Physics in Film: The Physics of Spiderman

Written by Rachel Weinstein

In Spiderman 2, Peter Parker manages to stop an out of control freight train, thereby saving all of its passengers from imminent death, using his supernatural strength and his incredible web.  There are interesting physics behind this scene, which exemplify how extraordinary Peter Parker is compared to an average spider.

 http://www.youtube.com/watch?v=GYOYewO_Veg

In this scene, the train is depicted as flying out of control at around 80 mph (35.76 m/s).  Peter manages to stop the train in 50 s. 

Vinitial: 35.76 m/s

Vfinal: 0 m/s

T: 50s

A: -35.76/50 = -.715264 m/s^2 

The overall force that is needed to stop the train is equal to the mass of the train times the acceleration.  The average freight train weighs 120 tons.

120 tons x 2000 lb/ton x 1 kg/ 2.2 lb = 109,090 kg

F = ma

F = (109,090)(.715264) = 78,028.149 N in the opposite direction the train is moving in.

Peter generates this force by shooting 12 strands of web towards the buildings on either side of the train.  Assuming that these strands are shot out on an even plane at even and very small time intervals, the assumption can be made that the strands are of similar length and consequently, the force of tension on each strand can be considered to be about the same.  In reality, this is not exactly what occurred and the force of tension on each strand would be slightly different depending on the angle and length of the string.  The force of tension in reality would also be constantly changing because the strand is stretchy, but to simplify the problem, I assumed that it is maximally stretched and the force of tension is not changing.

Thus, the force of tension on each strand equals: 78,028 N/12 = 6502N

Because the clip shows some of the strands starting to snap, we can say that this force is the maximum force of tension that the thread can withstand.  If we assume that the strength of the thread is related to the radius, we can compare actual spider webbing to Spiderman’s webbing.  A regular spider’s web can roughly withstand 2.0 x 10^-3 N of force.  A single thread has a radius of roughly 3.9 x 10 ^ -6 m.  Spiderman’s strand of web can withstand 6502 N and is estimated by me to be a cm thick. So…

(2.0 x 10^-3)/(3.9 x 10^ -6) : 6502/.01

512.82 N/m : 650234.58 N/m

If a spider’s thread was as thick as Spiderman’s:

512.82 N/m x .01 m = 5.128 N

Spiderman’s webbing is stronger:

6502/5.128 =   1,267.9 times stronger than your average spider.

Figure Skating Physics Examined

Though we just got to witness the Olympics this past summer, it should not be forgotten that the Winter Olympics are just two years away. One of the most popular sports to watch is figure skating, not just for the beauty of the performances, but for the important laws of physics that underlie every move the skaters make.

The physics starts with the ice. One of the main reasons ice is a suitable surface on which to skate is its near lack of friction on the blades of the skates. The center of ice is made up of tightly crystallized water molecules, but on the surface, these water molecules are less tightly packed, forming a nearly liquid, frictionless surface. This allows the skates to glide along the ice, hardly losing any speed.

In order to glide along the ice, the skater must first generate a force to push themselves forward. The energy for this force is stored as chemical potential energy (ATP) in the muscle cells of the skater’s legs. When the skater extends their leg, pushing against the ice, this potential energy is converted into kinetic energy and they move forward.

Spinning is a common move in figure skating, and viewers are often puzzled at how fast skaters can make themselves spin without adding any extra pushing. Skaters spin faster because of conservation of angular momentum. When they start spinning and have their arms and/or leg extended, the radius of their spin is large. Their angular momentum is proportional to their radius as well as their speed, so by making their radius smaller by bringing their limbs toward their center, the speed must increase to keep momentum conserved.

http://blogs.scientificamerican.com/observations/2010/02/23/the-physics-of-figure-skating/

Catherine Stecyk

Ponytail Physics

The Ig Nobel Prizes were held on September 20^th. This ceremony is essentially a more comedic version of the Nobel science prizes, and is designed to honor achievements that first make people laugh, and then think. This year, the physics prize went to Joseph Keller, Raymond Goldstein, Patrick Warren, and Robin Ball for their work on determining the balance of forces that shape and move the hair in the human ponytail hairstyle. Past scientists have apparently been interested in hair as well (who knew hair was so exciting), including Leonardo da Vinci who felt that hair flowed like water. “Somehow,” Dr. Goldstein recalled, “a bunch of balding, middle-aged men sitting around a table came up with the idea that the ponytail was the embodiment of all this interesting physics.” Consequently, these men set to work examining the forces involved in the shape and movement of a ponytail.

The scientists examined individual hairs (in terms of curliness/springyness) and then assembled different ponytails and took note of the average shape of these ponytails. They developed a simple model to predict the shape of a ponytail based on the force of gravity, the force of tension, an elastic restoring force, and a swelling pressure due to the curliness of the hair. This model is able to describe the shape of a ponytail when the individual hairs are bundled together and is represented by a value the authors termed the Rapunzel number. In terms of shape, a short ponytail of springy hair (low Rapunzel number) will fan outward, while a long ponytail (high Rapunzel number) will hang down because the force of gravity on the bundle is greater than the springiness of the hair.

In terms of motion, the men wanted to know why a ponytail swings side to side when people run even though the head is only going up and down. The ponytail cannot in fact be treated as a single object, but rather the individual hairs that make it up must be examined. These hairs all exert elastic forces on each other. Essentially, they found that it was unstable for the ponytail to swing up and down (due to an unfavorable relationship between the jogging frequency and the pendulum frequency of the ponytail) and that a runner’s head prevents the ponytail from swinging forward and backward. Therefore, side to side swinging occurs. On a basic level, it seems like the upward force of tension (y-axis) and the downward force of gravity (y-axis) must cancel each other out, and the elastic forces between the hairs (x-axis) must be responsible for this pendulum like horizontal motion. In terms of the hair not swinging forwards and backwards (z-axis), it seems as if the force of the head on the hair may push back on the z-axis elastic force of the hair and prevent the hair from swinging forward.

I thought that this article was just a neat application of physics. It was interesting to gain some insight into the physics behind something we see nearly every day; the ponytail.

Related Articles:

September 2012 Article:
http://news.sciencemag.org/sciencenow/2012/09/ig-nobels-go-to-studies-of-swayi.html?rss=1

February 2012 Article with Additional Information:

http://www.nytimes.com/2012/02/11/science/ponytail-shape-is-determined-by-complex-physics.html?_r=1

Actual Ponytail Study:

http://prl.aps.org/pdf/PRL/v108/i7/e078101

It’s Just Rocket Science

By Sam Wopperer


"There’s a one-ton, automobile-sized piece of American ingenuity…sitting on the surface of Mars right now.” –John P. Holden, President Obama’s science adviser responding to doubts about America’s leadership in space exploration

On August 6th, the NASA rover Curiosity touched down on the surface of Mars. It aims to investigate Martian climate, geology, and ability to support life. NASA released the animation below to show how Curiosity landed on the surface.

http://www.youtube.com/watch?v=BudlaGh1A0o

It might surprise you, but the forces acting on the rover in its landing can be easily explained using what we’ve learned in the first two weeks of Physics 111. Here’s a free-body diagram of the rover’s descent into the Martian atmosphere.

The rover reaches terminal velocity (like the penny example we did in class) quickly after it enters the atmosphere of Mars. Terminal velocity is achieved when the force due to air resistance equals the force of Martian gravity, as shown in the diagram.  When the rover reaches a certain altitude, the parachute is deployed, which acts to further increase the effective force of air resistance by increasing the area term. This decreases the terminal velocity more and allows the rover to approach the surface at a less disastrous velocity.

When the it reaches a lower altitude, the rover is ejected and thrust boosters are activated in the direction opposite to the force of gravity to stabilize the rover and to allow it to be safely landed on the surface of Mars. The rover is then lowered using a pulley system. Here’s a free-body diagram of the rover being lowered onto Mars.

Landing on Mars is pretty complicated. A few years ago when the rovers Spirit and Opportunity landed, the landings were a little less sophisticated.

http://www.youtube.com/watch?v=KyktvC7w7Js

The Physics of Baseball

by Heather Frank

When I watch a professional baseball game I am often very impressed by the skill and coordination of the players. Many, like me, think that you are born with such talents and athleticism but after 2 weeks of Physics 111 it seems as if there must be much more thought and mathematical equations involved in being a talented athlete. One skilled baseball player that has recently been in the news is now being recognized for his pitch that seems to redefine the laws of Physics. In April of 2009 at a New York Yankees and Toronto Blue Jays Baseball game, the fastball pitch of the Yankees pitcher Freddy Garcia caught the eye of players and scientists a like. One particular Baseball journalist, Mike Fast, noticed this "fast" pitch and asked a Physics Professor at the University of Illinois to examine the interesting projectile path of the baseball out of this pitch. The Professor, who knew a lot about the physics of a baseball realized that this was more than the Magnus effect, which is the guiding principle responsible for the curve in a curveball. He realized that the side to side movement was not determined primarily by the spin but instead by something else. After much research and analysis this Professor asked another Physicist at the University of Australia if he could figure out the physics of the baseballs motion. This physicist, Rod Cross, hypothesized that the curve was due to the smooth patch effect which is due to airflow being disrupted by the raised and rough seems on a baseball: "the turbulence applies a force on the ball causing it to break. Wherever the ball is smooth, however, or not covered by seems, will cause it to go away from that direction. According to this theory Garcia's pitch is so difficult because he must enable the ball's spinning axis to pass through the smooth patch for as long as possible which makes the ball spin in a way different from any other pitchers throw. Garcia must hold the ball is a specific way so that the spin axes passes through the smooth patch instead of the stitching therefore causing the ball to curve in the opposite direction then expected. Garcia had little idea that he was redefining how physicists analyze the motion of a baseball, but he does realize that his pitch is a uniques skill and if the secrets of projectile motion were as obvious as the equations make them seem, then he would not be the star pitcher for the Yankees team.  

"Challenging Batters and Physics Experts Alike"

http://www.nytimes.com/2012/08/05/sports/baseball/pitch-by-yankees-freddy-garcia-tests-physics-experts.html?ref=physics

Get Angry: Physics Based IPhone Games are Big Business

Written by Andrew Long 

Almost everyone has played the addictive, yet maddening game, Angry Birds. It is interesting to think that just three years ago, the app was launched and changed the field of phone games. It has become a cultural phenomenon. The game has released multiple editions on multiple platforms and has sold over 1 billion copies, according to Rovio’s website (Rovio.com). The company has also released a line of clothing and stuffed animals. Although the physics of the game is not perfect, much of the game mimics the concepts of real life projectile motions.

If you have not played Angry Birds before, you should download the game immediately (unless you actually want to be productive, then you should avoid it at all costs). After playing around a little bit with the game, you will quickly find that the slingshot with the angry birds allows you to pull back the bird at different lengths to give the birds different initial velocities. In addition, you can change the angle of incidence to increase the speed in either the positive or negative y direction. This is important in order to hit the pigs and beat each level (especially at the higher levels), you have to hit the pigs at certain points with pinpoint accuracy. Although I doubt most people do calculations to shoot off their birds, you could use the formula V₀t+(1/2)at²=distance to determine the distance the bird would be shot at different velocities (related to how far back you pull the slingshot).  After trying that a bit you would realize you would need a positive y component velocity in order to reach the pigs on the far right side of the screen so you would have to break up the velocities into its components and solve for the angle of incidence using vectors.

http://www.youtube.com/watch?v=_iQbZ3KNGWQ

Physics is everywhere nowadays, and people are profiting greatly from physics in many unconventional ways. In addition to Angry Birds, there are other iPhone games that use the concepts of projectile motion in their format. My personal favorite iPhone game is called Tiny Wings by pressing the screen, you can increase the acceleration of the bird towards the ground. By pressing the screen the right amount, you can make the bird’s displacement the perfect amount to go slide along the hill. This is related to the formula V_it+(1/2)at²=distance. By increasing the negative acceleration (assuming you are on a coordinate system that define’s down as negative), you can decrease the distance traveled  by the bird. Of course, the physics of this game is worse than angry birds because you can gain speed by sliding down the hill and fly higher than you were before sliding down the last hill (this is mainly because you get a boost of speed by sliding down the hills, so the physics they use are not as bad as they sound), but, all in all it is an awesome game that makes you think a little bit about acceleration and projectile motion.

http://www.youtube.com/watch?v=VUnlE4cGgz0

article

http://www.el33tonline.com/past_article/2012/9/9/angry_birds_trilogy_preview/

Physics Can Be Hilarious

Physics can be really funny. Exactly how funny? Well, I'm alone right now and was laughing out loud not moments ago. As demonstrated by the following two videos (and a brief conceptual analysis thereafter), we can see that physics plays a fundamental role in all areas of our life, even the happy ones (though these people are probably not too happy).

What makes us laugh here? While one may not readily intuit it, its the person's very rapid deceleration, which causes an almost instant decrease of velocity to zero. Take our simplest kinematic equation: v^f = v_o + at. We know that v^f equals zero at the moment of impact with the glass. Let’s assume v_o, or initial velocity, equals he average human walking pace, which the internet tells me is 5.0km/hr, or 1.3m/s. The final variable we are going to assume we know is t; granted, I don’t actually know how long it takes for the person to stop moving as a result of running foolishly into a wall, but I think a very rough estimate would be somewhere between a tenth and a hundredth of a second (t = 0.05s). Putting these variables together, we get 0m/s = 1.3m/s + a(0.05s) --> -1.3m/s = a(0.05s) --> a = -26m/s². That’s really fast deceleration for just walking. And thankfully really funny too.

What about this?

While this video might not be as funny as the previous one, I have a personal connection to it (sophomore year, my friends wedged a plank under my door handle and couldn't stop laughing...meanwhile I had to use the bathroom, felt claustrophobic, and panicked; Campo got involved). I thought this video ties in wonderfully with our analysis of different types of forces, notably the force of tension. Why can't the students open their doors? It's because of the force of tension acting in the direction opposite of the person opening the door. A free-body diagram of a situation when the door is closed and the rope taut could be represented with a circle as the doorhandle with the force exerted by you moving in one direction and the force tension moving in exactly the opposite direction. While only the x components of force here play a significant role, there would also be a downward force of gravity and an opposite normal force exerted by the frame of the door holding the doorknob in place. An interesting note, though, is that as a person exerts more pulling force on the door handle, the rope exerts an increasing force in the opposite direction. The person will only be able to open the door if the pulling force exerted by their arm exceeds the maximum amount of tension force the rope can exert back on the door, at which point it will break...or if their friends just let them out. Also important to note is that this problem is a little more complicated than the situation I've described; this is because the direction of force will be changing at every point the door swings open. The free-body diagram one would draw for this situation would have to be specific to an instant in time where the force exerted by you on the door would have a particular direction.

Babies Need to Face the Rear!!!

Physics in the News

            In March 2011 the New York Times ran a story about the significance of rear facing car seats.  The article explained that a study demonstrated that children under 2 are 75% less likely to survive a serious accident if they are not facing backwards.  The article gives the explanation that an infant’s head is large in relation to the rest of the body meaning that the supporting bones are not fully ready to stabilize the head.  While the straps will often protect the infant’s body, when a severe impact occurs the baby’s head is likely to snap forward and cause acute trauma.  With a rear facing seat the impact will be absorbed throughout the hard shell of the seat and the head of the infant will be protected. 

            The physics behind this research relates to the forces that will be pushed on the baby during impact.  A head on collision with a baby facing forward will result in both extreme force being pushed on the fragile body as well as a potentially lethal head snap.  The baby will be the primary recipient of all of the force.  The hard shell of the seat will not prevent the forces from being exerted on the baby.  With the seat facing the rear of the car the hard shell will be able to absorb and take the brunt of the force from the impact.  The normal force of the seat pushing on the baby will be able to prevent the potentially severe head snap and the infant will suffer a less severe injury.  Of course this would be reversed for a car that is hit from the rear. 

Source:  http://www.nytimes.com/2011/03/22/health/policy/22carseat.html?_r=1