy they add to the system. Since mechanical energy is conserved in a closed system, the potential energy at your highest point equals your kinetic energy at your lowest point. Therefore, the higher you are able to go, the more kinetic energy you will have at your lowest point, which means that you will travel at a higher velocity at the bottom of your swing.

## Physics of Hot Rod

One of the most amazingly idiotic movies ever created is Hot Rod, starring Andy Samberg as stuntman Rod Kimble. In one scene, he attempts to jump a public swimming pool while on his moped. He fails miserably, as the video below illustrates. How could he have successfully jumped the pool? In order to determine this, lets consider the physics behind the situation. Lets say that the ramp is angled at 45 degrees to the horizontal. Lets also say the the the two ramps on the two sides of the pool are at equal heights. The width of the pool is approximately 15 meters. How fast would Rod need to be going while at the top of the ramp in order to clear the pool? We can use kinematics to solve this problem. Let v = the velocity at which he leaves the top of the ramp in order to clear the pool. The time for which he is in the air (t) equals the change in vertical velocity over the acceleration due to gravity [ t = (Vfinal-Vinitial)/g ]. Since the initial velocity in the vertical direction is Vsin45 and the final velocity in the vertical direction is -Vsin45, t can be solved for in terms of V. Therefore, t = (2^(1/2) / g) V . Now lets look at the horizontal plane. t = (2^(1/2) / g) V , acceleration in the x direction equals 0 m/s^2, and his displacement in the x direction equals 15 m. Since x= Vinitial t + 0.5at^2 and a = 0, x = Vinitial t . Since the horizontal component of V is Vcos45, we can solve for V by plugging in 15 meters for x , (2^(1/2) / g)V for t, and Vcos45 for Vinitial. Through this calculation, we find that Rod would need to be traveling at a speed no less than 12.12 m/s at the top of the ramp.

We can also think of the scenario in terms of energy in order to determine how much work his moped will have to do in order to reach this velocity at the top of the ramp. Lets say that the weight of his moped is 275 kg. Lets also assume that friction is negligible, meaning that mechanical energy is conserved in this situation. Where he begins at the top of the hill adjacent to the pool is about 2.0 meters higher than the top of the ramp (y = 2m). He travels about 10 m before reaching the top of the ramp. Also, his bike starts from rest. When he reaches the top of the ramp, all mechanical energy is in the form of kinetic energy. Therefore, an equation to model the conservation of mechanical energy in this scenario could be:

mgy + work done by the moped = 0.5mV^2

We can solve for the work done by the moped through algebraic rearrangement and by plugging in our known values: y = 2 meters and V = 12.12 m/s. Therefore, the work done by the moped is 14882.5 Joules. Since Rod travels a distance of approximately 10 meters before reaching the top of the ramp, and since Work = Fd, the force that his moped would need to apply for him to be able to clear the pool would be 1482.25 Newtons. He might need to buy a more powerful bike in order to be successful in doing this stunt.