In this video, I explain and demonstrate what a harmonic is. But first, we have to establish what a standing wave is. A standing wave is when the wave appears to be stationary and has no nodes in between the two ends of the medium as well as vibrating at a specific resonate frequency. They also have a wavelength that is 2 times the length of the string. Harmonics occur when that resonant frequency changes by either a change in the wavelength or by the rate at which it is oscillating. In the video, I changed the resonate frequency by changing the wavelength and adding another node at the middle of the guitar string. This change in wavelength had to change the frequency due to the fact that velocity is a constant over a specific medium. That's why we hear a different pitch when parts of the guitar are pressed down. We also could do this if we created nodes every third of the way down the string which would create the third harmonic. This would have resulted in a wavelength that is 2/3rds the length of the original one. This can be continued onto the fourth harmonic with nodes at at fourths down the string and so on and so forth.
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I have been playing basketball for a good part of my life and up to this point it has dominated my life. This is something that I am involved with on a daily basic and given my recent surgery, I haven't able to play as much. So when I was given the assignment on incorporating physics into something involving my daily life, I figured I had to pick basketball as a way to get back into the game in some small way. Physics is used in many different aspects of basketball such as: The Shot: A basketball shot is arguably one of the most important aspects of the game because it is how you score. It is very easy to apply Physics because while the ball is in the air it is a projectile meaning that the only force that is acting on it is gravity. When you learn how to shoot you are taught to launch the basketball with enough arc so that it just falls right over the rim. This website shows that the optimal launch angle is between 43-47 degrees depending on the height of the player and their distance from the rim. Picture via: ihttps://www.wired.com/2011/10/optimizing-a-basketball-shot/ Let's derive a problem using me as an example. I am 2.001 m tall shooting a basketball at an initial velocity of 7.5 m/s in both the x and y directions at a hoop that is 3.05 meters off the ground from a distance that is 7 meters away then how long does it take to reach the hoop and what is the angle that I shot it at assuming it travelled at a constant velocity towards the hoop and air resistance is negligible. As is shown in this problem for someone at my height shooting a ball with the circumstances that are highlighted above. Given that I would need to shoot the ball at an angle of 49 degrees and it would take 0.93 seconds to reach the hoop. Dribbling: Dribbling is the perfect example of energy. When I am dribbling a basketball the ball starts with a certain amount of gravitational potential energy. If i were to just drop the ball then it would hit the ground and then, in most cases not make it back up to my hand. This is because when the ball hits the ground, it transfers some of the kinetic energy that it gained by falling into the ground as well as into sound which is why it does not bounce back up to my hand. It obeys the law of conservation of energy in this scenario. When push it down in the form of dribbling, it comes back up to my hand easily because I am increasing the velocity that it travels down to the ground at and therefore increasing its kinetic energy. That way when it bounces off the ground and loses some of that energy it still has enough to make it back up to my hand. In this picture, it shows the energy transfer of the basketball as it falls to the ground, hits the floor and bounces back up. It does not show the little kinetic energy that is lost when it hits the floor but does demonstrate the hand pushing it down and increasing the kinetic energy so the ball can bounce back up. http://ffden-2.phys.uaf.edu/webproj/212_spring_2015/tyler_compton/13427931675535db809aae3/dribbling.html Another thing about the shot is that the basketball is spinning. Using this article I found that this spin actually helps the ball stay in the air for longer. This is because of the balls backspin while it flies through the air. This backspin is on an axis that is perpendicular from the balls direction of travel. As we learned in class the ball is rotating faster at the top of the ball than it is at the bottom. This creates an unequal drag force that is applied upward against the force of gravity and allows the ball to stay in the air for longer. The Shoes: Every basketball player loves their shoes and every shoe company is trying to come out with the next best thing that everyone will love. One of the major things that they take into account are the traction on the shoes. Better traction means that there is a higher coefficient of friction which means that the players will slide less when using them. This video describes how the coefficient of friction can effect how far a person slides. In the case of shoes. Companies are trying to minimize this distance of slipping by increasing the kinetic frictional coefficient of the shoe so players are more effctive. Charges: People are out of control all of the time in basketball. When a person bulldozes another person once someone has established position (is not moving) it is considered a charge. This is because of their forward momentum.that continues them in a forward motion until acted on by an impulse in this case, a defender. This is an example of an inelastic collision because kinetic energy is lost in the process of the collision but the law of conservation of momentum is still upheld. This is because during the collision some of the momentum of the person who was moving is transferred to the person that was standing still. This increases the initially standing person's velocity but decreases the initially moving person velocity. In the end both momentums should equal the initial momentum before the collision. This video highlights what I just discussed and gives a visual example.
The reason that the modification to the turn in the road is safer from a Physics standpoint is because there is now a bigger radius which means that there is less Centripetal Force that is acing on the car. This is because of the formula v^2/r. The turn was more dangerous before construction because the force moving outward would have been greater than the friction holding the car to the road because of the small radius of the turn. With making the radius greater it makes the forces acting on the car less and makes it safer to drive.
Yes I feel that enrolling into AP Physics was the right choice. I feel a challenge that I would not otherwise experience in a lower level class as well as peers that seem more motivated and experienced to help me when I am struggling. I am looking forward to a challenging and exciting year in AP Physics this year because of that.
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AuthorJack Dolan, AP Physics Student 2018-2019 |