Take an object such as a speaker that will emit waves evenly distributed from itself. This idea can also be seen is a droplet of water is released into a pool, the waves will ripple outward from the contact spot. This is the case for when the contact point or the origin of the waves is stationary or not moving. However, what happens when your source is moving, what does the spectator see or hear? Or if the source is stationary and your spectator is moving, what does the spectator see or hear then? This phenomenon of the spectator or the source moving is known as the Doppler Effect. The formal definition of the Doppler Effect is an increase or decrease in frequency of sound, light, or other waves as the source and observer move toward or away from each other. In simpler terms, as the spectator or source are moving the frequency or pitch in this case will be changed. For the first instance, take for example a stationary person standing in the middle of a hallway. Then you have a person with a speaker running throughout the hallway. As the person with the speaker comes closer to the spectator, the bunch up in front of the speaker making the frequency larger and thus the pitch higher. The same goes for when the person is running away from the spectator. The opposite side will be bunched up, so the waves facing the spectator will be farther apart and result in the spectator hearing a lower frequency and pitch. This example is shown in the video below. For the second instance of the Doppler Effect, the spectator is now moving and the person with the speaker is stationary. In this case the occurrence is the same with the waves bunching up as the spectator moves closer. This is because as the spectator moves closer the waves travel a shorter distance to get to the spectator and will increase in frequency thus increasing the pitch. The same goes for moving away, the spectator will become farther and farther and the waves take longer to reach them, resulting in a decrease in frequency and a lower pitch.
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Projectile MotionAfter a serve or any hit in tennis, the ball that is hit becomes a projectile. A projectile that is defined as an object that has no forces acting upon it except gravity. The force of gravity exerted on the ball at any time is -9.8 m/s^2. Because of this the tennis ball will travel in a parabolic shape as shown in the video below. Because of the way projectile motion works and the equations corresponding with it such as X=vi*t+1/2*a*t^2 and other kinematics equations, we are able to determine where on the court a tennis ball will land. Although we can't actually calculate where the ball will land in our heads while we are playing, through practice and a good understanding of projectile motion a player is able to approximate where the ball will land and will have their contact point and contact angle of the racket set up to accommodate the conditions for the projectile motion and landing point where they want. ForcesThere are a few forces that a tennis ball feels throughout its course of motion and throughout a game. The first of which is an applied force by the person through rotational motion (explained later). In addition to this force by the racket, the ball will also feel a frictional force caused by the racket and that will allow it to spin through the air. After the ball leaves the racket, a gravitational force will be exerted on the ball, there is always a gravitational force on the ball, however during this time when the ball is in the air, gravity is the only force being exerted. Next, when the ball hits the ground there is once again a frictional force that will help determine how fast and far the ball will go after it hits the ground. A normal force is also introduced when the ball hits the ground because it balances out the gravitational force and the ground surface will always exert a normal force on an object. After this process is done, it is usually repeated multiple times throughout a game and the players will go back and forth exerting these forces. EnergyWhile the players are rallying the ball back and forth there is a transfer of potential and kinetic energy through the ball and rackets. In the initial serve, there is gravitational potential energy stored in the racket, and when it is raised the hit the ball it gains kinetic energy. This kinetic energy is then transferred to the ball as soon as the racket hits it. The ball then travels through the air and loses kinetic energy to potential energy and loses more when it hits the ground due to a elastic collision not perfectly elastic collision. After the ball bounces once, the other player does the same process and the ball is then given more kinetic energy to repeat the same process once again. This process then continues until a player misses the ball and it bounces until it is out of energy and stops moving. MomentumWhile serving, the ball has an initial momentum when it is being thrown up. As soon as the tennis racket hits the ball an impulse is then transferred and the momentum is then increased. This increase in momentum allows the ball to travel faster and go farther, per the equation p=mv, where p is momentum, m is mass, and v is velocity. So when the momentum is increased due to the impulse the other side of the equation must balance itself out, and the only way to do that is to increase the velocity, making the ball travel faster, since the mass of the ball is not going to change. Additionally, after the ball leaves the racket and begins its descent the ball has a certain momentum. Then the ball hits the ground; this collision between the ground, usually a court, and the ball can most likely be described as an elastic collision since the ball bounces off of the ground once it hits. During an elastic collision, momentum is conserved, but some energy is dissipated due to the collision not being a perfectly elastic one. Because of this loss in energy, the ball will not travel as high or far as the initial shot, and in result the opponent is able to return the shot. RotationWhile serving a tennis ball, your arm tennis racket become a torque arm and the action of swinging your tennis racket is rotational motion. Because your arm and the tennis racket become a torque arm, there are several variables that affect the ball and many of its properties. For example, if the player has longer arms, this would affect the rotation velocity of the ball. Looking at the equation I=mr^2, where I is rotational inertia, m is mass, and r is radius, we can see that if the radius was increased, there would be more rotation inertia, which makes it harder to exert a torque. So a player with longer arms would therefore have a large torque arm and larger radius which would make it harder to exert a torque. In addition to this, looking at the equation L=Iω, where L is rotational momentum and ω is rotational velocity, since our momentum is conserved and will stay constant, if our rotational inertia is increased, the rotation velocity will have to decrease, and the ball will spin slower. In addition to this, players with longer arms will also have to exert a greater force from their bodies because a larger rotation inertia means it is harder to rotate the torque arm. An opposing side to this and another variable would be for the player to have a lighter racket, this would affect the mass part of the equation I=mr^2, the same steps take place but this time the rotational inertia would be less because the mass is decreased and in turn the rotational velocity would be higher, causing the ball to spin faster. The rotational velocity of the ball affects the way it hits the ground and where it travels after. The following diagrams show how rotational velocity and backspin play into how the ball moves after it hits the ground. The first image depicts what would happen if there was no backspin, but a lot of forward spin, such as after a standard serve. The ball has lots of rotational velocity and once it hits the ground the frictional force counteracts the ball's movement and adds an additional forward force to the already existing forward velocity. This type of hit would result in the ball traveling very fast and far after the bounce and this can be used to serve aces or if you are trying to hit a fast shot across the court to the opposite side of where your opponent is to not let them get to the ball in time. This image shows what would happen if there was lots of backspin, after a backspin serve or backspin heavy shot. The ball is the complete opposite of the first, the ball is moving the other direction so the frictional force would be back towards the player who hit the ball and that would cause the final velocity to be less than the original speed of the ball when hit. This means that the ball will travel at a greater height than length and it will not travel far. This shot is suited when a player is trying to have a player run from the baseline to the net quickly and possibly miss the ball. This can be taken further until the ball has so much backspin that the frictional force that balances out that backspin is the same as the ball's velocity and the ball will go up then down with no horizontal component.
Below is a picture of the intersection before and after some road construction to make this intersection safer. This will be especially safer during the winter time when road conditions may be icy. Using your knowledge of physics that you have learned in class, explain why this right-hand turn was dangerous before the construction (especially during the winter). Then explain why it will be safer after the construction The picture above gives us the two equations that help us solve and interpret the question. The bottom one gives us the value of centripetal force (F꜀) needed to keep an object moving in a circular motion. As we can see, it is dependent upon the mass of the car, velocity, and radius. The original turn without construction has a smaller radius, which inversely effects the centripetal force. So, with a small radius a large amount of force would be needed to keep the car in circular motion to move around the turn safely. Additionally, if the car wasn't able to make the centripetal force required to keep it in circular motion, it could skid off in another direction posing a threat to any cars or pedestrians near by. This means the second turn is much safer than the first because of the larger radius and the lower centripetal force required to make the turn.
Looking at the top equation, we see that the centripetal force is the frictional force between the road and the car. The frictional force is dependent upon the surface of the car's tires and the road. This means during winter, when conditions such as snow and ice are possible on the roads, there is a possibility of less friction between the car and the road. This means a smaller centripetal force, which may not be able to match up to the required force to keep the car in circular motion causing it to skid or crash. This is especially dangerous on the original turn which required a large centripetal force to turn. So far AP Physics 1 has had its ups and downs. Starting the class I felt very anxious, knowing that this specific class is one of the hardest AP courses that any school offers. However, I believe I have the right type of skill set and hard-work to help me push through this class and present myself with a challenge I have not seen in biology or chemistry classrooms. This is my first time taking a physics class in high school, although I feel I have a very wide variety of skills in math, I believe those skills will only take me so far in this class. This class is definitely the right fit for me; I have a large passion for science and would like to further pursue it through my academic career. Although physics is not technically as related to life sciences as are biology and chemistry, being able to expand my horizons and work in a new class that is outside of my comfort zone strongly appeals to me. I am definitely concerned and worried that my proficiency in this class may not be up to the standard that I am used to. I am taking a variety of Honors, AP, and Post-AP classes this year, which totals up to 7 classes, a full schedule. Additionally I have taken on two new leadership positions in clubs this year and have a lot on my plate. This means I will have to work to the best of my ability and beyond. That can include staying up some nights without sleep, but most importantly pacing myself and working on time management and commitment. If I do not have those two things nailed down by the mid-year I will not be able to proceed through this course as I hoped. All in all, this year will be a great challenge for me to take on, and I hope that I will be able to learn a lot from this experience, not just in the aspect of physics, but academically as well.
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AuthorMy name is Aryaan Hussain. I am a junior at the Flint Hill School. I am currently taking a variety of classes including AP Physics 1. I participate in clubs such as Model United Nations, Math Center, Medical Society, and Bioresearch Club. Archives
April 2019
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