Physics of Pole Vaulting: Part 1

Pole vaulting, one of the most exhilarating and technologically complicated events in track and field, is only pursued by the most daring of individuals. In pole vaulting a vaulter's goal is to clear, or get over, a horizontal bar at set hight. In a typical competition, a vaulter may make seven or eight jumps. During a jump, a vaulter is trying to convert his energy from his horizontal velocity and transfer it into vertical energy. There are many factors that effect the outcome of a vault. This makes it difficult to look at the cause of a mistake or error, for all the factors are interrelated to each other. By neglecting certain factors it makes it easier to see the physics behind the pole vaulting.

Suppose a vaulter sprints toward the pit at 7 m/s. When the vaulter reaches the pit, his pole launches him at an angle of 83 degrees with the horizontal toward the horizontal bar. In what time will the vaulter reach his peak? What height will this be? (Think of the vaulter as a projectile)

Consider your answer. What factors do you think would affect the height of a vaulter? (There are many!)

MythBusters' Math Mistake?

Screenshot from 11/12/2011

I caught the last 5 minutes of MythBusters last night (episode "No Pain No Gain"). They were testing to see how "cursing" affects the amount of time people can tolerate having their arms in a tub of ice water--the myth being that cursing will increase one's pain tolerance.

Look at the screenshot of the MythBusters' results. Grant was able to keep his arm in the ice water for 38 seconds without cursing and for 118 seconds while cursing. The column labeled "% Change" strikes me as very odd.

1. By using the MythBusters' data, try to determine the formula or process they are using to calculate "% Change."
2. How should percent change be computed? What data should appear in that column?
3. Did the MythBusters make a mistake? If so, make a post on the forum for that episode and leave a link here to share with us.

The Physics of Iron Man: Flight

Being the extreme science fiction fan that I am, I have always favored Iron Man as my favorite superhero. Not only does he fight crime, but he fights crime... with science. Or so I thought. A few years ago I found myself in the seat of a movie theater, revving up my action engines and preparing for the onslaught of awesomeness the Iron Man movie planned to deliver. With this superhero brought to the silver screen, however, I found myself mumbling under my breath about how just about everything he was doing was physically impossible. Or was it? By making a few assumptions about his fictional technology, I decided it was time to make a few calculations. Thus, this short series was born.

Over the next few weeks, I will be occasionally be posting a physics question regarding Iron Man's comic book and "big screen" technology. This, of course, is the first post.

Today's question is about Tony Stark's (Iron Man's actual name) flight. This is truly a spectacle to behold, and one of the original purposes for the creation of the suit, according to the film. In fact, it was this very feature that allowed Tony to escape the terrorists in the film! But let's take a closer look at that scene...

During the scene, Tony builds a gigantic robot that needs the help of mechanical power in order to actually allow it to move easily. In other words, it weighed a lot. So, with the assumption that his main resources was stainless steal (The terrorists were supplying him, remember!), the suit probably had a mass of about 2,360 kilograms. This includes the many dense plates of armor that he was wearing, along with the weapons, and the fuel reserves. Tony, being an average human adult male probably weighed about 75 kilograms.

Photo by Daniel Spiess.

Later in the scene, Tony walks outside of the cave he was trapped inside, and, in a way to escape the terrorists, uses his first rocket boots about 20 meters from the mouth of the cave to propel himself into the air. Unfortunately, Tony is only able to sustain his flight for roughly 7 or so seconds.

This brings us to question #1: How much force was actually needed to lift the first Iron Man (Tony in the prototype suit) off the ground? This is assuming that the acceleration of gravity in the Middle East is 9.8 m/s^2.

Now for question #2: Assuming that he is able to obtain enough force to instantly accelerate him to a flight speed of 90 m/s, and he sustains this speed for the length of his flight, how high will Tony get before he runs out of fuel if he launched himself at a 35 degree angle?

Question #3: At the top of his flight, Tony runs out of fuel. From here he falls down onto the ground in a crash. Assume that Tony leveled himself out the moment he ran out of fuel. How far from the mouth of the cave is he at this point, assuming he traveled in one direction?

Question #4: How fast will Tony be falling just before he hits the ground?

Now, lets look at how much force his rocket boots are creating.

Question #5: How much force would be needed for Tony to lift off of the ground WITHOUT the suit?

Final Question, #6: How many times more is needed for a suited Tony to lift off as compared to an unsuited Tony?

Discuss your findings. It's kind of ridiculous.

Coming Soon: Guest Authors

We are pleased to announce that there will soon be three new authors joining the Yale High School Physics Blog. These authors are students at Yale High School currently taking Independent Study Honors Physics II. They will be writing posts about  physics topics that enrich content covered in the physics classroom, physics as it appears in popular culture, and how physics topics impact people in their daily lives. The authors are eager to read feedback about their posts.

Please be sure to check back often as these posts are published. Let's get a dialog going!

Physics from a Historical Perspective

Photo by Thorne Enterprises

Charles Day from Physics Today writes a very interesting column comparing how students learn US government to how they learn physics. Please read Day's excellent article before posting a comment here.

The US Constitution is the foundation upon which our entire government is built. Even though it was written in 1787, the Constitution is not only relevant but fundamental to any study of US government. Students of US government often are asked to directly read and study this document.

In physics, many (if not most) topics of study have changed radically since 1787. Physics teachers rarely ask their students to read or study physics books or papers from that far in the past.

1. Day talks about several topics of modern physics that were not even known when the Constitution was written. What specific topics does he mention?
2. One of the texts mentioned in Day's article is Newton's famous work usually called simply Principia. What is the full title of this work? When was it written? What is it about, and why is it so important?
3. Do you think physics students would gain a deeper understanding of physics if they studied historical texts like Principia? Why or why not?