Football Collision

     As a football player, I wanted to understand the physics of a collision between two football players. Everyday, a football player takes part in countless collisions with their teammates and prospective opponents, but the question is how hard is this collision? How much force is one player exerting on another?

    We're going to look at one play that occurred in the Clemson vs Syracuse game in 2017: 

    A Syracuse Defensive player reads the play and comes to make a tackle on the opposing team's wide receiver. We see the defensive player get low in his stance to make a textbook tackle on the offensive player resulting in a huge hit. The reason as to why the defensive player got lower in his stance is to attack the center of gravity of the opponent. By doing this, he has a better probability of getting the opposing player on the ground, but also achieves a greater impact during the collision. Here we will analyze the collision between these two players and how much momentum the defensive player is generating. 

(the video on here isn't working so if you're curious what the hit looked like click the link below and forward to 6:34)

https://youtu.be/cQfv6rpqx4A 

To understand this collision, we use two formulas: 

By using tracker, we find the velocity that which the football player accelerates to hit the stationary player. 

• Initial velocity of moving player: 6.05 m.s 
• Initial velocity of still player: -1.33 m/s 
• Final velocity of both players: 3.03 m/s 

    By using these values, we can calculate the momentum for both individuals and see the final momentum after the collision. We know that the momentum before the collision is equal to the momentum after the collision, so we can use the equation below, which  deals with conservation of momentum, to understand how much force was used in the tackle. 

    We find the initial momentum, prior to the collision to be 469.5 kg*m/s and the final momentum to be 579.1 kg*m/s. We understand that the difference in momentum is due to outside forces such as the normal force exerting a force from the ground. Through this equation we find that in 0.2 seconds, a net force of 548 Newtons occur after the collision of both players. But if we just analyze the player accelerating, we see that he pushes off the ground with a net force of 2577 Newtons. As we can see, football players generate a great amount of force when expecting a collision, and in turn, the hits can be very painful and devastating. 

Works Cited: 

https://www.wired.com/story/how-to-deconstruct-a-football-tackle-with-physics/

The physics behind archery

     Archery is a well known sport that displays many physics principles. In archery, a bow is pulled back and propels an arrow towards a target. Archery has been used for many years for hunting, war, and as a sport. 

    The main physics principle displayed through archery is the conservation of energy. Just as a ball at rest on the top of a hill has only potential energy then only kinetic energy at the end of the hill, a bow and arrow follows a similar principle. Before the arrow is shot and the bow string is untouched, there is no energy in that system, but as you put in work by drawing back the bow string, there is an increase in potential energy. This is a special potential energy, and as we learned in class, this is spring potential energy. Firstly, we will deal with the work of drawing the bow string back. As we know, the equation for work is W=Fd cosθ. The force in this case would be the force that you pull the bow string back, d would be the value that you displace the string, and assuming that you are pulling back the string with an angle of 90 degrees relative to the bow, the cosθ would be zero. 

For the potential energy the bow acts like a spring, so we know the equation is ½ kx^2. The value of k, or the spring constant coefficient is different for each bow, with a thicker, stronger bow string having a greater value for k and a child's bow having a much lower value for k. The x in this equation would be the displacement of the bow string. Additionally, if the bow is held above the line you make y=0, there would be gravitational potential energy, but for this purpose we will set y=0 level to the bow and arrow. When the bow is drawn back and the arrow is released, according to the conservation of mechanical energy, all energy will be turned into kinetic energy (½ mv^2). This is assuming that there are no other forces acting on the system, which we know that there are such as air resistance and friction of the arrow on the bow, but for these purposes we will ignore those values. Thus, if you know the spring constant of the bow, the displacement of the bow string, and the mass of the bow, you can solve for the velocity of the arrow. With these equations you cannot determine whether or not the arrow will perfectly hit the target; however, you can tell how fast the arrow will leave the bow.

https://www.wired.com/2014/12/much-energy-bow-goes-kinetic-energy-arrow/ 

http://ffden-2.phys.uaf.edu/webproj/212_spring_2015/Addis_Gonzalez/Addis_Gonzalez/bow.html https://arxiv.org/pdf/1511.02250.pdf

By: Zack Kraushaar

Dr. Charlotte Hagen

    Computed tomography, otherwise known as CT scans are popular in medical practice as they give healthcare workers a look at bones and other internal structures of a body without having to physically go inside. However, this seemingly noninvasive technology actually poses some concerns because the x-rays involved expose patients to relatively high levels of ionizing radiation. Enter Dr. Charlotte Hagen and her colleagues at University College London, who are working to develop a less harmful technique to carry out CT scans! Their approach is referred to as "cycloidal" and this new CCT method is simple enough to be implemented in the hardware that's already out there.

    Their CCT involves masking some of the radiation by placing a shield in front of the x-ray beam to protect the patient. Unfortunately, getting a high resolution image from these weakened beams is rather challenging and technicians would have to use a process known as "dithering" which involves more stopping/starting and slower movements in lateral and angular increments around the subject. This ultimately does little to reduce a patient's net exposure to the radiation. Hagen and her team figured out a way to keep the protective mask but to avoid dithering by moving the x-ray beam both laterally and angularly at the same time. The so-called cycloidal method allows for 50% or less of the radiation that a patient would otherwise be exposed to with dithering for the same resolution image.

    In regard to her background, Hagen is based at UCL in the department of medical physics and bioengineering. She has her name attached to nearly 60 publications and much of her work centers around x-ray imaging. In 2018, she was one of seven people to be awarded a fellowship from the Royal Academy of Engineering which lets her undergo five years of funded research with 3D imaging techniques for tissue engineering. Other than this, she seems to be rather illusive as my investigation into more of her history took me to many dead ends. In any case, her work is impressive and a good reminder that we can improve upon existing technologies. Just the other day I had to have an x-ray for a foot injury and while I was acutely aware of the radiation I was going to be exposed to, I went along with it because I didn't feel like there was any other option. Knowing now that there are people like Dr. Hagen working on ways to lessen the harmful impacts of x-rays without compromising the quality of the image resolution is exciting!

Works Cited:

Aut, M. (2020, July 30). New beam-masking technique reduces radiation exposure during medical imaging. Retrieved November 29, 2020, from https://physicstoday.scitation.org/do/10.1063/PT.6.1.20200730a/full/

Ucl. (2019, February 07). Charlotte Hagen. Retrieved November 29, 2020, from https://www.ucl.ac.uk/medical-physics-biomedical-engineering/case-studies/2018/aug/charlotte-hagen

https://www.researchgate.net/profile/Charlotte_Hagen

The Physics of a Dog Tug of War

 My family recently got a new dog which means that we now have two little dogs - Bonnie and Maisy. They love playing with each other, and their favorite toy to ‘share’ is a frog-shaped rope (see photos below). Although they’re approximately the same size, the older dog, Maisy, always seems to win the tug of war. I got to thinking about how physics (specifically the principle of torque) may play a role in her domination of the toy war. Torque is a good way to convey the force that Maisy exerts on the rope as she shakes her head back and forth in a somewhat circular motion. In this model, the puppy’s mouth grabbing one end of the rope is the pivot point and the force is being applied by Maisy on the other end of the rope Maisy has found that by grabbing onto the very end of the rope, rather than the middle of the rope, she can more forcefully tug the rope and successfully yank it from Bonnie's mouth. This relationship can be explained by the principle of torque, and the relationship between the lever arm radius and the corresponding amount of torque produced.

Measurements

• From knot to knot (the points at which the dogs grab), the rope is 0.25 m long

Assumptions

• Maisy is applying a force perpendicular to the lever arm

• Bonnie is grabbing onto the other end of the rope at a constant point (the pivot point)

• We do not know the force (F) exerted by Maisy, so we are using F in place of the actual value

• The force (F) exerted by Maisy is the same in both scenarios

Calculations

The torque of Scenario 1: 

In scenario 1, Maisy would grab onto the rope at a point closer to the pivot point, thus making the lever arm (r) shorter.

Torque = rFsin

Torque = 0.10F

The torque of Scenario 2: 

In scenario 2, Maisy would grab onto the rope at the point farthest from the pivot point, thus making the lever arm (r) longer.

Torque = rFsin

Torque = 0.25F

Thus, the torque in Scenario 2 is 2.5 times that of Scenario 1.

Conclusion

Despite not knowing the exact force Maisy is exerting on the rope as she pulls, we can use the equation for torque to look at the relationship between where she grabs the rope and the torque exerted. There is a direct relationship between the length of the lever arm and the torque, suggesting that Maisy exerts a greater torque (rotational force) by grabbing onto the end of the rope as opposed to a location closer to the point of rotation (i.e. where Bonnie is holding onto the rope). Thus, in an attempt to win the tug of war, dogs unknowingly use the laws of physics and elongate their lever arm to win!

The Physics of Rowing

     The sport of rowing, although not very well known, is a great example of multiple parts of physics working together. In this sport, there are eight people lined up in a narrow boat facing the direction opposite the boat’s motion. Each rower sits on a sliding seat and is strapped in by his or her feet. Each rower holds an oar, which pivots around a rigger. Rowing combines the concepts of momentum, energy, and resistance to achieve its motion. 

    First of all, the rowers use momentum to move the boat. When the boat is not moving, the total momentum of the system is zero because there is no velocity. However, the boat starts moving when the rowers begin to apply pressure on their blades, which in turn moves the water in the direction opposite of the boat’s movement. The forward momentum of the moving boat must equal the backwards momentum of the water. You can see this by looking at the water once the blades are in the air- there are swirls of water clearly moving towards the back of the boat. 

    You can achieve the same amount of momentum by either moving a small amount of water quickly or by moving a large amount of water slowly. By looking at kinetic energy, it becomes clear that it requires less energy from the rowers to move a large amount of water slowly than it does to move a large amount of water quickly. To increase boat speed most efficiently, you want to increase the momentum of the water while minimizing the change in kinetic energy of the water. You want to minimize kinetic energy because that energy comes from the rowers, so the less effort they have to put in to increase boat speed the better. The equation for kinetic energy is KE=½mv2. Because the velocity is squared, the faster the water moves the more kinetic energy it has. Therefore, if you want to minimize the energy but you have to increase either the mass or the velocity of the water, it makes more sense to increase the mass, which has a smaller effect on the KE. That’s why the blades of the oars are fairly large and why rowers always try to keep their blades deep in the water for as long as possible- to increase the mass of the water they are moving.

    Finally, if you think about the free body diagram of a boat, you have to think about friction. There are several forms of drag opposing the motion of the boat. The main three forms of drag are friction, which acts because of the hull of the boat moving through water, form drag, which is due to the turbulence created by the boat, and wave drag, which is energy lost due to creating waves. Friction accounts for 80% of the resistance and is increased when rowing into a strong wind. These forces greatly slow down the speed of the boat and mean that the rowers need to supply 8 times more power to double the speed of the boat.

References:

http://eodg.atm.ox.ac.uk/user/dudhia/rowing/physics/basics.html

http://eodg.atm.ox.ac.uk/user/dudhia/rowing/physics/rowing.pdf 

Dr. Anders Nilsson

     Dr. Anders Nilsson is a professor at Stockholm University. He has been published in more than 300 papers with a wide range of disciplines. Dr. Nilsson has been published in Nature, Science, PNAS, Nature Chemistry, Nature Communications, Physical Review Letters, JACS, Angewandte, JCP, Nano letters, and many more. He has even gained his recognition by being cited more than 20000 times on google scholar, 15000 times on ISI Web of Science, and once in an edited book. His knowledge has obviously not gone unnoticed. Dr. Nilsson took an interesting approach to his education. For example, for high school, he went to a technical high school which was focused on chemistry. Then he got his master’s of science in chemical engineering. Nearly nine years later he got his Ph. D in physics where his thesis was specialized in “Core Level Electron Spectroscopy Studies of Surface and Absorbates.” Lastly, he got his docent in Physics. All of this education stayed in Sweden. 

Starting in 1978, Dr. Nilsson began a long line of academic professional experience. He started as a teaching assistant, graduating to a research assistant, to a visiting scientist, to a lecturer, to an associate professor at Stanford University, to the chair of the Photon Science Faculty at Stanford, and currently as a professor in chemical physics at Stockholm University. However, his academic experience extends into many other professional services as a co-organizer for workshops, lecturers, committee members, representatives of meetings, national coordinators, members of boards, directors of programs, deputy directors, faculty opponents on Ph. D thesis reviews, to many more experiences. His time stretched across the globe to Japan, Baltimore, the U.K., Denmark, and many more places. Over his time he earned many awards and honors that proved his educational experience. Lastly, he was an invited speaker at more than 130 international conferences and 90 colloquiums at Universities and National Labs. One thing I found interesting about his educational experience was his combination of chemistry and physics. He started his professional career and interest in chemistry, but then grew into getting a Ph. D in physics. He was able to connect two of his interests into one area of research that he excelled at which led him to the top of the physics leader boards.

In 2004, Dr. Nilsson started his research with water and it became one of the top 10 most important scientific breakthroughs of the year and he has continued that research up until now. His most recent research being posted in Physics Today on November 19th, 2020 titled “Fast X-Ray Scattering Reveals Water’s Two Liquid Phases.” This new experiment was brought forth by Dr. Nilsson and his team that combines low temperature, high pressure, and fast measurement to examine the phase transition that has been hypothesized many times before. This allows for them to look at the states of matter when water is in between the liquid-water phase. This new approach is heating amorphous ice then zapping a thin film of the high-density amorphous ice with an IR laser pulse. This will allow for a small amount of liquid to be made. This liquid will quickly decompress then refreeze and during that expansion, the researchers can probe it with an x-ray pulse timed with the IR pulse to reveal the never-before-seen water phase behavior. The figure below shows the distinct liquid phases of lower density and overall the liquid-liquid transition can be experimentally examined. This work is very groundbreaking and allows for many possible future experiments to occur by studying water’s unusual behavior.

Works Cited: 

Anders nilsson—Stockholms universitet. (n.d.). Retrieved November 28, 2020, from https://www.su.se/profiles/andersn-1.186733

Aut, L. M. J. author. (2020). Fast x-ray scattering reveals water’s two liquid phases (world). https://doi.org/10.1063/PT.6.1.20201119a

The Physics of Golf

 Many people have tried out the sport of golf during their quarantine period. As some would say it is an easy sport, but it is anything but that. Golf takes extreme focus, mental toughness, strength, and precision. For example in a par 3 hole, you must hit the ball just right so that it goes down the fairway straight. Then you must hit it again at the right spot to get it in a good position on the green. Next, you must hit the ball with careful precision to have the ball role in tandem with the hills on the green to land perfectly in the hole. A tad right, you miss; a tad left, you miss; not enough power, you miss; too much, you miss. There are so many instances that golf sets you up to fail. So how does Dustin Johnson, hit a golf ball so perfectly to be the winner of the 2020 Masters?

Many factors go into hitting a perfect golf swing. One of the main factors is angular motion. The golfer wants to have their maximal velocity at the bottom of their swing in order to transfer the most kinetic energy to the ball. According to The Physics of Golf, the kinetic energy is proportional to the mass of the clubhead and the square of its velocity. Another factor is the twisting motion of the club that creates torque. This torque is what affects the angular velocity which can cause the ball to move in different directions. 

Dustin Johnson can reach a club speed of up to 125 mph at the bottom of his swing. However, not only does his angular velocity matter but the angle between the club shaft and the clubface matters as well. Research done by Raymond Penner in British Columbia found that the optimal angle for a speed at 125 mph at the bottom of the club is 7.5 degrees. Now, for someone like me who cannot hit it very fast, I would have an optimal lie angle of around 20 degrees. This angle would compensate for the slower angular velocity. 

Some other factors that influence how the ball is hit are the flexibility of the golfer so that a longer range of motion can be attained, quick motion through the torso with little movement after the movement to concentrate the build-up of velocity, driving through the ball with hips, shoulder, and wrists to concentrate where the force is put into the ball, and having the clubhead follow all the way through past his back to continue its momentum instead of coming up short. Additionally, environmental factors need to be taken into account like wind, snow, rain, etc. Then picking the right club for the distance the golfer is trying to achieve and lastly, putting requires an even more precise hit because the hills, friction, and distance come into play. 

Don’t underestimate the sport of golf. Not only does it require a lot of physical effort, but it also requires a lot of physics. 

Works Cited: 

The Physics of the Golf Swing. http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/josh_fritts/swing.html. Accessed 28 Nov. 2020.

The Physics of the Double Bass

    The double bass consists of four strings, each with a different thickness and tension. The tensions on the string are caused by the attachment of the strings to the four tuning pegs at the top of the instrument and the tailpiece at the bottom of the instrument. The tension of the strings can be adjusted (tuned) accordingly by turning the tuning peg. This will either loosen the tighten the string, and changing the tension in the string will change the note/sound that the string produces. A tighter string will produce a note with a higher frequency, which means that the number of soundwaves produced per unit of time will increase and produce a note of higher pitch. Thus, the tensions of the strings are very important in producing the different notes of the double bass, as different string tensions will create different notes.

    Friction is also essential in bowing, which is when you use a bow to produce sound by gliding it across the strings. In order for sound to be produced, the bow must vibrate the string. Therefore, I always put rosin onto my bow before I play. The rosin is made from tree sap, which is sticky and increases the friction between the string and the bow hair. Varying the pressure that you apply onto the string will change the volume of the sound that you produce as well. When you increase the pressure that you apply, the force of gravity acting on the bow and the string will increase. This means that the normal force on the string also increases, and the force of static friction will increase. As a result, the work that you must do to overcome the force of friction and drag the bow will increase. 

    A cool technique that you can perform on the double bass is spiccato, in which the bow bounces off of the string. The bow travels in an angular motion as it bounces from left to right. It is easiest to start doing spiccato at the fulcrum, which is the location of the bow’s center of mass. We can also think of it as the bow’s axis of rotation when we’re doing spiccato. Your hand is exerting a torque on the bow and causing it to bounce from side to side, rotating about the fulcrum. The reason why spiccato is done near the fulcrum is because it requires less effort from the musician. When you are bouncing the bow at the fulcrum (Point A), the amount of work that you are doing can be calculated using the following equation W=τΔθ= (rFsinθ)Δθ. However, if you bounce the bow closer to the tip at Point B (axis of rotation is now higher), the radius (rB) of the applied force is now farther from the axis of rotation. Therefore, the torque that you exert is now greater than if the fulcrum was the axis of rotation. This means that in order to rotate the bow through the same angle, you need to put in more work if your bow is the axis of rotation than if your fulcrum was the axis of rotation. Thus, if you want to make playing spiccato easier, you will want to play at the fulcrum and closer to the frog than at the tip of your bow.  

The Anatomy of a Forward One and a Half Dive

  I was a competitive springboard diver throughout high school and will discuss the physics behind a “forward one and a half” (103C) in a tuck position, from start to finish.

In springboard diving, a major component of diving is having the diving board work to your advantage.  In order to do this, divers perform either a hurdle (for forward facing dives) or a board press (for rear facing dives).  Let’s look at a basic hurdle.  One of the most basic hurdles involves the diver starting several steps back along the board, taking four slow steps forward while gentling swinging their arms in pace with each step, and then taking one final leap forward to the very edge of the board.  At the edge of the board, several things occur.  As soon as the diver’s dominant foot lands on the end of the board, they bring their other knee up to make a right angle (this is called the “skip” at the end of the hurdle).  They then circle their arms all the way around from back to front.  Once they have landed on the board again and depressed it completely, the diver’s hands are above their head once again.  They proceed to jump up and throw their arms forward while pulling into a tuck position, grabbing their ankles.  Once the diver has completed one and a half rotations, they “kick out” by extending their arms and legs and tightening their core.

Now, in terms of physics.  As the diver progresses down the board for their hurdle, their mass exerts force on the board.  The end of the board acts as a spring, which they depress with their jump.  It is as it recoils to its normal position that they leave the board.  The diver holds their arms high above their head and swings them forward in a wide arc to generate momentum.  They then tuck in their body and grab close to their ankles.  Many people playing around on diving boards and doing flips without proper training will grab their knees as they rotate, but by grabbing one’s ankles, one decreases one’s radius, which allows for a faster rotation/greater linear velocity.  An added benefit is that it is less likely that the diver will lose their grip as they rotate.  When it is time to kick out, the diver throws their arms out above their head and kicks their legs straight again as well.  This is meant to increase the radius and slow down the diver’s rotation.  Half rotation dives (or those in which the diver enters headfirst) are typically easier to slow down because the diver throws out both their hands and feet compared to full rotation dives in which the diver straightens only their legs.  This is because their raised arms significantly increase the radius of rotation.

The board itself also possesses many physics properties.  In addition to acting as a spring, the diver exerts torque on the board as they jump on it.  Competitive boards are adjustable in this way and have a circular dial to rotate the fulcrum that the board rests on.  If the diver rolls the fulcrum forward, they decrease the lever arm of the boards and it is less “springy”/more resistant to motion.  If they roll the fulcrum backwards, the opposite is true and it is “bouncier.” 

Image links:http://springboardsandmore.com/wp-content/uploads/2015/06/70-231-524-G-550x413.jpg 

http://media.gettyimages.com/photos/woman-springboard-diver-in-a-tuck-position-picture-id119791199?k=6&m=119791199&s=170667a&w=0&h=E_XzDzzzxxJ1R2J17fEvidvPtepT5DFoHvriXoURKAg=

The Physics Behind Tonya Harding’s Triple Axle

 

Tonya Harding made history at the 1991 at the US Figure Skating Championships in Minneapolis, Minnesota when she successful completed a notoriously difficult, some say physics-defying, triple axle. The triple axle consists of a skater releasing off the outside edge of one skate, rotating 3.5 times in the air to land backwards on the outside edge of the opposite skate. The physics behind the jump makes it easier said than done. 

First, the skater must generate enough vertical velocity and height to give enough time to complete 3.5 rotations before landing. This requires a great amount of strength and body control to obtain a velocity to start rotating as quickly as possible while getting enough height to finish all the rotations in the air. This relies on the skater exerting a large force on the ice to accelerate upwards against the force of gravity to obtain a large vertical displacement and velocity. The skater will only successfully land if their landing leg is positioned to absorb the force exerted by the ice which takes a bent leg to reduce the force on the landing leg. This is a consequence of the impulse momentum principle. Since the time of impact increases by bending the knees, the average force exerted is reduced (Impulse=F𝚫t). 

The skater must also generate enough rotational velocity. This ultimately decides the difference between a single, double, or triple axle. The triple axle requires the greatest amount of rotational velocity to complete the rotations in the shortest amount of time. Skaters use the principles of  angular momentum to increase their rotational velocity. 

Angular Momentum = L = mvr 

As you will notice when watching this maneuver, the skater will start the rotations with their arms and legs farther from their body and start to bring them closer as they increase speed. Since momentum is conserved because no external forces are acting on the skater, decreases the radius will increase the angular velocity to conserve momentum. Therefore, skaters will bring their arms and legs tightly around them to decrease their radius and increase their angular velocity. With all these different factors contributing to the difficulty of the move, the move has become a notoriously difficult move and a sign of a technically great figure skater. 

References:

https://www.vox.com/videos/2018/2/12/16978946/triple-axel-tonya-harding-mirai-nagasu

https://www.scientificamerican.com/article/the-physics-of-figure-skating1/

https://www.vanderbilt.edu/AnS/physics/astrocourses/ast201/angular_momentum.html

The Physics Behind Walking Up the Dreadful Colgate Hill

  

            When physics class used to be in the chapel, walking up the hill right near the library was always an ungodly experience as I would always be out of breath and sweating by the time I reached the top. The move of physics class to TIA downtown has made walking to physics class much less of a struggle. Why is it such a tiring experience to walk up a hill versus flat land one may ask? The answer is not simple, but with a basic knowledge of physics one will be able to understand the feeling of shortness of breath as you near the top of a hill. 

            When walking on flat land, similar to my walk to TIA, without knowing it you are applying a force to your foot which applies a force to the ground. Surprisingly, the ground applies an equal and opposite force onto your foot which in turn pushes you forward. This agrees with Newton’s third law that states “for every action (force) in nature there is an equal and opposite reaction” (Source 1). In the case of walking, the applied force is one’s foot and the equal and opposite reaction force is the force that the ground exerts back onto you causing a movement forward. The force of gravity is also a key component because without this force acting in the downwards direction, one would not stay on the ground. Related to the downwards vertical force of gravity is the normal force which acts in the upwards direction vertically. The normal force is responsible when walking on flat land, for balancing out the downwards force of gravity. In the case of flat land, the normal force fully compensates for the gravitational force therefore one does not need to work against gravity when walking on level ground. However, on a hill the normal force does not act entirely in the vertical direction it acts in the vertical direction of the object, therefore when walking up a hill the normal force is acting in an upwards diagonal direction in which it cannot entirely balance out the force of gravity (Figure 1). The normal force on a hill only compensates for a part of the downwards gravitational pull, making the gravitational pull on a person walking up a hill stronger compared to one walking on level ground as gravity is no longer fully canceled out. On a hill, the force of gravity is acting upon you therefore, pulling you downwards. In order to move up the hill, this downwards force of gravity must be opposed, when walking on level ground it does not because gravity is fully compensated by the normal force. The steeper the hill is, the larger the force of gravity is on someone, pulling them down the hill harder making it more difficult to move as one needs to do work and exert energy. When walking up the library hill you need to climb as well as move forward in which energy is being exerted and work is being done. If you are walking on a flat ground level road, you stay at the same level in Earth’s gravitational pull or force in which the normal force and gravitational force cancel each other out because they act in equal but opposite directions. However, when walking up hill the normal force is not vertical to the gravitational force and cannot ‘cancel’ it out, therefore one must oppose a portion of the force of gravity on a hill themselves by exerting more energy and doing more work. For every elevation raise, like climbing up a hill, the more energy it takes to oppose the force of gravity. For every degree of incline, at a constant distance you are putting in extra work hence why one becomes out of breath walking up to campus. Walking uphill takes work while walking on a flat level does not. 

Below are the free body diagrams of a person walking up a hill and the forces acting on him/her versus the forces acting on somebody on flat land (Figure 1). Through the diagrams it is evident that the main reason why it is so much more difficult to walk uphill is due to the normal and gravitational forces. One must do more work when trying to walk up a hill therefore exert more energy to overcome the gravitational force as you are working against gravity. In order to move or walk in this case the force of gravity must be opposed, while on the other hand when walking on flat land one does not have to overcome gravity to move as the normal force takes care of that for them. This basic knowledge of physics explains why one is usually out of breath by the time they reach the academic quad at Colgate when walking from downtown. 

Figure 1. Free-body diagram. Above are the free-body diagrams for walking up a hill (left) versus down a hill (right).

Sources:

1. https://www.grc.nasa.gov/www/k-12/airplane/newton3.html

2. https://scienceblogs.com/startswithabang/2010/03/10/the-physics-of-an-inclined-tre

3. https://www.physicsforums.com/threads/why-is-there-no-work-for-someone-walking-on-flat-            plane.795810/

The Physics of the World's Fastest Car

The Bugatti Chiron is perhaps best known in the automotive world to be the world's fastest car. It has a measured top speed of 302 mph, set just last year on a stretch of track in the forests of Germany. To put it into perspective, that top speed is approximately 25mph higher than the top speed of a Japanese bullet train. Both are pictured below. 

But just how is the Chiron able to reach these ludicrous speeds?

When reading an article on the ridiculous speed of the Chiron, I came across a graph depicting the velocity vs time data for the record-breaking run:

The graph was split into 4 distinct slopes, each of which I recognized to be parts in the car's acceleration. What I found the most interesting is how the car was still accelerating prior to the brakes being applied presumably in the last 10ish seconds. Wouldn't the car reach a "terminal velocity" so to speak much like a falling object does, due to the nonconservative forces at work against it at its top speed? I decided to analyze it further.

In considering a car's acceleration, there are several factors to consider. The most crucial one is obviously the force provided by the engine on the rear wheels (contributing to torque), called the traction force, or simply the applied force. The Chiron has an estimated torque value of 1600 Nm, mindboggling numbers even for a supercar. We all know well that the torque is equivalent to rFsin(θ), and in this case, the Chiron's incredible torque provides it an immense angular acceleration, as well as a powerful traction force provided by the turbocharged 1500 horsepower, 16-cylinder engine powerhouse that rests in the rear of the car. Provided the torque value and assuming the force is acting at a 90 degree angle and that the diameter of the tires is approximately 20 inches (0.508 m), the force would be approximately 6299 N for one wheel. However, nonconservative forces will work to counteract the car's acceleration, especially at higher speeds, explaining the decrease in rate of velocity change as time passes. These forces are the drag force and the force of friction. If these forces balance out the traction force, the total force is zero, and the car cruises at constant velocity. However, if the traction force exceeds that of the drag and frictional forces combined, the car accelerates. From this data and from the calculated traction force, it appears that this traction force would have to be greater than the combined nonconservative forces for the car to continue accelerating. To test this, I calculated the drag force and force of friction:

 F_drag =  0.5 * C_d * A * rho * v²

    where C_d = coefficient of friction
    A is frontal area of car
    rho (Greek symbol )= density of air
    v = speed of the car

C_d for a Chiron is 0.28. A is 2.1 m². rho is 1.2133 kg/m³. 

At 300 mph (just shy of top speed) (134 m/s), the F_drag is approx. -47.8 N. 

Ffr = μK * mg.  The mass of the Chiron is 1978 kg. the μK for asphalt track is approx. 0.6. 

The Ffr is approx. -11630 N. 

This means that the total force for the car while moving at basically top speed is 6299(2) - 11630 - 47.8 = 920.2 N. 

This is a positive value, and it indicates the car still accelerates somewhat before braking, supporting the chart trend. This also shows how powerful the engine is, generating all that force on the two rear tires to allow this machine to continously accelerate to such high speeds, all while combating the effects of air resistance and friction. Truly an engineering marvel.

Reference video of the run: https://youtu.be/PkkV1vLHUvQ  

Article: https://www.wired.com/story/bugatti-chiron-speed-analysis/ 

Second article for Bugatti Chiron specifications: https://drivetribe.com/p/technical-analysis-of-a-high-speed-P7t71_CaSSOMFdALcj_CWg?iid=G0-Lctx9R8GGnjd_hMCgGw

Resistance to Chemotherapy

Biophysics and Cancer Biology

Julie Guillermet-Guibert is a researcher at INSERM (French National Institute of Health and Medical Research), a research institute in France. She obtained a Ph.D. at Paul Sabatier University, which has an affiliation with INSERM as a joint research unit. Her Ph.D. work was on the signaling pathways of somatostatin G protein-coupled receptor and their selectivity for normal and cancerous cells. She is currently the team leader of SigDYN at INSERM. Her team investigates the signaling pathways of cancer cells specifically focusing on pancreatic and ovarian cancer cells. She was awarded a Jean-Marie Lehn Excellence Prize for her work with Dr. Maximillian Reichert on the resistance of pancreatic cancer cells to signal-targeted therapy. 

One of her more recent publications, “Mechanical Control of Cell Proliferation Increases Resistance to Chemotherapeutic Agents”, is about the resistance of cancer cells to chemotherapy. Through experimentation using pancreatic cells and theoretical modeling, the research team found the reason for the reduced effectiveness of chemotherapy drugs is due to compressive stress. The cancer cells under compressive would experience mechanical alterations which one of the alterations is decreasing cell proliferation. This reduces the efficacy of chemotherapic drugs because the drugs target rapidly proliferating cells so when cancer cells proliferate at a slower rate, they would not be affected by the drugs as regular cancerous cells would. The team came up with a solution suggesting to use sensors, coupled with chemotherapeutic agents, to enforce the proliferation of cancer cells under compressive stress. 

References

F. Rizzuti et al., “Mechanical control of cell proliferation increases resistance to chemotherapeutic agents,” Phys. Rev. Lett. 125, 128103 (2020)

https://physics.aps.org/articles/v13/147

How to Run Up a Wall

I’m sure most of us have seen some form of wall-running in movies or films, but if not, there’s a link to a video below. The person in the video appears to walk up between two walls by jumping from one wall to another. I want to explore the physics behind how this is possible. 

The physics concepts being applied here are friction and momentum. The force of friction acts on the person when he is in contact with the wall. The equation for friction is
Ffr = μsFN 
where μs is the static friction coefficient and FN is the normal force. There is a change in momentum (product of an object’s mass and velocity), which is also known as impulse (change in an object’s momentum) when the person is jumping towards and away from a wall. Impulse occurs when there is a force acting on an object for a certain amount of time (product of the force applied to an object and the amount of time it is applied). The equation we are using is 
Δp = F/Δt
where F is the force applied to the object and Δt is the change of time. The force being applied in this situation is the force from the wall. Using Newton’s 3rd Law, when the person pushes against the wall he is applying force to the wall, the wall pushes back on the person with a force that is opposite but equal in magnitude to the force from the person. The person can only exert force on a wall for a short amount of time, so to maintain the momentum, he changes direction and pushes against another wall using the force the first wall exerted on him. As he repeats this action, there is a net upward force that allows him to go up the two walls.

The diagram gives a visual illustration of what’s happening featuring stick figures and a wall represented by a gray rectangle. 

References

https://www.wired.com/story/how-to-run-up-a-wall-with-physics/
https://www.youtube.com/watch?v=23QOy9Q2qNI&feature=youtu.be
0:07 - 0:12