Physics of Sports
Sports are a massive part of society, and in our modern world, we are constantly surrounded by stories of exceptional athletes and exhilarating games. Always in awe of the physical strength and skills required to succeed in this sports, it has never quite occurred to me how much science is involved in every throw, run, jump, and catch before this project. The San Marin High School Athletic Department recently approached my STEM class, and proposed to us a basic inquiry: “Can your class use STEM principles to help our athletes improve on the field/court?” Happily accepting the challenge, our STEM class proceeded to think, calculate, and learn over a period of four weeks in order to present our findings to San Marin Athletes in the form of a short movie.
For this specific project, I was grouped with James Wreden and Vanessa Diaz. When we were initially given this project, we went back and forth on what sport we should research, finally settling on researching the video game Super Mario. While Mario is not a traditional sport that is actually played on campus, we believed that it qualified as an E-sport. We also knew that many athletes played video games after games and practices as a means of relaxation. In our first week of this four week process, James, Vanessa and I started by writing a detailed shot list of our movie. This shot list would serve as a basic guideline for our filming in the future. The shot list included all camera angles and actions that would be included throughout specific parts of the film. We also wrote out a rough script of our movie that would be slightly altered throughout the filming process. In our second week of work, we proceeded to calculate all needed information such as vertical and horizontal velocity by using physics skills acquired during teaching sessions in class. In our third week of work, our group filmed all of our needed clips, making sure they were relevant to our movie and accurate to all of our calculations. Finally, in our fourth week, we edited the whole video and put it into a finished product by adding various pieces of audio, transitions, and small finishing touches that would make the project memorable. After making our video, we showcased it to the whole class in order to get constructive criticism on it. While showcasing our video, the majority of the class seemed to enjoy it, however, Mr. Williams pointed out multiple flaws within our calculations that we needed to fix. We took all of this feedback and input it into a newer, more accurate video that still had the same structure and gravitas as before. |
Vertical Divider
Physics of Sports Script!EXT Somewhere Daytime (Shows Izagani as Mario with a voice over giving basic information) VA: Mario is 155cm. or 5’ 1” tall. This is equivalent to the height of 61 raviolis. (Izagani shrinks) By human standards, he also weighs 209 pounds, equivalent to the weight of 80 large pepperoni pizzas (Izagani gets fatter). Thus, in metric units, Mario’s mass would be 95 kg. The average 5’ 1” man weighs 116 pounds, which means Mario is classified as obese. He is 24 years old and runs a 5:30 mile. We found all of this by using canon data charts compiled by diehard fans over the years. Mario falls 3.5 meters in 0.435 seconds. We found this by timing footage of him jumping at max height and measuring out mario’s height and his jump height. If we plug these numbers into the equation d=½a(t2) to find that the mushroom kingdom has a gravity of 37m/s^2. This means mario is on a planet that is not our own, meaning mario is an alien. JA:Since Mario’s planet has a different gravity, this means he would have a different weight. Mario’s weight on his planet would be 790 pounds. That is the weight of 12,600 golf ball sized meatballs! We figured it out by dividing 37 by the acceleration due to gravity and multiplying it by mario’s weight Since mario falls 3.5 meters in 0.435 seconds and the acceleration due to gravity is 37m/s^2, we can use the equation for vertical velocity (v=gt) to find mario’s vertical velocity isv=37ms2(0.435s)= 16.1 m/s.We can also find his horizontal velocity by using the equation v=12.4/0.86 to find mario’s horizontal velocity to be 14.42m/s. We found this by finding footage of mario running at max speed and since we know mario is one brick tall and they are perfect squares, we know they are as long as they are tall which is how we found the distance. With both vertical and horizontal velocity, we can find the vector velocity to be 21.6m/s. We can also use mario’s total velocity, fall time and mario’s mass to calculate the force applied to the ground by mario’s foot. Using the equation mv=Ft we can plug in the numbers (On screen number plugged in 95(16.1)=F(0.06) to get the force of Mario jump to be 25491N. IZ:Now that we know the velocity mario jumps, we also have the time. We can use this to know how long we need to hold the jump button in order to jump at maximum height. Since we found the fall time, and the fall time is the same as the rising time, we know that in order for you to reach maximum height you would have to hold the button for 0.25 seconds. Since we also have his vertical velocity, we can find out how far mario needs to be from where he wants to land at the peak of his jump. He would have to be 6.2 bricks away from his target. We found this by using the equation v=d/t to find v/t=d and plugging in the numbers. |
Physics Concepts Used Througout This Project
FORCE OF IMPACT
Force of impact is defined as the resulting force created when 2 objects hit each other. The equation for force of impact is mass*velocity=force*time. The unit for force of impact is Newtons (N). In our project, we used this equation to calculate the force applied to the ground by Mario’s foot, eventually finding that it was 25,491 N.
MOMENTUM
Momentum is defined as the tendency of a moving object to keep on moving. The formula for momentum is P=mass*velocity, where P=momentum. The unit for momentum is Newtons per second or Newtons/second. Because P=mass*velocity, this physics concept is intertwined with the concept of force of impact stated earlier, which we used to find that the force applied to the ground by Mario’s foot, eventually finding that it was 25,491 N.
IMPULSE
Impulse is defined as how long and forcefully an object is pushed. The variable for impulse is J, and the equation is J=force*time. The unit for impulse is Newtons per second or Newtons/second. Because J=force*time, this physics concept is intertwined with the concept of momentum stated earlier. momentum=impulse which we used to find that the force applied to the ground by Mario’s foot, eventually finding that it was 25,491 N.
VERTICAL VELOCITY
An object's vertical velocity is defined as how fast it moves through the air vertically. The variable for velocity is v, and the unit for it is meters/second. the equation for vertical velocity is v=acceleration due to gravity (time). In our project, we used this concept to calculate the vertical velocity of Mario’s jump, finding that it was 16.1 meters/second.
HORIZONTAL VELOCITY
An object's horizontal velocity is defined as how fast it moves through the air horizontally. The variable for velocity is v, and the unit for it is meters/second. the equation for horizontal velocity is v=horizontal distance/time. In our project, we used this concept to calculate the horizontal velocity of Mario’s jump, finding that it was 14.42 meters/second.
TOTAL VELOCITY
An object's total velocity is defined as how fast it actually ends up moving through the air. The variable for velocity is v, and the unit for it is meters/second. To find the total velocity, you would use the Pythagorean theorem of a^2+b^2=c^2, where a and b are the legs of a right triangle and c is the hypotenuse. For the context of physics, a would be the object’s vertical velocity, b would be the horizontal velocity, and c would be the total velocity of the object. In our project, we used this concept by finding that the total velocity of Mario’s jump is 21.6 meters/second.
GRAVITY
Using the equation distance=0.5(acceleration)time^2, we found that the gravity on Mario’s planet was 37 meters/second^2, different from earth's gravity of 9.8 meters/second^2. We found that Mario falls 3.5 meters in 0.435 seconds after jumping, so we plugged these numbers into the equation to find the acceleration due to gravity.
Force of impact is defined as the resulting force created when 2 objects hit each other. The equation for force of impact is mass*velocity=force*time. The unit for force of impact is Newtons (N). In our project, we used this equation to calculate the force applied to the ground by Mario’s foot, eventually finding that it was 25,491 N.
MOMENTUM
Momentum is defined as the tendency of a moving object to keep on moving. The formula for momentum is P=mass*velocity, where P=momentum. The unit for momentum is Newtons per second or Newtons/second. Because P=mass*velocity, this physics concept is intertwined with the concept of force of impact stated earlier, which we used to find that the force applied to the ground by Mario’s foot, eventually finding that it was 25,491 N.
IMPULSE
Impulse is defined as how long and forcefully an object is pushed. The variable for impulse is J, and the equation is J=force*time. The unit for impulse is Newtons per second or Newtons/second. Because J=force*time, this physics concept is intertwined with the concept of momentum stated earlier. momentum=impulse which we used to find that the force applied to the ground by Mario’s foot, eventually finding that it was 25,491 N.
VERTICAL VELOCITY
An object's vertical velocity is defined as how fast it moves through the air vertically. The variable for velocity is v, and the unit for it is meters/second. the equation for vertical velocity is v=acceleration due to gravity (time). In our project, we used this concept to calculate the vertical velocity of Mario’s jump, finding that it was 16.1 meters/second.
HORIZONTAL VELOCITY
An object's horizontal velocity is defined as how fast it moves through the air horizontally. The variable for velocity is v, and the unit for it is meters/second. the equation for horizontal velocity is v=horizontal distance/time. In our project, we used this concept to calculate the horizontal velocity of Mario’s jump, finding that it was 14.42 meters/second.
TOTAL VELOCITY
An object's total velocity is defined as how fast it actually ends up moving through the air. The variable for velocity is v, and the unit for it is meters/second. To find the total velocity, you would use the Pythagorean theorem of a^2+b^2=c^2, where a and b are the legs of a right triangle and c is the hypotenuse. For the context of physics, a would be the object’s vertical velocity, b would be the horizontal velocity, and c would be the total velocity of the object. In our project, we used this concept by finding that the total velocity of Mario’s jump is 21.6 meters/second.
GRAVITY
Using the equation distance=0.5(acceleration)time^2, we found that the gravity on Mario’s planet was 37 meters/second^2, different from earth's gravity of 9.8 meters/second^2. We found that Mario falls 3.5 meters in 0.435 seconds after jumping, so we plugged these numbers into the equation to find the acceleration due to gravity.
Reflection
One of the greatest skills I was able to acquire from this project was the ability to persevere through all situations and approach all obstacles with confidence and grace. During the very last part of the project, our group suffered a major snafu when Mr. Williams told us that a great majority of the calculations we made were incorrect. While my group and I could have easily started pointing fingers at other in an effort to blame the mistake on a single person, we quickly evaluated the inaccuracies within our math and quickly recalculated most of our physics. We were able to stay calm in the very tough situation, and the problem we had only further united us as a group. This lesson that I learned within this project will serve me greatly in the future.
Another skill that I was able to hone during this project was being a good leader. Throughout the project, I found myself actively assigning roles to the rest of my group, so we could ultimately “divide and conquer” the project. While I was able to use this skill in the previous Rube Goldberg machine project, I found that my utilization of leadership within the physics of sports video only furthered my understanding of how to take initiative and take charge. I believe that I can continue to improve upon my leadership skills throughout the year, and that this improvement will be reflected on the quality of my work.
Another skill that I was able to hone during this project was being a good leader. Throughout the project, I found myself actively assigning roles to the rest of my group, so we could ultimately “divide and conquer” the project. While I was able to use this skill in the previous Rube Goldberg machine project, I found that my utilization of leadership within the physics of sports video only furthered my understanding of how to take initiative and take charge. I believe that I can continue to improve upon my leadership skills throughout the year, and that this improvement will be reflected on the quality of my work.
A skill that I would like to work on is being more focused during the full duration of the project. During the project, I sometimes had the tendency to wander around to other groups and talk to my friends. This sometimes delayed the production of the video, and while we finished filming in a timely matter, I feel that we could have finished earlier had I not wandered around during filming.
I would also like to work on being a positive leader during projects in the future. Throughout the project, I could tend to get frustrated and say rather vulgar things under my breath and at times directly to my own teammates. When I was frustrated with something, I would sometimes get angry and let my words reflect how I was feeling. In the future, I would like to say more positive things in order to serve as a more positive leader for my team.
I would also like to work on being a positive leader during projects in the future. Throughout the project, I could tend to get frustrated and say rather vulgar things under my breath and at times directly to my own teammates. When I was frustrated with something, I would sometimes get angry and let my words reflect how I was feeling. In the future, I would like to say more positive things in order to serve as a more positive leader for my team.