Finding Treasure

In class, we've talked about how the location of a buried treasure can be described by using a displacement vector. If a treasure hunter knew where to start (the origin) and the displacement vector, he or she would be able to find the treasure.

What about other coordinate systems? Suppose instead of a displacement vector, the treasure hunter knew exactly how far the treasure was away from two fixed points. If this were the case, would he or she be able to dig up the treasure on the first try? How many possible locations for the treasure would there be?

Pythagorean Triples

Photo by Gavin Keefe Schaefer

As we've been studying vector addition in class, I've been coming up with examples to use on the board. I usually deliberately choose the addends so that the magnitude of the resultant will be a whole number. How do I do this?

I choose the addends so they are two members of a pythagorean triple--three integers that are sides of a right triangle. Have you memorized any pythagorean triples?

1. Is there a pattern or formula that can be used to generate pythagorean triples?
2. Is there a size limitation? Is there such a thing as the largest phythagorean triple or the last pythagorean triple?
3. Do you think there are any pythagorean triples in the photo at the top of the post?

Compass Confusion

Photo by Calsidyrose.

When talking about directions, high school students are often presented with conflicting coordinate systems. In physics (and engineering, navigating, and surveying) we assign north to be 0°, and we then work around the compass in a clockwise manner. In contrast, mathematicians assign the positive x-axis to be 0° and then proceed in the counterclockwise direction.


Physics teachers (and physics textbook authors) are faced with a dilemma: should we stick with the same coordinate system used in the students' math books, or should we teach students the coordinate system that they are likely to see on a real-world compass?

1. There is no "right" answer to this dilemma, but what do you think is the best solution?
2. Is there an angle where a student using the "physics" coordinate system and a student using the "math" coordinate system will agree on the same value? In other words, which angle(s) is the same in both coordinate systems?
3. Many people have and use GPS navigation devices. These devices are capable of reporting the current course heading. If you own or have access to such a device, experiment with it by moving in a known direction. Which coordinate system does your device use?

Vector Addition

In class, we talked about how a vector is a mathematical quantity that has both a magnitude and a direction. Graphically, we can represent a vector as an arrow--the magnitude is indicated by the arrow's length, and the direction is represented by where the arrow points.

In physics, we will find it necessary to carry out mathematical operations with vectors. One can understand how vector addition works by using graphical representations (arrows). In class, we discussed two common ways to graphically add two vectors--the "tip to tail" method and the parallelogram method. Play around with the interactive vector addition tool at http://phet.colorado.edu/sims/vector-addition/vector-addition_en.html.

1. Which method of vector addition do you prefer?
2. Is vector addition commutative, e.g., if A and B are vectors, is A + B = B + A always true?

Distributed Computing

Can you imagine doing an experiment so large in scope that a real limit is that it would take a modern computer thousands of years just to process the data? In fact, there are many experiments that have this exact problem.

One solution to the problem is to use a very expensive and/or specialized (super)computer. This is often not possible. Many scientists and computer scientists have taken an alternate (and creative) approach. They tackle these huge data sets with a technique called distributed computing. Essentially, they use the internet to share the data in small portions to thousands of normal computers around the globe. Computer users allow their computers to process data while they would otherwise be idle. Read more about the technique at wikipedia.com.

Many of these experiments are physics projects. Perhaps one of the most famous examples of distributed computing is SETI@home.

1. Research some current examples where distributed computing is being used to solve a problem. What examples are the most interesting to you?
2. Would you be willing to allow your home computer to be used for distributed computing? Why or why not?
3. Do you think our school should allow all of its computers to participate in a distributed computing project? Are there any costs associated with it? Would it cost the school money or would it essentially be free?

Balloon Car Challenge 2010

Last Wednesday and Thursday, Core Physics students competed in Yale High School's First Annual Balloon Car Challenge. The goal was to design a balloon-powered car that was capable of driving 5 meters as fast as possible. Students had a lot of fun, and there were a variety of creative solutions! Students were asked to think about how Newton's Third Law can explain the motion (forces between the balloon and the air inside the balloon). Check out the slideshow of some of the competitors at the bottom of the page.

1. Besides Newton's Third Law, can any other laws or concepts of physics be used to explain how the car moves?

Morning News

I was reading the headlines this morning with Google News, and I noticed that the Walt Disney Company was listed as a top story. I clicked on the lead to see what Disney was doing that was newsworthy. As I skimmed the headlines, one caught my attention. It reads

"Shares of The Walt Disney Company today lose -3.06%"

Is this what the author really means? Would this have looked a little "off" to you if you had read the headline without me first directing you there? Is it a big deal?

Never Teach a Hammer ... ...

One of my sons' favorite shows is Handy Manny on Disney Channel. In the show, Wilmer Valderrama's Manny has many helpful, talking tools. Whenever Manny has a job to do, he discusses it with his tools and they all get to work.

I imagine a scenario where Manny asks his hammer Pat to drive a nail into a board. The conversation goes something like this... ...

Manny: Please drive in that nail.

Pat: I can't

Manny: What do you mean?

Pat: Well, I learned about Newton's 3rd Law--for every action there is an equal and opposite reaction. When I hit the nail, the nail will hit me back with just as much force.

Manny: Go on... ...

Pat: Since the forces are equal and opposite, they will cancel. There's no reason to even bother--with equal and opposite forces, there's no chance the nail will move.

What's going on here? Is Newton's 3rd Law not really correct, or is there a problem with Pat's logic? What do you think?

Forces, Forces, Forces!

In an effort to look for patterns and to simplify things, physicists study the ultimate origins of forces. The current theory is that all forces in the universe can be classified as one of four fundamental forces. In no particular order, they are:

• Gravity
• Electromagnetic
• Weak nuclear
• Strong nuclear

Sometimes, the electromagnetic force and the weak nuclear force are combined together and called the electroweak force.

1. How do physicists believe these forces are transmitted?
2. Gravity is by far the weakest of the fundamental forces, and yet it has a huge impact on our universe (consider the Earth orbiting the Sun--almost exclusively because of gravity). What attributes does gravity have that makes it something that cannot be ignored?

Modeling the Restoring Force Present in a Spring-mass System

The experimental set-up.

In class, we used a force sensor coupled with a computer to monitor the restoring force present in a spring-mass system as it bounced up and down. The graph of force vs. time is partially shown below.

1. What is the period of this oscillation?
2. The mass attached to this spring was 150 grams. What is the spring constant (k) for this spring?
3. Calculate the acceleration of the mass at t = 26.0 seconds.

Many students noticed the similarity of the actual data with the shape of the familiar sine graph (shown below).