Why Curling Stones Curl

This weekend I was at club curling practice in Utica and the coach was teaching the new members about sweeping. I happened to overhear her explain that sweeping helps to decrease the frictional force on the stone, and realized that I had no idea about the physics behind the sport that I’ve been playing for three years. I was interested in the motion of curling stones and why exactly they curl in way which is so characteristic of the sport. Curling stones move in a counter-intuitive way: if a stone is delivered with a clockwise rotation it will curl to the right, however if you push a cup along a table with a clockwise rotation the cup will travel to the left (no cups were harmed in the testing of this motion). This is an effective comparison because the stone only touches the ice with the running band, which is a thin, round surface on the bottom of the stone similar to the rim of a cup. There are two theories for the cause of this motion: the scratch theory and the asymmetric friction theory. The first states that the rough running band causes microscopic scratches in different directions on the ice. As the stone moves down the ice, the front of the stone scratches the ice in one direction and is then followed by the back of the stone traveling in the opposite direction, thus causing the back of the stone to experience greater frictional forces than the front due to encountering these scratches. This ultimately causes the back of the stone to slow at a faster rate than the front, and causes the stone to follow the direction of motion at the front of the stone. The second theory states that as the stone slows, is begins to “lean forward” slightly in an attempt to tip over. This same tipping motion is observed in the cup analogy, so there must be something else causing the strange motion of the stone. In fact, the increased force on the front of the stone causes the ice at the front of the stone to melt slightly from the pressure (just like ice skates). The thin liquid layer at the front significantly decreases the coefficient of friction between the ice and the stone, so similar to the first theory, the back slows at a faster rate than the front and causes the stone to follow the direction of the front. Both of these theories are convincing from a physics point of view and both may very well be correct. The science of curling is still disputed and emergent data is currently being collected which may prove these theories or come up with a completely new theory to add to the debate.

Sources:

Bradley, J. L. (2009, December 8). The Sports Science of Curling: A Practical Review. Journal of

Sports Science & Medicine, 8(4), 495–500.

Natural Sciences And Engineering Research Council. (2004, October 13). Why Rocks Curl.

ScienceDaily. Retrieved October 31, 2017 from

www.sciencedaily.com/releases/2004/10/041008024015.htm

Normani, F. (n.d.). Physics Of Curling. Retrieved October 31, 2017, from

https://www.real-world-physics-problems.com/physics-of-curling.html

The mechanism that puts the curl in the curling stone revealed. (2013, May 15). Retrieved

October 31, 2017, from https://phys.org/news/2013-05-mechanism-stone-revealed.html

Spector, D. (2014, February 14). Why Curlers Sweep The Ice. Retrieved October 31, 2017, from

http://www.businessinsider.com/why-curlers-sweep-the-ice-2014-2

Popping Champagne (The Wrong Way)

Over the weekend, for no particular reason, I found myself thinking about the physics of popping a bottle of champagne. I realized that a cork shooting out of a bottle of champagne could be considered an inelastic collision, due to the fact that it is two objects coming apart. In inelastic collisions, momentum is conserved, but energy is not. Because the cork shoots out in one direction, in order for momentum of the system to be conserved, the bottle must theoretically move in the opposite direction. The reason that this is barely noticeable is because of how the mass of a champagne cork is far smaller than that of a bottle of champagne, so to achieve equal momentum as the fast moving cork, the bottle doesn't have to move very much in the opposite direction. This may also be stopped by the person who is holding the bottle anticipating its slight movement backwards.

This is not the only physic phenomenon that occurs within a bottle of champagne. The actual dislodging of the cork out of the bottle requires that unequal forces act on the cork. When a cork is at rest in an unopened bottle, there is pressure acting on the cork from the dissolved CO2 molecules in the champagne. This pressure force is balanced by the static frictional force between the cork and the walls of the bottle, keeping the cork at rest. Once the cork is moved slightly, the frictional force moves to kinetic friction, which is traditionally lower due to the fact that it is easier to keep an object in motion than to put it into motion. The unbalanced forces cause the cork to accelerate and shoot out of the bottle.

So this New Year's Eve when the clock strikes 12:00, make sure to grab a bottle of champagne and a camera to record it being popped, and the immediately upload the video to Tracker in order to determine the speed of the cork leaving the bottle.

Taking a Nasty Whipper: Can Anything Break?

Two weekends ago I went out sport climbing at Thatcher Park in Albany, NY. Unlike top rope climbing, where the rope is always taught against you so even if you fell off the wall you would be caught immediately by your belayer, sport climbing involves you clipping into the wall as you make your way up the wall. Top rope climbing the rope goes all the way up to the top of the climb and then back down, whereas sport climbing your bing the rope up from the bottom of the climb.This means that while you are climbing to your next clipping point (known as a bolt) there is slack that is paid out into the system.
So as I was climbing up to the top, the first thing that went through my mind was: if I cant do this, whats is the first thing that is going to break? Would it be me? My rope? My Carabiner? My harness? Wow. Many more things that could break than I realized. Well. In order to find out I decided to do some quick thinking physics while I was in the middle to decide whether or not I should have fallen from that height.
My known mass was about 72kg, and on this specific climb there were about 6 bolts spaced out over 60 feet. So my best guess was that there was about a ten foot gap between one bolt and the next, and I was about to be clipping in. So after doing some quick conversion in my head, I realized that my height was 3.0m. Therefore, the amount of slack that was in my rope was 6.0m, but since I like to have extra slack in my rope because I am ~nuts~ I had an extra meter, so I had 7.0m of total falling to do -- if I were to fall. So. We could find my final velocity via the change in energy. My initial potential energy was m*g*h, however my mass cancels out with the kinetic energy equation 1/2*m*v^2, so as a result my final velocity when I reached the length of the slack in the rope would be 12m/s. Wow. thats fast. We could then find what the force of the fall would be on my rope, my carabiner, and my harness, along with me, with the impulse equation, where force=p/t, and I would stop in about 0.01 seconds, if I were using a static rope. Therefore the force that I would experience would be on the scale of 84,000N! Wow. I would most definitely be dead, since the carabiner I was falling on could hold 22,000N of force, and the rope cant hold even close to that, and my harness couldn't have held that either since it can hold only 16,000N o force. My body definitely can't hold that much. My legs may have stayed on the wall and my torso would probably be down on the ground.
That made me pretty scared to fall. Like really scared. But then I realized that my rope was not static! It was dynamic! So instead of stopping over .01 seconds, I am really stopping in 1-2 seconds. Because of that I would only experience between 840N-420N, safely in the range where i wouldnt break anything.
So I realized that I could fall without being worried. And so, I continued climbing without falling getting to the top and looking out over Albany.

video of someone taking a whipper: https://www.youtube.com/watch?v=_0XuntyZg74
The moment when I did math-->
The moment that I looked out over Albany-->

float like a butterfly, sting like shrimp

The peacock mantis shrimp (Odontodactylus scyllarus), is a species of crustacean that is unique in having the world’s fastest moving appendage. It uses its club-like front appendage to bash or stab its prey with explosive speed, resulting in a powerful punch that effectively kills its prey. It is so powerful in fact, that mantis shrimps have been known to break the 1/4 in. thick glass that is used for aquariums. When measured by Sheila Patek, a researcher from UC Berkeley, found the mantis shrimp to punch at 52 mph (or 23 m/s) with an acceleration of 104,000 m/s^2, over a time of 0.0027 s (Patek et al., 2004). Using the F=ma equation, and the fact that it weighs 0.015 kg, the force at which the mantis shrimp strikes is 1560 N, about the same force as a .22 rifle. Patel estimates that the amount of power needed for a strike of this force is 4.7x10^5 Watts per Kg (Patek et al., 2004), which, using the equation P=W/t and t=0.0027 s, gives 1,269 Joules of work. The mantis shrimp is capable of producing this much energy due to the energy storing abilities of its limb structure. Instead of simply pulling back with its lateral extensor muscle and swinging forward, like a human would punch, the mantis shrimp uses the combination of a latch mechanism and a spring mechanism. The latch mechanism is a series of latches within the mantis shrimp’s appendage that locks the limb into place until the muscles are fully contracted (Burrows and Hoyle, 1972).This latching of the limb allows a greater buildup of muscular potential energy, PEmuscle, leading to a greater kinetic energy, and force, upon release. However, this mechanism alone does not produce enough potential energy to make such a fast strike possible, since muscle fibers can store only a limited amount of energy (Alexander and Bennet-Clark, 1977). In order to have enough energy for its strike, the mantis shrimp also uses a spring mechanism. The spring mechanism is composed of a saddle-shaped spring that compresses when the mantis shrimp pulls its limb back for the strike. (Figure 1). This compression causes a massive increase in the spring’s potential energy, resulting in the necessary amount of kinetic energy needed for the strike when the limb is released. Overall, the work-energy equation for the peacock mantis shrimp’s strike is Wnet=PEmuscle + 1/2Kx^2.

Figure 1: The saddle-shaped spring of the peacock mantis shrimp compressed (above)
and released (below) (Patel et al., 2004).

Citations:

Patek, S. N., Korff, W. L., & Caldwell, R. L. Nature 428, 819-820 (2004).| doi:10.1038/428819a

Burrows, M. & Hoyle, G. J. Exp. Zool. 179, 379−394 (1972).

Alexander, R. M. & Bennet-Clark, H. C. Nature 265, 114−117 (1977).

Seeing 3D in 2D??

How do 3D films work?

After seeing a 3D film, you wonder how the 2D image in front of you somehow becomes translated into a 3D image after putting on a flimsy pair of glasses. 

Our left and right eyes see what is in front of us from slightly different points of view. If you close only your left eye and then close only your right eye you will see the image in front of you shift back and forth. This is the principal used to create 3D films and is called stereoscopic projection. 

Using physics, we can manipulate the images that both our eyes are seeing (for movies this manipulation comes across through the 3D glasses). The filmmakers set two images onto the screen, one meant for our left eye and one meant for our right eye. One of these images is composed of light polarized horizontally and the other is light polarized vertically. Polarized light waves vibrate on a single plane, rather than on all planes. Isolating these two images to these two planes allows us to select which eye sees one image or another. If we allow only horizontal light through the left lens (by making the polarizing filter vertical, and vertical light through the right lens (by making the polarizing filter horizontal) we can create the illusion of two separate points of view in front of us, therefore making a 2D image into a 3D one. Higher tech 3D glasses will polarize circularly, polarizing the light counterclockwise for the left eye and clockwise for the right eye. This allows the viewer to tilt their head without compromising the resulting image. 

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 (M_AV_A+M_BV_B=M_AV_A’+M_BV_B’) 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/

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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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 13^th inning so tensions were high. At some point in the 13^th 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!