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The objective of this lab was basically to have the egg touch the paper without cracking. Our group went through many calculations and measurements in order to get a solution to this problem, and during this process we made a big mistake that went unnoticed until the application of our calculation failed miserably. We went through many measurements in order to find the spring constant of the 2 rubber bands put together. We found an experimental spring constant of many different masses hanging on the bands and then put these together on a graph in order to get an equation we could use to find the amount above the paper we needed to allow the egg to fall in order to just touch without cracking. The spring constant was found by integrating the equation given to us by the graph and plugging that value into the equation U=.5kx^2. This got us our final answer that we should give the egg 37 centimeters above the paper in order for this lab to be successful. (we decided to add a small amount to this because we realized that the punishment was greater for going 1 centimeter below, aka cracking the egg, rather than above the paper). This was where our group made a very foolish mistake. In a simple conversion, we multiplied by 1000 rather than 100. So truly through our calculations, our answer should have been about 3.7 rather than 37. When dropped based on that value of 37 cm, the egg didn’t even come close, and I quickly realized where our error came from. On a re-drop just to test if the answer we should have gone with in the actual application of the lab was accurate, the egg performed much more like how we expected to on its drop, with small human errors definitely impacting its overall performance. All in all, my group executed this lab pretty well aside from a major mistake in attention to detail. In this future we will definitely make it a point to check for any silly mistakes like that in order to avoid completely messing up a lab. Not to say our normal answer was completely perfect, but it performed much better than our original, flawed value did. Another error that I believe our group encountered, especially on the second drop, was not accounting for the weight of the tape added to secure the egg to the rubber band. This wasn’t necessarily substantial, but it was by no means negligible. Accounting for this weight wouldn’t have changed the major inaccuracy encountered on the first drop, which is why that is so much of the focus of this explanation. But on the second drop, it certainly would have helped get an even more accurate value.

Something that I've been noticing since I was a little kid is that on car commercials, when they are showing the car driving, it often times looks like the wheels are spinning backwards and the car is going forward. It wasn't until recently that this concept was explained to me. What really causes this is the fact that the frames per second of the video camera is slightly greater than the rotations per second of the wheel. This makes it so that in each new frame that is recorded, the spokes on the wheels are a few degrees short of the position that they were in for the prior frame. This causes the illusion that the wheels are spinning in reverse while the car is going forward. This is known as the wagon-wheel effect. Also less commonly but maybe a little bit cooler, the wheel can look like it isn't moving at all. This is caused by the same concept, except the spokes of the wheels are in the same position for each new frame, meaning the frames per second of the camera is equal to the rotations per second of the wheel, or that they have a perfect rotational symmetry. This effect is evident in the clip of the helicopter, as the rotor blade spins in a similar way to a wheel on a car. (for more on helicopters, look at my previous blog post) If you haven't noticed this before, look out for it the next time you're watching a commercial or a movie. There's a good chance that you could notice the wagon-wheel effect, in effect.

I'd like to take this time to explain a little bit of how helicopters work, because they're really cool. Helicopters basically fly by sucking air from above the big rotor blade on top of the machine and forcing it downward with a thrust greater than the force of gravity acting on the helicopter. This allows the helicopter to get lift off the ground and fly into the air. Not only does the thrust created by the rotor blades have to be stronger than the force of gravity, or the weight, of the helicopter, it also has to be able to overcome the drag force created by the rotors. A thing about the rotor blades is that they continue spinning at the same speed the whole time. They do not slow down or speed up in order to change the height that the helicopter is flying at. The rotor blades do, however, control the amount of "lift" that a helicopter has, or the height at which it is flying, in a different way. Helicopters change their height by altering the angle at which the rotor blades make contact with the air. The pilot of a helicopter can increase or decrease the angle of the blades in order to go up or down. Another thing about helicopters is that they do not fly in straight lines, they are able to move side to side. This is also made possible because of the angles of the rotor blades. By altering the angle of each individual blade, a pilot is able to control the way in which the air contacts the blades in order to fly either to the left or to the right. Nifty stuff.

Recently I saw a commercial for a phone that said that the screen of this phone could not be cracked. This got me thinking of all the stories that people have told me about their phone cracking and what truly causes this to happen. A few times I have dropped my phone and assumed that when I picked it up it would be completely shattered, but I was wrong. Why is it that a phone can shatter on a short fall, while other times it sounds as if it were hurled at the ground and it ends up without a scratch on it? That question can simply be answered with luck. The likeliness of a phone to crack is dependent on where on the phone makes initial contact with the ground. If the phone falls directly on the face it is not very likely to crack because the impact is spread throughout the whole surface of the face. If a phone is dropped on its corner, the force of contact with the ground is much more concentrated in one area, making it more likely that the glass screen will not be able to survive the fall. A phone that falls from a short height and lands on its corner is more likely to crack than a phone that falls from a greater height and lands directly on the face. The strength of a phone screen is dependent upon both the surface compression and inner tension of the phone. This strength determines how many blows the screen can take before shattering. Glass only shatters if the force of an impact is greater than the surface compression. So if a phone is only dropped from a short height, it is not likely that it will contact the ground with enough force to shatter the screen. You can't really measure the exact strength of a piece of glass because that is dependent upon the makeup of the glass, but you can get a pretty good idea of how strong a glass phone screen is. The likeliness of a phone to shatter is also dependent on the surface that it lands on. It seems obvious, but a phone is more likely to crack on concrete than on a pillow because there is a greater force applied to the phone upon impact when it hits the concrete rather than the pillow. So if you ever drop your phone and are worried as it falls through the air that it is going to crack, just hope that it falls directly on its face. Or, better yet, buy a good case for your phone. That way you won't have to worry so much about the ability of your phone to take the force of impact with the ground.

For myself and the thousands of other people that simply golf for fun, one of the most frustrating parts of the game is putting. It seems like it should be so easy to line up a putt and hit it in the hole, but it is truly one of the hardest and most important part of the game. Not only is it important, it's also far different from any other aspect of the game, and this can be seen in the physics of the putt. For starters, basically any other good shot in golf is hit in a projectile motion. The ball is hit high in the air and comes down much further down the fairway or the green or in the rough, depending on how well the ball is struck. Putting is different because the ball generally doesn't leave the ground, although it could for a split second on much longer putts with more force applied to it. The reason the putter doesn't hit the ball into the air the same way that all the other clubs in golf do is because the putter head is a nearly flat surface where it makes contact with the ball, although they usually have a very slight angle to them, while the heads of any other club are angled a great amount in order to get the necessary loft on the ball. When the golf ball is rolling, it is a sphere rolling on a flat surface, which means it is impacted by the coefficient of static friction rather than kinetic friction. In golf, there are many different types of greens. On some the ball travels very fast, some it travels very slow, some have many different slopes scattered over it and some are flat. The fast greens obviously have a lower coefficient of friction acting on the ball, and the opposite for a slow green. A majority of putting greens are not completely flat in order to make putting more difficult. This forces a golfer to voluntarily hit the ball up a slope in order to get it to go on the proper path to the hole. Once the ball reaches the hole, the ball must be traveling at a low enough velocity in order for it to be angled properly once it goes over the hole in order to go in. If the ball is still traveling at a high velocity once it reaches the hole, the ball will likely only slightly go in the hole and hit the back lip and pop into the air, or roll right over the hole as if it wasn't even there. If it is traveling slow enough, it will be angled properly in order to fall into the bottom of the hole. Even looking at the physics of a putt it doesn't seem too difficult, but this doesn't account for how hard it can be to line up the ball with the right path for the hole, and how challenging it is to apply the proper force to the ball in order get it moving the proper velocity. It's pretty darn hard.

"What would be a cool blog post idea?" The only suggestion I received was slap shots, which I decided to change to just hockey in general. I am not a very big hockey fan, but upon hearing this I definitely felt like this could be a very cool blog. Initially all that popped into my head was the thought that the coefficient of friction of ice obviously makes for a sport not all that similar to any other sport. Diving deeper into the subject, I learned that my initial reaction was very much true, but there's a lot more interesting physics going on in this sport. One of the most important skills to possess for any hockey player is the ability to shoot the puck, for obvious reasons. For any shot, a player is required to apply a force to the puck that is much larger than the very small frictional force being applied on the puck by the ice. An important aspect to any shot is getting lift on the puck in order to avoid the goalies attempted saves. Players are able to create this lift because the blades on hockey sticks have a small "tilt" angle, similar to that of a driver in golf. Blades also have a curve to them that allows a player to put spin on the puck. The greater the follow through on a shot, the greater the launch angle and more spin will be placed on the puck. Spin on a puck allows for it to be more stable and accurate during its flight. On a slap shot, the force applied to the puck is much greater, allowing for a much faster but less accurate shot attempt. Once a puck is in the air, it's traveling with a parabolic projectile motion. A player wants the puck to enter the net while it is still going up in its projectile motion (before the velocity vector in the positive, assuming up is positive, y direction reaches 0), because this makes a shot more difficult to save, and also likely means that the x component of its velocity has not decreased by too much due to the force of air resistance acting on it while it flies through the air. Knowing a lot of the physics of hockey should be helpful for any of my future endeavors in this sport. If only knowing the physics could teach me how to skate.

Like many CYO ballers such as myself, one of the most surprisingly challenging parts about the game of basketball is shooting foul shots. It seems so simple when you see a professional do it: they spin the ball around a couple times, throw it up and it goes through the net. But looking at the physics of the elusive foul shot can possibly help explain why this task can prove to be so difficult for many. For starters, a foul shot is a shot taken standing still 15 feet from the basket. The objective is to take an uncontested shot and put the 9.5" diameter basketball through an 18" diameter hoop. This obviously makes it challenging because these sizes don't leave much room for error. A major factor in the likeliness of a foul shot to go through the hoop is the launch angle of the shot. The ideal launch angle for an average sized player is about 45 degrees. For shorter players, a steeper angle will be required and the opposite for taller players. The problem for many players is that their launch angle on foul shots is too low. If your launch angle deviates 15 degrees or more lower than the ideal launch angle, then your shot will almost certainly hit the back of the rim. This does not mean it won't go in, but the likeliness of it going through is far lower than someone that launches the ball at the ideal angle. Another important factor impacting whether or not you will find success at the charity stripe is the spin put on the ball. A ball with a lot of backspin on it will decrease greatly in velocity once it makes contact with the rim due to the frictional force of contact, making it more likely for the ball to fall through the hoop rather than ricochet off. Hopefully this new found knowledge will translate to your performance at the line. If not, work on perfecting that launch angle and maybe things will turn around for you.

Something that I am definitely interested in doing in my life is going skydiving. Like many other amateur skydiving enthusiasts, I assume that the best way to start my expedition from 10,000 feet would be to understand the physics behind the fall. Every great skydiving adventure starts with a voluntary jump into the sky. Once having jumped, a skydiver accelerates downwards until they reach terminal velocity, where the force of air resistance prevents the force of gravity from accelerating the subject any further. A subject falling in a spread eagle position will reach terminal velocity faster than someone falling head or feet first. At a certain point, the falling person must open their parachute in order to decelerate themselves in their descent. A parachute works to decelerate a falling human because it increases the cross-sectional area of the falling person, which in turn leads to an increase in air resistance, which should slow the parachute utilizer to a speed that allows them to make contact with the ground with a force that does not break every bone in their body. This device allows for people everywhere to enjoy the sensation of falling to their death without actually falling to their death. Unless of course your parachute fails to open and you have no back up. In that case you should try to land on your feet and hope the damage is small.

There are hundreds of ways to sustain an injury like a concussion. (getting hit by an object, falling on the floor, falling off of a tube, etc.) It may be strange to think about, but a concussion is truly caused by a basic physics concept: the law of inertia. Take the example of falling on the floor. When a head makes contact with the floor, the skull will obviously stop traveling in the direction of the floor. The brain, however, will continue moving until acted on by an outside force because it did not make direct contact with the floor. This causes the brain to keep moving until it makes contact with the skull, which causes the concussive energy to flow throughout the brain and ultimately lead to a concussion. So next time you fall off of a tube connected to the back of a speed boat and smack your head against the water at such a force that gives you a concussion, you can blame your misfortune on the fact that your brain is made up of matter and therefore influenced by the law of inertia.

Implying that your friends were getting the correct flight trajectory.

For anyone that has watched or played baseball, hitting a homerun has to be one of the most exciting plays that can happen. Looking at this play deeper, the physics of hitting a baseball over a fence is very fascinating. One of the things that makes this play so difficult for major league hitters is how quickly the ball is traveling, and how small the area of the bat you have to hit the ball with is in order to make it travel so far. The "sweet spot" on a bat where you will likely have to contact the ball is very small, around 4-6 inches long on the bat. Hitting the ball in this spot will minimize vibrations of the bat and possibly maximize the transfer of energy between the bat and the ball. For a baseball traveling in excess of 90 miles per hour towards the batter, contacting the ball with the sweet spot of a 32-inch bat can allow the ball to leave the bat at speeds exceeding 110 miles per hour, which can cause the ball to travel as far as 475 feet, not accounting for wind and various other factors acting on the ball in flight. Major League Baseball has begun to realize how fascinating the physics of the sport can be for fans, and has recently started to track many more of the physical measurements that occur during a baseball game, on top of just pitch speed. The league now broadcasts the distance the ball travels, the speed it travels initially after contact, and the apex height of the ball in its flight. They've also started to measure the speed that fielders and base runners run with, and the efficiency of the route that they take to the ball. All of these measurements add to the intrigue of the sport, even for people who do not understand anything about physics. This revelation in baseball shows how fascinating the physics of sports can be, for any sport.

I wish I had such a talent when it comes to minute rice

Like everyone else, this is my first blog post for Physics C. Outside of school, I really enjoy to golf, play CYO basketball, be around my friends or attend sporting events. I love to watch baseball and football, and that's how I spend all of my time that isn't taken up by calc, physics and econ. My biggest strength in school is that I generally understand things pretty quickly, but I could definitely benefit from an improved work ethic. In the future, I plan on attending college like most other kids in my position, but I really have no idea what I want to do once i get there. I am taking AP Physics C because, as I said, I really have no idea what I want to do in the future, so I figured the best way to set myself up for the future was to take the most challenging classes possible. What I do know about my future is that I want to be as successful as possible, and really intend on selecting a major that will best set me up for this. You're always told to major in something that you are passionate about, but I don't think many colleges offer a major in the arts of watching the New York Mets. Through this class, I hope to gain a better work ethic and improve on working in a setting like this where you have to learn a lot of things more independently. I also hope to understand Physics to a greater extent than I do now, because I feel like this topic could definitely be an important one for me going forward. The thing I am most excited for this year is the day I finish my final AP exam, because once that day comes I will have survived senior year. I am very anxious for the decisions I will have to make about my future over the course of this year, especially regarding college. Just saying the word college is enough to make me anxious. I am definitely excited to see what's in store for me in this course, and I look forward to writing many, many more blogs.