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DavidStack
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After not performing as well on the practice physics test as I would have hoped, I began to think about the physics of test taking, mainly using energy. We've learned that kinetic energy = .5mv^2 and that potential energy = mgh. In this instance, m = the question number, v = the speed that I answer questions, g = how easy the test is (the greater g is, the easier the test is), and h = my confidence. Therefore, my potential energy at the beginning before I take the test is converted to kinetic energy throughout the test taking process. Since mgh will equal .5mv^2 by the end of the test, the m's cancel out, showing that the question number does not matter in this scenario. By this equation, my velocity by the end of the test will equal (2gh)^(1/2). With this equation, it is clear that when I am more confident and have an easier test, I take the test faster and more efficiently. Also, my velocity can vary throughout the test since g is a constant but h is a variable as my confidence can rise or fall depending on if I get questions right or wrong. So, my goal for this midterm is to either study a lot and gain confidence, or just hope that we get a really easy test.
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Reflecting on my Christmas presents, I immediately think of the incredible gift that my sister Julia got me, these super comfortable moon boots. But why are they so comfortable? As with most things, physics offers an explanation. As we've learned way back with momentum, impulse is equal to the force multiplied by the change in time. Impulse also equals the change in momentum, and given that momentum is conserved when only conservative forces are acting on the object, the impulse does not change. Therefore, when the time that the force acts on the object is lengthened, the force felt by the object decreases. This is where the moon boots come into the scenario. Ordinary sneakers have little padding between the sole of the sneaker and the wearer's foot, so the time of impact from the floor to the foot is relatively short, meaning a relatively large force. The moon boots, on the other hand, have a great deal of padding, extending the time of impact of the wearer's foot and the floor. This reduces the force felt by walker and provides them with a lighter, more comfortable feeling as they feel almost like they are walking with less of a gravitational force (as on the moon, hence the name of the shoes).
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A dear friend of mine and I have recently started playing NCAA Football 12 on his 360 and most of the time I win, thanks to my knowledge of physics. Because I understand the concepts of conservation of momentum, work, and air drag, I very often run the ideal football play - the running back slip screen. For this play, the offensive linemen break their blocks on some of the defensive players who are rushing the quarterback. Lured into the illusion that they can have an easy sack, these linemen and/or linebackers charge towards the quarterback. At this time, the running back breaks his block and turns towards the quarterback for the easy dump pass, like this:
After that, the linemen that "missed" their blocks before now block for the running back, who has many blockers and open field in front of him. He does not need to worry about the defensive players behind him because of the law conservation of momentum: the defensive players are sprinting in one direction and they need a strong force (which comes from their muscles power) to reverse their momentum to the opposite direction. On the other hand, the running back's blockers are always moving in the right direction, so the do not need this strong force and their momentum aids them in delivering solid blocks. Not only so, but this play works much more consistently than a pass down-field because of the principles of work and drag force. The simple equation for work is force times displacement, so to throw the ball far down the field, the quarterback must do a lot of work. The correct amount of force needed for a far throw is difficult to consistently deliver, making this pass much harder. The drag force on the ball also applies because the ball travels in the air longer for farther passes, so the drag force acts on the ball for a longer period of time, affecting the consistency of the throw. Thus, because of my understanding of mechanics, I can lead a well poised offense to give my Michigan Wolverines the win every time.
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Although I had to quit indoor track because of an ankle injury, I did learn a lot about the precision of triple jumping form from my coach. Previously, I had run my approach with my chest not perpendicular to the ground but slightly more forward and my knees did not move very high. With this form, my momentum (which points perpendicular from my chest) was pointed into the ground, preventing me from jumping as far as possible. My knees also needed tweaking, since a lot of the power from jumping comes from the knee drive. Because my knees moved little as I approached my jump, it was hard to suddenly rip my knee up when I took off, due to the conservation of momentum (it takes an external force to change the direction of my momentum, but if my momentum was already directed up and forward, that force would not be necessary). With a continued knee rise throughout my approach, I could develop a more fluid and powerful jump. While these adjustments to the approach slightly decreased my speed, they vastly improved my control and jumping power, greatly lengthening the distance I could jump.
This world class jumper displays this approach form, leading him to a record breaking jump:
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Because I have a habit of bouncing from activity to activity, I chose to participate in the musical this winter after my body failed to push through the pain of indoor track. With my luck, it turns out that the musical this year has multiple tapping numbers, so i get to learn how to tap dance! So I wondered, how do tap shoes make the noise that they do?
The physics is really quite simple. When the tapper pushes their foot to the ground, a lot of the kinetic energy is converted into sound energy, dispersing a crisp noise. Tap shoes produce a louder and crisper sound that the average shoe because tap shoes have metal plates on the ball of the foot and the heel, and metal (because of its free flowing electrons) conducts sound better than rubber - the typical bottom of a shoe - does. Tap shoes also produce a crisper sound when just the ball or heel of the foot makes contact with the floor because when the whole foot is on the floor some of the path way of the sound is trapped under the foot, creating a somewhat muffled noise that sounds more like a stomp than a precise tap. Thanks to physics, I understand how to make a crisper noise when I dance which will hopefully improve my dancing ability!
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As the playoffs are underway, Bills fans (the sad category that I put myself under) have the same dilemma as they have since the 21st century began - which team are they going to root for in the playoffs this year? Year after year, the Bills struggle to qualify for the post season, a big reason being that they never have a strong quarterback. Their most recent excuse - Ryan Fitzpatrick. So lets look at why he's so awful:
When you look at an elite quarterback like Tom Brady (as much as I hate to admit that he's good), you witness extremely precise and accurate throwing mechanics. He uses the potential energy from his lower body (by bending his knees, creating a buildup of muscle power, and then stepping with his opposite foot) to provide the power for his upper body to move fluidly and transfer this potential energy to the kinetic energy of the ball. With these mechanics, he can make 60 yard passes accurately and effortlessly (at least so it seems).
Ryan Fitzpatrick, on the other hand, does not exhibit these mechanics. He uses mostly his upper body to deliver speed and distance to his throws, making him look like he throws in body in order to throw the ball. Because of this, he fails to use the huge supply of potential energy that his lower body has to offer, reducing the power of his throws. Not only that, but his upper body now has to focus of both the power and accuracy of the throw, which makes more of Ryan's throws off target. Even though Fitzpatrick graduated from Harvard, he seems to struggle with the concept of conservation of energy as he does not know how to efficiently convert the potential energy of his muscles to the kinetic energy of the ball, leading to many inaccurate, under-thrown passes and unhappy fans.
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Given that this is my first post of the second quarter, it's fair to say that I am not always on top of my Physics work. And since I have not been doing as well on our tests as I would hope, I have a couple new year's resolutions regarding Physics:
1) Do my blog posts before the weekend that they are due!
2) Continually look over equations so as to hammer them into memory
3) Study more diligently before tests instead of "hoping for the best" as I often do
With these resolutions, hopefully I can see my test scores rise and my stress levels fall (known as David's theory of the inverse relationship between stress and test scores, which will hopefully prove true).
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No doubt, the weakest part of my tennis game is returning hard serves. I often try to hit powerful shots, so i take a large backswing. But, when returning a serve, the ball already has a high velocity, so a large backswing is not needed to hit the ball back with a high velocity. Actually, a small swing is much more effective and accurate. This is because of the principle of momentum. When hitting a serve, a large swing is necessary to give the ball a high speed because the ball, right before contact, has a momentum very close to zero. So, a large force is needed to produce a large momentum. But, when the ball is traveling to the opponent with this large momentum, the opponent does not need to generate a large momentum in return, they only need to redirect the momentum. Thus, a large backswing is not necessary; the opponent just needs to hit the ball with a short and quick swing. If you watch professional tennis players, you will notice that they rerturn really fast serves with fast returns with a small and quick swing, as they have learned of the physics of tennis and know to simply redirect the momentum, not try to create new momentum. Once you understand the physics of tennis, you'll be looking like this guy.
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So good thing I spent half an hour trying to figure out how to make a post, and then thought, 'hey, maybe I should actually look at that sheet that Mr. Fullerton gave us,' only to realize that all I had to do was verify my account, and that I wasn't supposed to make my real name my user name. But anyways, here is my post. The first thing to know about me is that I love Jesus, and really the reason there's any need for you to know that is because that is why I'm taking AP-C Physics. I would love to become a Civil and Environmental Engineer, and create better water filtration and water collection systems for impoverished countries, much like the Ugandan Water Project, also using the civil side to help design more efficient infrastructure in these countries. I've been on numerous missions trips, most recently to Peru, and have discovered a love for serving others and teaching others about Jesus. In the class specifically, I'm excited to be challenged and start making connections to what I learn now and how I'll use that in the future, but I am a little anxious about discovering the many complexities of physics. And other than all that, you should know that I love the Bills (which obviously is thoroughly depressing), I really enjoy talking to people and hanging out with my friends and playing sports, and I quit when things get hard.
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In the wake of the costly hurricane Sandy, its interesting to look at how physics explains the dangers of those extremely powerful winds. In my backyard, the gusts snapped a horizontal branch off of one of my trees on monday night, so I wondered how dangerous it would be if I was standing under the branch when it hit the ground. The branch was about 4 meters high. Assuming that the wind was moving completely horizontal and perpendicular to the branch, the branch would have had no vertical force acting on it, neglecting air drag. Thus, you can calculate the vertical speed of the branch upon hitting the ground with conservation of energy. K = U, so .5m*v^2 = mgh, so v = (2gh)^(1/2), so v = (2*9.8*4)^(1/2), so v = 8.85 m/s. The wind was moving at 35 mph (15.6 m/s), so that is the horizontal speed of the branch. Given these two speeds, the final speed of the branch is calculated by taking the square root of the sum of the squares, so v = 17.94 m/s (40.13 mph). I don't know about you, but I certainly would not want anything crashing into me at 40 miles an hour, so Sandy was dangerous even as she was cooling off.
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As we dive into impulse and momentum in this independent physics unit, I am reminded of my only car "crash" I've ever experienced, if you can even call it that. When I was backing up in a small parking lot several months ago, the back of my car bumped into a small pole that I didn't see, jerking my car to a stop. Due to the minimum speed my car was moving at (5 mph or 2.24 m/s), my car was not damaged at all. So I was interested in finding out what speed it would have been damaged. Given that the car accelerates from 0 m/s to the collision speed in 1 second, its acceleration will equal the collision speed. The force of the collision is measured by F = ma, and with a mass of 1000 kg (close to the mass of my Toyota Corolla), F = 1000 * a. A 1000 kg car can withstand an impulse of about 1000 N*s without damage, so with a collision time of .2 seconds (for the car, not the driver), and the equation J = F * change in time, J = 1000 * a * .2. Thus, 1000 = 200 * a, meaning that the car can top out at an acceleration of 5 m/s^2, or a collision speed of 5 m/s (11.2 mph), without damaging the car if the car starts from rest.
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So, we all know that everyone in our AP-C Physics class has to be a nerd to be crazy enough to take this class, and i think we could come up with a lot of great nerd costumes. For spring potential energy and conservation of energy, someone could attach a spring to the front of his or her clothing and then run into people and bounce off with equal kinetic energy. Or, for centripetal motion, someone could carry around a rope which he or she hands one end of to random a random person and then runs in a circle around the person, holding the other end of the rope. Or, for the grandest of all, we could have a class atom costume, where a couple people are protons (all blue clothing with a giant "+" on the front) and a couple are neutrons (all gray clothing with a giant "o" on the front) and the rest of the class--hopefully the smaller people--as electrons (all yellow clothing with a giant "-" on the front) running around the cluster of the nucleus. Next Halloween is about to be bumpin'.
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If you have ever watched Hot Rod, one of my favorite movies, then you understand the joy/hilarity of poorly thought out stunts. My brother and I have always enjoyed puting ourselves in harms way of the purpose of an awesome video, but I've discovered that we are much more willing to do painful stunts if we are landing into water instead of on solid ground. Most recently, we went to some pier that was 10 or so feet off of the ground and attempted backflips on our bikes off of a ramp into the water. I don't think either of us would even imagine attempting such a thing if we were to land on the ground. But why? It has to do with molecular structure, a topic concentrated in Chemistry but still very important in Physics, as molecular structure impacts things like air drag and electrical forces. So, solids have a stiffer molecular structure than liquids because they move less, and likewise liquids are stiffer than gasses because they move less. Due to the cusion-like complection of water, it is safer to land in than landing on dirt. Professional stuntmen in movies often land in air-water mixtures instead of actual water because the air-water mixture is much less stiff, breaking the fall of the stuntman more than water would. This all relates back to impulse, as the less stiff structures provide a longer time of impact, reducing the force felt on the person.
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Ping Pong has always been one of my favorite leisure time activities, and after embarrassing a good friend of mine yesterday with my ping pong skills, the physics of the sport came to mind, especially the physics of my favorite shot: the top spin shot. Arguably the most effective shot, the top spin increases your accuracy with more powerful shots, and is very difficult to return. But why?
The picture above shows how the spin of the ball forces the air below the ball to take a longer path, while the air going over the top of the ball has a shorter path, thus moving faster relative to the ball. Because of this difference in air speed, there is a downward force on the ball, causing the dip of the ball soon after it is hit. With this dip, the ball falls faster than a non spinning ball, allowing the player to hit the ball with more force and still have it drop on the other side of the table, giving the player more accuracy. Then, the forward spin of the ball couples with the forward direction of the ball upon impact of the table, increasing the speed of the ball and making it difficult to return. This very interesting physics of air flow is used in designing air planes, rockets, and many other inventions.
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Continuing with the physics of recreational sports, I'd like to talk about the physics of tether ball, a sport I'm not quite as good at. But, tether ball clearly demonstrates centripetal motion, and is very interesting to delve into. A player will hit the ball with a horizontal force F. Neglecting air resistance, this will temporarily be the only force on the ball, and will equal the mass of the ball times the acceleration of the ball. Centripetal acceleration equals (v^2)/r, so, given that the mass of a tetherball is about .27 kg, and the rope (which is the radius in this situation) is about 2.25 m, F = (.27 * v^2) / 2.25. Given this equation for velocity, a player can figure out how to beat his or her opponent. If a player know that his or her opponent cannot return a ball traveling greater than 10 m/s, he or she knows to hit the ball with at least an F = (.27 * 10^2) / 2.25, or F = 12 N, assuming the rope can sustain this force. So, even though air drag has an affect on the ball, and it is very hard to figure out how to hit something with a certain force in newtons, the physics of centripetal motion helps one to attain a better knowledge of how tetherball works.
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Depressingly, I followed the whizzing ball as it flew past the 50, the 60, the 70, and even the 80 yard mark. Our costly (both with time and money) trebuchet could not compare to the spring loaded demon of a catapult that bested our yardage by 44. But, this project certainly did improve my engineering knowledge. Comparing my trebuchet to another very similar one that flung the softball farther, I saw that with a stiffer structure, we could have had more success. If we had used screws instead of nails, and secured the pole that our level arm swung on with bolts instead of duct tape, we could have supported more counter weight and had a more fluid, straight, and speedy projectile. Also, the record-tying trebuchet showed me that a bigger catapult is not necessarily better, as that trebuchet was less than half the size of mine but shot the ball so much farther because of the very powerful springs and bungee cords. So, I can say that our catapult did fairly well, I enjoyed the creativity and problem solving that the project required, and I am better prepared for projects in the future.
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