1) What is the direction and magnitude of the current?
2) What is the funniest movie David has ever seen? (You need to answer this correctly in order to get the cookie.)
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DavidStack
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Alright Charlie, I'm writing a cookie problem just for you. You might need to get the cookie from Liz, but I figured I'd write one since you said there haven't been enough. And continuing with the Disney theme, here goes: Mulan is curious about how current and magnetic field interact, so she inserts her charge filled sword (which temporarily acts like a wire) of length 1 m into a magnetic field of 2 T in the postitive i direction, creating a force a 2.5 N in the positive k direction.
1) What is the direction and magnitude of the current?
2) What is the funniest movie David has ever seen? (You need to answer this correctly in order to get the cookie.)
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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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After spending about two hours in a hot tub the other night and therefore having excessively pruney hands, the question that I've always been curious about came to mind: why does our skin get pruney when it's been under water for a long time? I looked up some things, and discovered that at first, scientists believed that it was simply due to the different layers of skin we have. The outermost layer of the outermost layer of our skin has cells that are filled with keratin, a protein that keeps your skin hydrated by absorbing a lot of water. When underwater, the keratin absorbs a lot of water, expanding the cells and thus expanding the size of the skin layer. Since the second outermost layer doesn't expand, the outermost layer has to fold in order to adjust to the new size difference. This made perfect sense until it was discovered that people with severed nerves don't get pruney, which leads to the claim that our nerves "tell" our skin to get pruney. When our nerves sense that our skin is underwater for a long time, information is transferred along the neural pathways to "fold" our outermost layer of skin in order to increase the mew of our skin and thus increase the force of friction between our hand and whatever we touch (since F(f) = (mew)F(n)), thus giving us better grip in order to fight against the now slipperiness that the water on our hands creates. It's crazy how intelligently our bodies were created!
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Gravity.
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As I perpare myself mentally, physically, and spiritually for the upcoming CYO basketball season, I can't help but think of the physics that partner with a fluid and successful basketball shot. Players that have perfected their basketball shot, like Ray Allen, have found a combination of enough leg bend, a straight-armed follow through, and an effective wrist flick. With these three key components, the ball travels with arc and backspin in a projectile motion, sailing through the hoop. The potential energy developed through the bend of the legs is stored in the leg muscles (which act much like springs), which is then transfered through the arm to the ball and converted into kinetic energy, giving the ball the energy to travel to the hoop. Basketball shots that have arc are much more effective than flat shots because the ball moves less in the horizontal plane in the time it takes the ball to travel through the hoop, so the ball has less of a chance of hitting the rim and bouncing out. Also, the backspin creates a softer bounce of the rim, giving the ball a greater chance of bouncing into the hoop off of the rim. So, through my knowledge of physics, I can focus on getting the power in my basketball shot from my legs instead of my upper body, and making sure I have an effective amount of arc and backspin.
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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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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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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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I recently played a very poor serving tennis match and sit here thinking about why my serve was and often is so inconsistent, realizing that it comes mostly from my toss. The racket should contact the ball when the hitting arm is fully extended, but I often toss the ball short and contact the ball while my arm is still bent. By hitting the ball at the highest possible point, I maximize power and accuracy - the ball is at its maximum potential energy so more kinetic energy results when it is converted, and a higher height above the net means that the ball can be hit at a greater range of angles and still land in the service box. With a higher toss I can improve the consistency and pop of my serve so that I'll be like this guy :glee: and not this guy :banghead).
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After spending quite some time with the Kerbal project, I am starting to understand how the program works. Building the biggest rocket possible doesn't really work; you need a balance between fuel level and weight, aerodynamics, the necessary seperators and parachutes, and a knowledge of when to hold off on burning fuel, the SAS, and other things like that. Thus, our first couple launches were not as successful as we would have hoped, but as we learned to decrease the drag force by improving the rocket's aerodynamics and not just stack fuel tank on fuel tank, which decreased the engine power by making the rocket too heavy, we started having successful launches. While the game is definitely interesting and I have learned a decent amount about space exploration, I wouldn't mind if there were other options for an end of the year project, given that I don't necessarily love video games and there are topics that I would love to explore, especially things involving engineering. So to recap, the program is a great idea for an end of the year project, but other options would be much appreciated.
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To add to the benefits of the Kerbal space program listed in the previous post, it helped us with the bottle rocket mostly in terms of simplicity. Instead of trying to make a giant rocket with parachutes or other complicated things, we decided to go with a simple rocket because we learned the importance of aerodynamics and weight balance through the Kerbal space program. My group realized that all we really needed was the two liter bottle, fins, a nose cone, and some weight on the top of the rocket in order to help it fly straight and keep the center of mass towards the top of the rocket, while the drag force was towards the bottom of the rocket. Even though our rocket wasn't flashy or put together incredibly precisely, it had the basic components to fly for over 5 seconds, which I consider to be a success. - Read more...
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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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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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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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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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In the famous Bible story of feeding the 5000, Jesus and his 12 disciples feed 5000 men with 5 loaves of bread and 2 fish. But, the 5000 only counts the men, and since these people have been following Jesus for over 2 days, it can be assumed that they are with their families. On average, we'll say that each man has a wife and two kids, speaking that some of the men weren't married and some of the men had much larger families. That means that this story is actually the feeding of the 20000.
First, let's look at how much bread and fish would be needed to feed these people. According to Mark 6:42, the people "ate and were satisfied." These people hadn't eaten for 2 days as they've been following Jesus, so to eat and be satisfied, each person would need at least 2 fish and a loaf of bread. There needed to be 40000 fish and 20000 loaves of bread, meaning that Jesus multiplied the amount of fish by 20000 and the amount of bread by 4000, and that doesn't even include the extra 12 basket-fulls of bread that the disciples picked up afterwards. That's crazy!
We can also see how long it would take to pass the bread around. The passage states that the people were divided into groups of 50 and 100, so if the groups are close to equal, there are 133 groups of 100 and 134 groups of 50 (267 groups in total). With large groups like that, the distance between the center of one group to the center of another was probably around 30 meters (close to 100 feet). The disciples had to pass around a lot of food to each group, so they likely stayed all together. Thus, they had to walk a 26700 meters to go to each group, and since the people ate and were satisfied, they probably wanted seconds, so that's actually 53400 meters with an average velocity of 1.4 m/s (the average walking speed). Using kinematics, we know that v = x/t, so t = x/v. Therefore, it would take 38143 seconds for the disciples to pass out that food, which is about 10 hours and 36 minutes. That's a lot of time!
By understanding physics, you can appreciate the incredible awe of this miracle.
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There's more to the knowledge I've gained from the Kerbal Space Program. First of all I couldn't get the screen shot to work; I guess the F1 key doesn't like me. And yes, I did just use a semi-colon outside of English class. But another very important thing I've learned through the Kerbal Space Program is how to correctly get a lot of power to your rocket. While I previously thought that either putting one engine at the bottom of stack of fuel tanks (the engine doesn't have enough power to lift up that much weight) or that having layer upon layer upon layer of fuel tanks and engines (the rocket becomes too wobbly and essentially combusts) were good ideas, I soon discovered that two separate layers of fuel tanks and engines, one on top of the other, is a great combination since it makes the rocket not too wide so that it flies straight but also gives the rocket enough power to get off the ground and eventually orbit in space.
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There are a few things that come into the physics of punching something. First off, impulse plays a huge role in punching somehting. Obviously as you punch something such as a wall or a person you will experience an impulse as you have a change in momentum. Therefore the thing that you are punching will feel the force of the punch as well as the impulse delivered from the punch. Due to Newton's second law you, the puncher, will also feel a force driving backwards in your direction as every reaction has an equal and opposite reaction. This describes the physics of punching something with your fist.
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So apparently there's more to dropping a ball than just gravity... who would have thought?! Well, for starters, when the ball is above the ground it has potential energy, due to the equation U = mgh. (See? Gravity is key!) As the ball comes closer and closer to the ground though, that potential energy is steadily converted to kinetic energy in the form of velocity (k = .5mv^2). Since m is in both equations, the mass of the object does not affect how fast the ball falls nor the time it takes the ball to fall. HOWEVER, an important thing we learned in Physics C this year is that not all of the potential energy is converted to kinetic energy, due to the fact that a drag force acts against the object falling. This drag force creates friction, which heats up the object, and that heat accounts for the "lost" energy. So that is the physics of dropping a ball, although, as I previously stated, it can really be summed up by this: gravity.
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Well this is kind of bittersweet, finally being done with blog posts but also realizing that high school is completely over, as is Physics C with a fantastic teacher. I've learned so much during the year, from angular analogs to retarding forces to induction to the sheer brilliance of Walter Lewin's ability to draw a dotted line; it's been quite a year. I've appreciated this blog posts as much as I've hated them, mostly because they forced me to truly learn the stuff that I write about. And now when I struggle with physics in college, I'll always be able to go back to APlusPhysics and ask for help. I encourage anyone and everyone to take Physics C - it's certainly challenging but I can't see how you could regret it. So, farewell APlusPhysics, I'll likely come crawling back in no time at all.
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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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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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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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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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