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Everything posted by IVIR

  1. IVIR


    This past weekend, I saw a giant game of Jenga at MIT. Literally. The blocks were nearly 2x4s, and the structure was taller than I am. While I did not stay to watch, it is interesting to think about a few of the different strategies that I remember from my childhood days. First of all, I used to believe that the faster you pulled the object out, the less chance a collapse would occur. While I'm not sure of my logic behind this reasoning, I most likely imagined that hopefully the structure just wouldn't have time to collapse if I pulled it fast enough (Yeah, I know). However, after the block is removed, whether quick or slow, the structure will still have the exact same properties regardless of speed. Another theory may be to reduce friction, but it is important to note that the frictional force does not rely on velocity, it relies on the normal force. The one factor that does effect the result of the turn is how straight you are able to pull the block out. By pulling the block straight out, you are minimizing the normal force, but if you tilt to one side or another, you are increasing the normal force and creating a larger frictional force. Another concept of the game Jenga is torque. Since torque is F x r and the r in most jenga games is relatively small, the structure can often withstand the removal of blocks that may have seemed impossible. The middle block is at the center of the fulcrum, so the r would be 0, allowing players to theoretically remove all of the outside blocks while keeping a cross pattern in the middle. This is much easier said than done due to the friction caused by uneven pulls (an even perfect pulls as the wood has a large surface area) and the fact that even a small breeze can cause enough torque in the other direction to knock the tower down. A horizontal breeze may have a small force, but since the center point is technically the ground in this plane, the r would be as tall as the tower. Hopefully, the physics of Jenga could help people improve their gameplay, but to be honest, isn't the best part watching it all fall?
  2. IVIR


    Cars, especially sports cars, often have their horsepower compared as a somewhat ignorant method to determining the faster car. However, this is not the most accurate way of making judgement because there are other variables, some much more important, in determining a cars acceleration or top speed. While an engine's horsepower provides the force, accelerating the car, it is important to remember the basic fact that F=ma. Therefore, a 4000 lb car with twice as much horsepower as a 2000 lb car will accelerate at the same speed. This is the reason that lightweight sports cars that are often half the price of supercars have similar accelerations. Especially with the Porsche 911 GT3, any possible excess weight is removed to allow for the greatest acceleration, one that can compete with Lamborghinis and Ferraris. Also, when people assume that more horsepower is equivalent to a greater top speed, they are ignoring a very important concept: terminal velocity. Yes, it is important to have a large enough engine to accelerate the car at a great rate, but ultimately when you start getting into the 200 mph area, design is much more important than power. As we learned earlier this year, air resistance is directly related to velocity. However, the extent of the air resistance varies greatly depending on the shape of an object (For example, dropping a book vs a sheet of paper). Therefore, it is necessary for car designers to minimize air resistance while still creating downforce in order to create the best results. The balance of these two goals and new advances in materials/aerodynamics is the reason that street legal cars have been increasing in performance greatly, but also the reason that creators are having a hard time creating a road legal car that hits above 250 mph, while still looking/feeling comfortable.
  3. Have you ever dropped a ball and had it bounce once normally before taking a crazy second bounce? I'm always watching out for this phenomenon when I have a lacrosse ball on a hard surface, but I've never really understood what was going in. The main factor causing the crazy second bounce is actually the spin on the ball acquired during the first bounce. As the ball falls, it usually has a small amount of spin or is traveling at an angle that isn't 90 degrees. As the ball hits the ground, the ideal,perfectly elastic collision does not happen as there is friction between the ball and the ground. This friction is responsible for creating a backwards force of the surface of the ball, resulting in a much greater spin than before. When the ball then hits the ground the second time, the spin takes effect as the ball shoots off in the direction of the spin, reaching a low vertical displacement but far horizontal displacement. Because of the role friction plays in adding the additional spin on the first bounce, this effect is not as prevalent with balls that do not have high coefficients of friction with other surfaces. Since rubber does have a pretty high coefficient of friction with other surfaces, lacrosse balls and most bouncy balls follow this abnormal pattern, causing disaster for any ignorant owner who happens to drop it.
  4. In the past few years, Madden NFL video games have adopted real time physics, an extremely complicated technology that allows the players in the game to react according the actual physics. In previous Maddens, a spin move would result in one of four tackles, and there were only about 10 different types of tackles, making the end of plays appear too staged. However, real time physics enables the characters in the video game to react to a force from an opposing player as they would in real life, causing an infinite number of tackles. For example, if a linebacker hits the running back with the "hit stick", the running back may fall down immediately, stumble for a few steps before falling, or even regain balance and keep running. Real time physics is also used for fluency in movements as making a catch no longer seems robotic. While Madden may be incorporating real time physics into their game play, I've started to think that the NFL enjoys testing the limits of physics with crazy coincidences and plays. For example, the front flip touchdown seen below, is a classic example of angular momentum along with torque. The player was relatively stretched out with the intent on diving into the endzone, but the defender hit his feet. Even though the force was not great, the long distance of the lever arm to his center of mass created a high torque, causing the runner to tuck their body in, now realizing that they are going to complete the revolution. And all of this happened in a few seconds.
  5. IVIR


    The simple art of Kan Jam or any other frisbee related game seems skills based, but it may help to have knowledge on the physics of the flight as well. The first aspect of a frisbee is the design. Most frisbees are relatively thin with curved edges, which make it more aerodynamic, creating lift while in flight. Similarly to cars, the curved shape at the front of the frisbee allows for air to pass over the frisbee faster than air passing under it, making the air above the frisbee at a lower pressure than the air below the frisbee (aka lift). Also, it is obviously important to make the frisbee spin in the air in order to create stability by increasing angular momentum that the simple force of air resistance has a hard time overcoming. Therefore, the more spin you put into your throw, the more stable its flight will be. This is perhaps the most useful piece of information as newcomers to Kan Jam often toss the frisbee gently, which only results in the frisbee sliding to one side or the other. In ultimate frisbee, there is a "kickoff" type of event in which one team tosses the disk as far as possible (or so it seems). On a single throw for distance, it would appear to be extremely beneficial to try to optimize the launch angle in order to provide a proper amount of lift without too much drag, but also achieve a sustained projectile motion flight with a large x component. Here's some frisbee trick shots for fun
  6. It is not surprising that shape has a lot to do with the movement and speed of objects, but it may be surprising that dolphins pose such a question to researchers when it comes to their advanced swimming techniques. The shape of an object can determine numerous factors of an object that are integral to its performance. For example, race-cars are built with a specific shape in order to produce high amounts of downforce while airplaines are built with their wings in order to create lift when piercing through the air. Downforce is produced by channeling air above a specific shape, causing the air resistance to have a small impact on overall speed, but have a significant impact on providing a force down on the object. Lift is the opposite, as airplanes are designed to channel air underneath the wings in order to keep the plane steady in the air, as gravity and the generated lift can hopefully come close to canceling each other out. Since air resistance is related to the velocity of the object, lift and downforce rely on the velocity of an object as well. The faster an object is traveling, the more air being channeled over/under the object and the higher the resulting force. This is why it is even potentially dangerous to go at lower speeds in an airplane or F1 racecar. Dolphins travel quite fast through the water compared to their complexion, making researchers wonder why they are such fast swimmers. Although not all of the answers have been found, it has been discovered that dolphins reduce drag throughout the water by shedding their outer layer of skin every few hours. Again, people are still not sure why this process would be beneficial, but it is quite cool nonetheless.Another important aspect of a dolphin's complexion is its tail fin. This fin is slightly curved in order to provide a greater thrust than a flat fin when stroking through the water, helping the dolphin obtain high speeds. It is pretty cool that dolphins pose such a big mystery to physicists and biologists alike as they swim more efficiently than what seems possible, making them able to stump humans.
  7. IVIR


    As usual, I found myself watching quite a bit of YouTube over break, especially different BMX videos. While I could only dream of pulling off the tricks the professionals do, watching it makes me feel nervous as I realize the potential consequences of a nasty fall. I have kind of a lot of blogs on landings/falling, so I figure I will use this blog to tackle one of the most crazy things a bmx rider will do: grind a downward sloping railing on one peg. For those not extremely comfortable with BMX biking, pegs are a small metal attachment that can go on either side of the front and back wheels. BMX riders actually jump onto a railing, balance on one peg for a short amount of time before landing comfortably. They make it look easy, but there are numerous factors at play. First of all, the rider must have a clean takeoff in order to hit the railing in the desired location. Secondly, the rider must withstand the impact of one peg landing on the railing without causing the bike to rotate. Since a single peg is on a single side of the bike, landing on one peg creates a torque as one corner of the bike is on a stable surface while the other side is still in downward motion. It is up to the rider to shift their weight at the point of impact in order to offset this torque and remain balanced. Another component of the maneuver is to remain balanced on the rail throughout the entirety of the trick (even though they are not on the rail for long). You will see that riders will turn about 15 degrees from their impact time on the rail to the landing as the horizontal momentum of the back of the bike keeps going, since it does not have something to stop it like the front of the bike has the peg on the railing to stop the motion in that direction. Finally, the landing requires the rider to have a little "give" in his arms and knees, so the impact is not as strong as a force as it could be. Locking the arms or wrists often results in a broken wrist as the human body is not built to withstand large forces in recreational sports. Here's a little video of some cool tricks that I couldn't even start to describe the physics of...
  8. Playing sports in high school, you start to look forward to any opportunities to leave the swampy grass for the fresh turf field. Since Pinegrove fields are uneven, rocky and often have large spots of grass missing, the turf is always a better option. However, playing on turf does not always end well for a variety of reasons. The good: traction. Turf provides excellent traction as it increases the coefficient of friction between the ground and cleats, enabling for sharp movements. On grass, the force of pushing off of a foot could cause the soggy grass to move, but turf remains firm, even in the most adverse conditions. Also, grass contains numerous rocky/hard spots, where the force of a step is unable to penetrate the surface of the earth, causing a lack of traction. Without friction between the human and the ground, there is no force propelling the human forward, prohibiting movement. The bad: heat. While this may be a mixture of physics, chemistry and biology (I don't really know), the surface of turf heats up to extreme temperatures in the heat. One reason for this is that the tiny rubber pellets absorb more energy than they release during the day (when it's sunny), but also the fact that artificial grass cannot evaporate like normal grass. Evaporation causes cooling as it is an endothermic process, making its surroundings appear cooler. The heat may feel good if you lay down on the turf in April/May, but when I went to Maryland for some lacrosse tournaments in July, people's cleats were literally melting. The ugly: turf burn. Friction is always switching between good and bad, but necessary for life. We want less friction when we kick a soccer ball to make it roll further, but at the same time it wouldn't roll without some friction. While the friction on turf is a blessing for running, it becomes problematic when you end up on the ground in a game. Although I am personally unaware of the exact number, I can attest to the fact that the coefficient of friction between the turf and one's skin is extremely high. The high frictional force, dependent on the subject and his/her actions, can even demolish large amounts of skin, causing anything from a red mark to an open wound. Overall, I would take the average turf field over the average grass field any day, but nothing beats a perfectly groomed grass field on a sunny day, as it is safe and efficient.
  9. Boxing and UFC are both entertaining (when there are available without the astronomical pay-per-view prices), but the physics of each one is pretty different. If anything, UFC is a more dangerous sport, making boxing look like a children's show. The major difference is due to the different types of gloves used in each one. Boxing gloves are pretty well known, but I've included pictures of both types below to make the comparison easier. While boxing gloves have quite a bit of padding, UFC gloves barely cover one's hand. As we have learned in physics, padding makes quite a difference on the force felt by an object. Since the change in momentum of an object equals force x time of impact, it is obvious that a longer time of impact will lower the force felt by the individual. In the case of boxing, the opponents arm has the momentum, which is being changed to 0 by your face (hopefully just your body, but you never know). The padding from the glove makes the entire impact take longer, therefore decreasing the force felt by your face. In UFC, the smaller amount of padding means that your face feels a higher force. There is another big difference between UFC and boxing; you can kick in UFC. Sure, a punch by Floyd Mayweather may still knock you out, but kicking can provide even more force. Also, it is important to remember that no glove is worn on the foot, so any impact from kicking is not padded at all, increasing the force felt by the recipient. Most people's legs are longer than their arms, so people can generate much more torque with their legs than their arms, creating powerful kicks. I'm willing to bet the angular momentum and torque generated by a roundhouse kick will nearly knock somebody unconscious, but this is one experiment I wouldn't want to test myself.
  10. IVIR

    Tire Swing

    Growing up, my best friend had a tire swing in his backyard. While it provided trivial entertainment, looking back, a tire swing involves quite a bit of physics. First of all, there is the connection to the tree. The swing needs to be far enough away from the base of the tree in order to prevent accidental collisions, but it also needs to be sturdy enough to withstand human weight. The further out from the base of the tree you put the swing, the more torque that is applied to the branch as the lever arm is being increased. Perhaps this is why they have the "do not try this at home" warning on most innocent projects. Another aspect of the tire swing is the ideal motion of the swing, similar to that of a pendulum. Like a pendulum, the rope is nearly mass-less in comparison to the tire and human object, allowing for simple harmonic motion. However, air resistance and other movements prevent the pendulum from reaching its previous height each time, creating a dampening effect, even though it is extremely slow. In addition to this motion, the tire swing often rotates. Similar to the common figure skater example, a stretched out human will rotate slower than a balled up human, due to the indirect relationship between rotational inertia and angular velocity as they are multiplied to equal the consistent angular momentum. Finally, the tire swing usually ends up following an ovular or circular path instead of a straight line, so it would be interesting to study the exact physics of a pendulum in a non-linear path. It is also important to remember to hold firmly onto the swing, as a fall from the swing could result in serious injuries (Witnessed it firsthand) due to the acceleration of gravity, but also unforgiving nature of the ground, specifically tree roots. The hard surface of the roots keeps a low impact time, causing a high force to be felt by the person as their momentum is immediately changed to 0. EDIT: Didn't see Kate's blog on this, sorry kate :/
  11. Since we learn that objects consistently gain velocity in free fall motion due to the acceleration of gravity at 10 m/s^2, why doesn't rain and snow wreck havoc since it is falling from an insanely high distance? One reason for this lack of speed, especially with snowfall, is because of air resistance and drag forces. The net force on a snowflake would be the weight (mg) minus the drag forces acting on that object. Since snowflakes are relatively porous and non-aerodynamically shaped, the drag force is relatively large. Perhaps more importantly, a snowflake barely has any mass so the force of its weight is barely noticeable. Also, by the time the snow, or rain, reaches a height where we can see it, the snowflake or raindrop has reached its terminal velocity, which is not very high. Rain does indeed travel faster than most snow due to less drag forces, but there is a specific reason that rain does not hurt us instead of simply plopping onto our skin. Rain is a liquid, so when the raindrop does hit our body, the force isn't completely transferred to our body as the water droplet splatters itself. However, large bodies of water, like a large can still exert large amounts of force without absorbing a lot of the impact force. For example, if you cliff jump from an extremely high distance into water, the force of impact on the water is still extremely high. Part of this is due to relatively high surface tension of water, but the other part is that the water cannot dissipate all of the force of impact since it is a liquid, not a gas. These same reasons are also the reasons why hail and ice storms can cause serious damage as they are significantly more massive, and their shape/composition allows for lower drag forces. Large pieces of hail still reach a terminal velocity, but this terminal velocity along with its relatively large mass allow it to create immense damage, including puncturing car windshields. The car windshield and hail are in contact for such a little time that the impulse force felt by the windshield is incredibly large. Also for a follow up on my previous blog about bulletproof glass, a car windshield is layered with plastic as well, preventing it from shattering upon impact. This is also why bullet's penetrate car windows without shattering them for the most part. Rain and snow cause a ton of damage across the world each year, but on the bright side, there is no need to run for cover when these infamous particles are failing from the sky. If they are large hail particles though, put your car in the garage, cover your house with steel and get inside because it is no joke.
  12. In the great game the Denver Broncos happened to win, there was a critical personal foul called in which a Denver player blasted the New England receiver shortly after the receiver caught the ball, incidentally hitting the receiver helmet to helmet. Considering that the average NFL player can run 15-20 mph and weighs around 200 pounds (90 kg), that is a lot of linear momentum that the receiver is being hit with. When the player is hit, a lot of the energy is dissipated as the players come to rest almost immediately after the collision. Since this particular collision was helmet to helmet, this means that the momentum and energy from the defensive player was mostly transferred to the helmet of the receiver. Fortunately, helmets have padding designed specifically to increase contact time, and therefore lower the force felt from a collision. Despite the helmet lowering the force felt by the receiver's head, a large portion of the energy and momentum is transferred to the head of the receiver, whipping the head backwards. While this whipping motion can cause neck injuries due to the sudden acceleration of the head, it also causes concussions. The brain wants to stay still due to its inertia, but when the head whips, it causes the brain to whip back and forth. There is actually some room between the brain and the skull which allows this. The movement of the brain back and forth can damage nerves as well as the Brain itself, leading to a lot of NFL players developing mental health conditions after retirement. Unfortunately, players need to assess the risk of playing football because hard hits to the head are inevitable, even if everybody is doing as much as possible to prevent it. Denver deserved a penalty, but its hard to change your linear momentum when a player ducks into your tackle. This is why the NFL is investing so much money into concussion awareness and research.
  13. Way to steal my project
  14. Since I'm sure everybody is watching the Denver Broncos vs. New England Patriots game right now (its currently halftime), I'm sure many of you are thinking how could the Patriots miss an extra point. Well, if you are curious, visit my previous blog on field goal kicking. More importantly, I'm sure some of you are like me, nervous due to Peyton Manning's lack of throwing ability in his old age. After his neck surgery, and since he is approaching 40, his arm strength is decreasing, requiring him to throw the ball with more arc and earlier. This brings up some interesting physics as Peyton needs to alter the projectile motion of the football to suit his lack of arm strength. On a short route, a normal quarterback can zip the ball to the receiver with a high velocity, decreasing the time the ball is in the air, the height that the ball must reach and how far the quarterback must "lead" the receiver. When the ball is thrown with a higher velocity, it does not need to be thrown with as much arc to reach its desired target as it can be in the air a lower amount of time and still reach the target since there is no acceleration in the x plane. However, Peyton Manning introduces numerous possibilities of error since he needs to put more arc on the ball. Since he is releasing the ball with a lower velocity, he needs to increase the time the ball is in the air, which means throwing the ball sooner than the receiver is ready. While this could turn out very well if timed perfectly, a mistake by the quarterback or receiver could leave a floating pass available for the defense to make a play and intercept the ball. Another problem is that when trying to arc the ball more in order to compensate for a lack of velocity, Peyton needs to calculate the velocity and angle in order for the ball to reach the receiver at the right height. This is difficult when you have 300 pound lineman running at you, which is why Peyton is under-throwing some receivers while overthrowing others. One advantage of a softer pass is that it is often easier to catch. Since the mass of a football is constant, the momentum of the football is proportional to the velocity. Therefore, a higher velocity football has more momentum, which means that a receiver must try harder to catch the football as the force required to bring that momentum to zero is inversely proportional to time of the force applied. This means that a player must catch the ball "like an egg", or simply have strong enough hands to withstand the large impact force. The second half is about to start, lets hope Denver pulls out the dub!
  15. A trampoline is a great example of spring potential energy and a restoring force, but it also brings up another question: why is there a 'maximum' height and why can you "double bounce" someone to make them fly higher than that maximum height. As a person begins jumping on a trampoline, their kinetic energy is converted to spring potential energy when they contact the trampoline, and then converted back to kinetic and gravitational potential energy as the person leaves the trampoline towards the sky. Since the first bounce is small, the kinetic energy and therefore spring potential energy is low, but the subsequent jumping motion increases this energy, allowing the person to continue to reach higher heights. If a person does not bend their knees and contribute to the jump themselves, they will not get any higher, in fact they will decrease their maximum altitude as some of the energy is dissipated to surroundings. However, a person cannot continuously jump higher and higher as the force of gravity opposing the springs restoring force on the human decreases the potential height as well as limits to the stretching of the springs. Trampolines have a whole bunch of springs around the outside, working at an angle, but also arranged in series. Due to the large number of springs with relatively high spring constants, it takes much, much larger forces to displace them more than a few inches. In addition to the springs, the trampoline material itself is elastic, allowing the springs to maximize their effect. The last question is how one person can "double bounce" another person by landing slightly before them. The first person to hit the trampoline stretches the spring, storing potential energy, and then when the second person impacts the trampoline, the already stretched material stretches a bit more, and most of the total potential energy is transferred to the second person. The first person does not receive much of the potential energy because they are essentially waiting for the potential energy to spring them upwards, but then the second person concentrates the energy under their impact, propelling them upward while the first person barely moves. Warning: If you don't have a net around your trampoline (like my old one), be careful about double bouncing because it is easier for somebody to land outside of the trampoline on the ground. Don't ask me how I know.
  16. As it turns out, the physics behind the ability of bulletproof glass to stop the momentum of a bullet without shattering is in fact a lot of chemistry. However, this makes a lot of sense considering that a large portion of chemistry is simple physics applied on the microscopic scale. A bullet typical travels 400 meters per second, which creates a large momentum despite the fact that the bullet is only a few grams. Normal glass is relatively fragile, shattering upon impact of most bullets while sending small cracks in a spiderweb shape throughout other types of glass. However, bullet proof glass is both thicker and built out of more interesting materials. A few different types of polymers are used in the construction of bullet proof glass that are designed to transfer to bullet's momentum into vibrations among themselves, which in turn are spread throughout the glass and absorbed. Normally, these vibrations cause the glass to shatter, but the flexibility of the polymers allow it to absorb the shock fairly well while dissipating the bullet's energy in terms of heat energy. The vibrations transfer the kinetic energy to the glass molecules and since temperature is the measurement of kinetic energy, the temperature of the glass increases as well. Bulletproof glass is not completely bulletproof though, it is bullet resistant. In addition to numerous armor piercing rounds from high caliber weapons, a lot of "bulletproof" glass products are only intended to stop a certain amount of bullets. One way to counter these measures is to simply make the glass thicker, therefore allowing it to absorb more energy and allow the stuck bullets to affect its performance less. (This is what is done for President). The reason for bulletproof glass breaking down after a lot of bullets is simply the fact that the lodged bullets disrupt the transfer of energy throughout the glass and eventually interfere to the point where the glass begins to crack and then fall apart. If you are attempting to look out for your own safety, you are better off not creating any enemies as bulletproof glass will not solve all your issues, although it could have saved JFK.
  17. The B-2 bomber, commonly known as the Stealth Bomber, is an extremely expensive military aircraft capable over flying undetected across the globe. First of all, the bomber can travel over 6,000 miles without refueling due to its aerodynamic shape. The entire aircraft acts as a singular wing, due to its "flat" shape, which allows the resistance from air to hit the slightly angled bottom and push the aircraft up against the force of gravity. Since the aircraft can almost travel at the speed of sound, the force from air resistance is quite large. The aircraft's flat shape and lack of a tail makes sure that air resistance does not slow down the bombers horizontal speed. Another important aspect of the bomber is computer controlled flaps on each of the wings. If the bomber begins to turn too quickly or become unstable due to lack of stabilizers for stealth, the computer system raises and lowers a flap above each wing at an angle to adjust accordingly. These small flaps allow the bomber to stay on its desired path and stabilize flight, which is why the computer controlled mechanical flaps have now been incorporated in top sports cars as well to pop up at different angles at high speeds. Perhaps the most important aspect of the Stealth Bomber is stealth. In order to stay invisible to radar detection, the bomber is built out of a special composite and coated with special paint to absorb radio waves, rather than deflecting them. This radio absorbent paint and tape is extremely expensive as it does not allow radio waves to reflect off the surface and reach the radar station. In order to keep the premise of stealth, these radio absorbent paints and tapes are often applied to certain spots before every flight. Also, the exhaust of the plane is on top of the plane and the engine is designed for very low emissions as well as positioned in the middle of the bomber to avoid heat detection. As another counter to radar detection, the bottom of the stealth bomber is designed like a slightly curved mirror. This deflects any remaining radio waves in random directions away from the source location. As a whole, the B-2 bomber is a masterpiece of aerodynamic excellence and deflection/absorption of radio waves as well as emitting as few electromagnetic waves of its own as possible. Guess that's why it costs nearly $1 billion for one of these, and $2 billion if you count research and development and training.
  18. People have started to worry about the roads in Rochester as a thin coating of snow, or ice, can cause cars to start sliding due to the lower coefficient of friction between rubber and ice rather than rubber and asphalt. This sensation, although scary for most drivers, is often sought after by drifting. Drifting is the process of purposefully kicking out the back-end of a car around a turn, for the thrill and awesomeness, an then corralling the car as the driver comes out of the turn. Although one way to start drifting is simply approaching a turn with a high speed and cranking the front wheels, causing the force on the back wheels to overcome the coefficient of friction and start sliding, another technique involves using the handbrake. By locking up the back wheels, the handbrake causes the car to either stop at a low speed due to high coefficient of friction, or allows the rear wheels to kick out if the front wheels are turned even slightly. As the rear wheels lock and begin to kick out, they experience a centripetal acceleration due to their position relative to the front wheels, but the entire car is moving at the same time. Once the driver enters a drift, they begin to steer in the opposite direction of their spin to correct the car's direction and begin to accelerate. While it may seem like braking would help correct the car, that only helps the car continue to slide, instead of regaining grip. As the car begins accelerating, the wheels spin against the asphalt/concrete. The high coefficient of friction of friction between the two surfaces (around .70), allows the wheels to slip less and less on each revolution until they fully regain traction. This acceleration, and the force of friction caused by oversteering, allows the car to overcome its angular momentum and continue with only linear momentum. One of the most essential aspects of most drifting cars is being very light. The car needs to have a low mass because momentum is directly proportional to mass and velocity, so a lower mass means less momentum that needs to be overcome when correcting the cars direction. A heavy car often spins too much in either direction, which is why a lot of sportscar drivers spin out or crash their cars while attempting to drift even a small amount. This is also why a hallowed out Subaru is better at drifting than a Lamborghini.
  19. In honor of my Ovechkin's 500th goal (my favorite player on my favorite team), I decided to look into the physics behind the infamous slapshot in hockey. The basic physics of the slapshot include the windup that produces torque applied to the puck and the transfer of energy to the puck, but there is a lot more physics involved that launches the puck with such a high velocity. First of all, the collision with the puck is mostly elastic, but considering the huge noise produced during a shot, it is not completely elastic as some of the kinetic energy is transferred to other energy types. During the collision, the blade of the stick is in contact with the puck for hundredths of a second, creating a larger force applied to the puck since force and time are inversely related for impulse. However, one of the most important aspects of a powerful slapshot is actually making contact with the ice before making contact with the puck. This concept seems counter-intuitive since it will take away some of the momentum of the stick, but in reality it makes the shot stronger because the stick acts like a spring. Upon making contact with the ice, the blade of the stick bends backwards to a displacement of up to 3 inches from the normal position, which stores energy into the blade as potential energy. Since hockey sticks are made of materials such as wood or a mixture of carbon fiber, fiberglass and graphite, they do not bend easily so the "spring constant" is high, storing a lot of potential energy in even small displacements. When the stick makes contact with the puck, the kinetic and potential energy is transferred to the puck, sending the lightweight puck flying at a very high velocity since velocity is inversely proportional to mass for momentum. Because the flex of the stick is vital to the development of power during a slapshot, and even a wristshot, hockey sticks are sold with a variety of different "flex" options.
  20. In the winter, my favorite outdoor activity is snowboarding and sometimes, I get a little too reckless. However, this post will go through the physics of a simple 360 in the air on a snowboard, which can be applied to skis as well. The first important part in landing a 360 is making sure you can hit the jump with the perfect speed to clear the "table" part and land on the actual landing. This is critical because if you under/undershoot the landing, you will most likely fall due to the physics explained in my other snowboarding post. When you are ready to attempt the 360, you have to figure out how to convert your linear momentum into angular momentum to complete a full rotation. In order to do so, you have to wind up your arms in the opposite direction of your planned rotation (about 75 degrees), and at the top of the jump swing them into the direction you plan on spinning. To help start the rotation, it is also recommended to turn your snowboard slightly in the direction you are planning on spinning right before taking off. Although it may be frightening to turn your back on the landing for a second, if you hesitate, you might not get enough rotational momentum and have a slow angular velocity, resulting in an incomplete rotation which means a pretty nasty fall. Once in the air, it is hard to notice anything as your angular momentum rotates your body, but the hardest part of the process is the landing. In order to land safely, it is necessary to convert the angular momentum back into linear momentum. Unfortunately, the ground will do this for you, but it most likely means that you will fall as well. Once you feel yourself about 3/4 of the way through the rotation, it is important to try to bring your arms back to in front of you. Also, attempt to kick your back foot opposite of the direction of the spin. Obviously it is impossible to completely take away the angular momentum while in the air, but the goal is to have as little angular momentum when you make contact with the ground. This also explains why it is sometimes easier to land a 360 on a larger jump because it requires a slower spin and therefore a lower angular momentum that can be stopped easier. Similarly, a backflip is relatively simple (although it is extremely scary and you REALLY need to commit), but you still need to worry about stopping angular momentum. The first couple of times I tried a backflip, I landed well except my angular momentum was still very high and I would fall straight back immediately, hitting my head. Once I realized my problem, I aimed for more airtime and a slower rotation, and was able to stick the landing. So next time you are trying these tricks, or more likely watching the Olympics or X Games, pay attention to the awful effects of over-rotation due to the inability to stop angular momentum when trying to land.
  21. Since Brandon McManus and the Denver defense just rescued the aging Manning's playoff hopes, I thought I'd celebrate the victory with a blog post about the physics of the NFL field goal. The field goal post is 10 feet high, so the necessary vertical displacement is around 3 meters. The width of the field goal posts is about 5.6 meters. For an average NFL field goal, lets assume the kicker kicks the ball at a 45 degree angle. (Angle is greater for shorter field goals, but smaller for longer field goals). If we also assume that the ball leaves the kickers foot with a velocity of 35 m/s, With simple kinematics for a 40 yard field goal (36.5 meters), we can see that the ball would reach its apex at 2.54 seconds, 31 meters in the air. At this time, the ball would have traveled 62.8 meters, so the field goal would be good on its way up. Despite the seemingly easy nature of a field goal, numerous factors make it much harder during a game. First of all, air resistance is not negligible as the shape of the football is conducive to drag forces that slow its velocity in the x and y directions. Also, there is only a 2.8 meter wiggle room on each side, left or right, if a field goal kicker is aiming straight. Over the course of 40 yards, a 5 degree error right or 5 degree error left during the initial contact is enough to push the ball wide (@BlairWalsh). Also, in NFL games, wind and precipitation play a role in the trajectory of a football. The force of the rain on the ball over the course of the flight slows it down, while wind could help or hurt the football's path. Another important factor is the placement of the ball by the holder as a different hold could allow the kicker to make a vital error in kicking the ball sideways or at an angle too high/too low. Extra points have always been considered a free point, but after moving it back to the 15 yard line, 6 teams had an extra point percentage lower than 90%. Whether the kickers think about the physics of their job or not, the laws of motion clearly play a huge role in their routine extra points, game-winners or wide-right losers (Sorry bills). Go Denver!
  22. Walking may be one of the most underestimated phenomenons in the modern world as the simple act is done effortlessly by nearly every able human alive. When walking, the foot is planted into place since the force of friction between the foot or the shoe and the ground stops the foots velocity in the x-direction. Once the front foot is planted, the back foot is able to push off the ground, causing the normal force to push back against the foot and allow you to keep walking forward. While running, it is the same concept except the force of friction needs to be greater to be able to stop the foot from sliding on the ground. This is why cleats have such large spikes and running shoes have such carefully designed tread. Also, in a sport like lacrosse or soccer, the coefficient of friction between the ground and your cleats is very important to keep you from sliding, especially when making a sharp cut. One way humans inadvertently help themselves stay upright when making a sharp cut is planting their foot nearly straight down with a higher velocity, as that will increase the normal force and therefore increase the frictional force. This past weekend, I played a lacrosse tournament in Tully right after it had rained all night, and since the rain decreased the coefficient of friction of the ground and my cleats, I slid all over the place during the first game due to the fact I used a year and a half old cleats that had nearly no tread remaining. After switching to cleats with more tread and planting my foot at an angle closer to 90 degrees with the ground, I was able to stay upright for nearly the rest of the day. Looking at a bowling alley, the low coefficient of friction of the smooth lanes is necessary to keep the ball's path's integrity, but I recommend bowling alleys use a different material for the area where the people release the ball from. Bowling shoes and the ground have a low coefficient of friction, which often causes people to slip just walking on the surface, let alone when they are focusing on releasing the perfect shot. Although pros may be able to handle this low frictional force and tendency to slip, many people, including myself, have fallen while releasing the ball in front of the entire bowling alley which is quite embarrassing. Lastly, I Always thought of a bowling lane of having 0 friction with the ball, but now looking at it, I realize that there needs to be at least some friction in order for the ball to roll and for any spin on the ball to be meaningful. Without friction, the ball would slide down the lane, rather than roll (which sometimes happens to me anyway). Anyway, I think bowling alleys should let you use any type of shoes in the area when releasing the ball to get better traction, so you only have to focus on releasing the ball, not trying not to fall.
  23. I have always been fascinated with the mechanics of different types of guns, and since the impulse test was Tuesday, it is a good time to look at one of the more common questions surrounding "explosion" type collisions. One of the most powerful weapons is the Barrett .50 Caliber Sniper Rifle. Although there are multiple types of bullets used, an armor piercing bullet for a .50 cal is around 45.8 grams (just the projected portion), which is .0458kg. The bullet leaves the barrel of the rifle at speeds of roughly 856 m/s. This means the momentum in the forward direction is 39.2 J, which means that the momentum of the recoil of the rifle is 39.2 J as well. Since the rifle is often against the shooter's shoulder (some .50 cals have remote control shooting), the impulse felt by the shooter is 39.2 J as the rifle slows to a stop in a fraction of a second. To compensate for the large impulse during a short time, creating a very large force on the shooter's shoulder, the .50 Cal Sniper Rifle has a built in recoil pad in order to increase the time that the momentum is changing, therefore decreasing the force felt by the shooter. Another important part of shooting a .50 cal is accuracy since the weapon was designed to take out large targets from far away. In order to maintain a straight flight in the air, like all guns, the barrel has grooves so that the bullet starts spinning while being projected by the gun, keeping it stable during flight. Also, since the velocity of bullet as it is leaving the barrel is 856 m/s, without counting for air resistance or air pressure, the bullet would travel 856 meters in 1 second, and during that second the bullet would only fall 4.9 meters vertically. Since 858 meters is half of a mile, that is a very small vertical displacement. More importantly when shooting long ranges like this, the shooter must take into account wind conditions, humidity and air pressure (and their own breathing). Although it may seem that these small factors would not affect a small bullet traveling at 800+ meters per second, over the course of half a mile to a mile, even the smallest anomolies could be the difference between hitting the target and missing wide or high. Luckily, most snipers of this power have scopes that can calibrate the crosshairs based off the input of the air conditions and wind since accounting for these conditions with the human eye is virtually impossible. Taking into account these conditions is especially important since the maximum effective range of a .50 cal sniper is 1800 meters. For example, if a person aims .05 degrees (yes, that is .05) away from where they need to aim due to the conditions, the shot would miss by about 1.5 meters in the direction their error was in which could be the difference between hitting a target or missing it completely. Good thing only the best in the US military are trusted to use such powerful and precise weapons, especially since the cost of each one is over $10,000. The sniper looked at during this post was a military M107 .50 Caliber Sniper Rifle (aka M82). The .50 caliber is the diameter of the bullet (.5 of an inch), while this uses BMG (Browning Machine Gun) bullets which is the most powerful type of .50 cal bullets.
  24. After reading Zach's blog post on a phone cracking, I started thinking about the one thing I have been doing since I got my first cell phone to prevent it from cracking: kicking it. I usually try to catch the phone on my foot or at least slow its fall, but it is interesting to actually think about the advantage of doing so due to the physics behind the phone's fall and impact with any surface. First of all, the best way to prevent a falling phone from cracking is by trying to catch it with your foot like how you would catch a lacrosse ball. This means that you try to have the phone fall as softly as possibly on your foot by moving your foot downward as the phone is about to hit your foot. This would increase the contact time between the foot and the phone, therefore decreasing the force as force is inversely proportional to time when looking at the impulse of an object. Another factor is that the material that your shoes are made out of are most likely softer than the hard concrete, so the shoe has some "give" built it, further increasing the contact time. Most likely, the chances that you will be able to react quick enough to get your foot underneath the phone completely and try to "catch" the phone with your foot are slim to none, but there is still hope to save your phone from a disastrous fall. Even by making contact with the phone with your foot at least a little bit or even slightly kicking your phone will decrease part of the velocity downwards, decreasing the momentum while putting some force on the phone, but then the phone will not hit the ground at nearly as high of an impact speed, decreasing the impulse needed and therefore decreasing the force inflicted on the phone. So the next time you drop your phone, feel free to use your feet to slow the fall as even a little bit of contact can make a huge difference... Or you can use my alternative strategy that makes you look like a fool. Occasionally, when nobody is around and I happen to drop my phone above a concrete surface, I immediately fall on my butt and catch the phone on my thighs. It sounds ridiculous, but I have done this multiple times at it makes it really easy to catch the phone and prevent it from hitting the concrete at all, but also my thighs act as a soft landing spot so even if the phone bounces off me, the less than a foot drop to the concrete does not allow the phone to increase to a large enough velocity to truly hurt it. Either way, there is no worse feeling than picking your phone up off the ground and checking to see if it is cracked.
  25. IVIR


    As fall lacrosse is starting to end (last tournament this Saturday), I decided to think about the physics behind the sport I love. The first thing that comes to mind that involves a variety of physics factors in lacrosse is the shot. One of the most important factors in a successful lacrosse shot is the legs. First of all, since the body is rotating extremely fast during a lacrosse shot, in order to aim successfully, you have to keep your feet pointed towards the target in order to release the ball at the correct location. Also, in a "time and room" lacrosse shot, the wind up of taking a crow-hop (like baseball throws) or a back-step creates linear momentum so when you plant your front foot and start rotating your torso, the linear momentum is converted to angular momentum to help your upper body rotate faster. While shooting on the run, you cannot plant your foot, but it is important to turn your torso away from the goal in the wind up to get the angular momentum necessary for a fast shot. Another factor allowing a lacrosse shot to be 80-90 mph in high school (100-110 in pros) is that Torque is the product of Force and the length of the lever arm and the lacrosse stick acts as a long lever arm. It is important to extend your arms back as far as possible as well while winding up because that helps increase the length of the lever arm even more. When it is time to actually shoot the ball, the head of the lacrosse stick goes from behind your head, around your shoulder, and pointed towards your target in a fraction of a second, allowing a goalie to have less than half of a second to react. There is so much torque and whip generated during a successful lacrosse shot that during the shot, you can usually hear the air resistance against the lacrosse stick, making a "whoosh" sound. Hopefully, knowing the physics behind the shot will help me score a lot of goals this year. Photo is of Paul Rabil generating as much torque as possible on a shot on the run.
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