Monday, October 16, 2017

Momentum During a Tackle

Momentum During a Tackle
After our football game against Lehigh University on Saturday, I started to think about all the physics that are involved in football. The most relevant that I thought about was about the recent discussion of the conservation of momentum and inelastic collisions. The equation (MAVA+MBVB=MAVA’+MBVB’) is especially applicable to a hit in football. There was one particular hit at the goal line where our player made a hit on the running back but the running back was able to still fall into the end zone. Our linebacker made the hit without running his feet so his velocity must have been close to zero, while the running back had a 5-yard head start running toward the end zone. The linebacker who made the hit is about 240 pounds (109kg) and the running back is 190 pounds (86kg). Say that the linebacker had a velocity of 0.5m/s when he made the hit and had been pushed into the end zone by the running back, while the running back was running into him at -5m/s (1m/s above the average running speed of an adult human). The running back was running in the negative direction in this situation. Since this was an inelastic collision, the running back and the linebacker were essentially stuck together and their momentum became a single entity. The final momentum of both players, according to the conservation of momentum equation was -1.9m/s.
            This is why football coaches preach to keep your feet running during a tackle and to run them while you are being tackled. If the defensive player was able to make the tackle while running his, feet he would have more velocity going against the running back and would be able to stop him from reaching the end zone. Defensive coaches also teach their players to lift the running backs into the air when possible or take out the runner’s legs in order to stop the offensive player’s momentum.
            It is interesting to think about all the other aspects of football that have so much to do with physics. Every pass has to do with constant acceleration due to gravity, velocity and projectile motion, while every block has to do with angles and momentum. The kickers and punters also deal with projectile motion. Not only football, but everything in life has something to do with physics. Whether it be driving a car, playing baseball, or using the elevator, physics is all around us.

Here is a link to an article that talks more about the physics of football!

http://www.popularmechanics.com/adventure/sports/a2954/4212171/

Wednesday, October 11, 2017

Granny Throws

I remember when we would play basketball in elementary school and it was always funny to see kids throw underhand (and unfortunately, those kids were usually made fun of for it). I remember the teacher saying, "If can't throw the real way, then throw underhand," as if throwing underhand was not a "real" way to throw. However, he was mistaken, because retired NBA star Rick Barry threw underhand and had the fourth best free throw record in NBA history with a 90% success rate. A recent study from April 2017 has an explanation why this is so. According to a study by Madhusudhan Venkadesan of Yale University, an underarm throw produces a better parabolic trajectory than an overhead throw. Interestingly, as an underhand projectile has a lower speed so when it hits the rim the collision does not ricochet the ball as far back and thus it is more likely to go into the net than bouncing away. It all has to do with momentum, energy, forces and kinematics! Of course, as emphasized in class this is not a perfectly inelastic or elastic collision so it would be difficult to do the math for the collision but none the less we can begin to understand it in these terms. 

Interestingly, the authors comment that throwing underhand as an amateur is not advisable because you have greater chance of missing the target. So maybe our elementary school gym teachers should have read a physics journal and not advise this technique. 

In the end however: “So what if some call it the ‘granny throw’? What matters is that the ball goes through the hoop!” (Venkadesan). 

The scientific article can be found here:
 http://rsos.royalsocietypublishing.org/content/4/4/170136
and the commentary:
 http://www.iflscience.com/physics/throwing-granny-style-is-best-for-professional-basketball-players/

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Monday, October 9, 2017

Momentum and Impulse in Yankees vs Indians Game 2


           Watching the Indians play the Yankees on Friday night I was reminded of our discussion of momentum and impulse. The game was tied and was going into a 13th inning so tensions were high. At some point in the 13th inning, the umpire was hit in the head by a pitch that the batter had not swung at. Both the batter and catcher turned around and were visible concerned when this happened. When he was hit, the umpire stumbled backwards and braced his hands on his knees. He removed his helmet and collected himself for a few moments, then nodded that he was okay, put his helmet back on and resumed his position. There were many slow-motion replays of the impact during this time.
            These replays made me think of the equations for momentum and impulse we talked about before fall break and the importance of wearing a helmet, especially in sports like baseball. If the baseball was around 142.5 grams (the average weight for a baseball) which is equal to 0.1425 kg, and Dellin Betances of the Yankees was pitching at approximately 82.4 mph (his average pitch velocity) which is equal to 36.8 m/s, then the momentum of the baseball was 5.244 kgm/s. I found this according to the equation p = mv.

            If the umpire was not wearing a helmet, then the baseball would have hit him directly in the forehead and would have taken less time to stop. According to the equation, FΔt = Δp, the sum of the forces multiplied by the change in time will be equal to 5.244 kgm/s (the overall change in momentum). Thus, a shorter time for the ball to stop would correspond to a greater force. Because the umpire was wearing a helmet as is required, the time for the baseball to stop was greater. In this way, the force was distributed over a larger time so the overall force was smaller. Luckily, the umpire seemed to be okay after the incident. This is a good example of why helmets are so important!

Sunday, October 8, 2017

Gravity is Mean to Me

When I get incredibly stressed, like the past two weeks, I become restless in bed, meaning I toss and turn all night long. It was only a matter of time before one day I would just so slightly toss a little too far and fall out of bed onto the ground. So, low and behold, I fell. As I was falling, my first thought was obviously the physics of the event. If we call the top of my bed the max height and using my mass we can calculate my potential energy just before falling.

mgh= 68kg*9.8m/s/s*0.75m=500J

Coincidentally my potential energy at the top of my fall is equal to the work done by gravity during my fall (assuming I live in a vacuum of course). Next, as I fell I thought about all of that potential energy that was being converted to kinetic energy, and thought to myself, “I wonder how fast I’ll be going when I hit the ground”. Luckily for me, there is an easy way to find that using the principles of the conversation of energy.

mgh1 + 1/2mv21= mgh2 + 1/2mv22
500J + ½(68)(0)=68(0)(9.8)+1/2(68)v2
500J=34kgv2
v=-3.8 m/s

Then at the point right before I hit the ground, my mind went where most people’s minds would go, “What is my momentum at this point”. Once again, my physics training had enabled me to find this

mv= 68(-3.8)= -260 kg*m/s

Then as the ground caught me, I thought about how my momentum was changing and how much force I experienced as I hit the ground ( I would assume the amount of time for my body to stop falling to be 0.001s). Thus, I quickly got up off the ground and calculated the force applied by the force to stop my fall.

F∆t=∆p
F=∆p/∆t
F=260/0.001s
F=260,000 N = 58000 lbs. of force

Next, I thought about how that force would be distributed throughout my entire body so I divided the total force in pounds by my height in inches:

58000lbs./70in= 830lbs of force/Inch of John

Lastly, I thought about how quickly my velocity was changing as I came to my stop so:

F=ma= 260000=68a
a= 380 m/s/s

Luckily for me, however, is that as I fell I did not freefall nor am I an ideal atom falling in a vacuum; therefore, I did not sustain any serious injuries other than the embarrassment of falling out of my bed.