One of the contributions that Albert Einstein made to science was the Special Theory of Relativity. In simple terms, Special Relativity recognizes that all observers, regardless of their speed will measure the same value for the speed of light. This is inconsistent with Newtonian mechanics.

Imagine a person running along the top of a boxcar at 2 m/s, the boxcar itself is traveling in the same direction at 80 m/s. An observer sitting on the boxcar would measure the speed of the runner in relation to the boxcar as 2 m/s. An observer sitting on the ground would measure the speed of the runner in relation to the ground as 82 m/s. This is Newtonian mechanics. Extending this analogy, imagine a spaceship traveling at 2.50 x 10⁸ m/s, (83% of the speed of light) shining headlights in front of the ship. An observer sitting in the spaceship would measure the speed of the light from the headlights as approximately 2.98 x 10⁸ m/s, this is consistent with Newtonian mechanics. However, a stationary observer watching the ship go by would measure the speed of light from the headlights as approximately 2.98 x 10⁸ m/s as well, instead of the 5.49 x 10⁸ m/s that Newtonian mechanics predicts.

That the speed of light is a constant value has some interesting implications. One implication is that no ordinary object can actually reach the speed of light, let alone travel faster than that. There are other unusual things that happen to objects traveling close to the speed of light. Time is dilated and object lengths shortened.

"The Ultimate Kinetic Energy Challenge" introduces small objects moving at high speeds. It is not intended to explain relativity, but rather to illustrate that Newtonian mechanics has limits, and ask the tantalizing question "Why is there a limit to the speed of the particles?" Advanced students may want to explore this question.

• Computer with Internet connection (See our Technical Support page for assistance.)
• Lab notebook
• Student Packet - This is a printable version of the lab materials (instructions, tables, questions).

All teachers have unique and original ways to introduce new topics and ideas. Presented here are a couple of ideas for introducing this lab activity.

1. One way this activity can be used is as an example of limits to scientific laws. Conduct a class discussion about the difference between laws (descriptions of phenomena) vs. theories (explanations of phenomena). Ask the students to share both laws (Newton's three are appropriate here) and theories they are familiar with. Ask them to think of situations where these laws don't apply.. Tell the students that the computer activity they will be conducting looks for the limits to Newtonian mechanics.

2. With more advanced students this activity is a good introduction to special relativity. For this group, lead a discussion about laws and theories as before. This time try to bring in some history, how scientific ideas change as our knowledge of the universe expands. Discuss some early theories that no longer apply, as well as some that still do. For example, we know that the earth is round, but we still use a Cartesian coordinate system for most of our problems. Why? For most objects at the surface of the earth, the Cartesian coordinate is a very good approximation. The same is true with Newtonian mechanics. For most objects, Newton gives a very good approximation. Tell the students that this computer activity will look for the limits to Newtonian mechanics, and later they will learn about the theory that explains the new phenomenon.

As the students conduct the online lab, the role of the teacher should be one of facilitator. Allow students as much freedom as possible. Ideally, they will discover the relationships on their own. It is best if students work in small groups, no more than three students per group. Two is ideal.

The teacher should conduct the lab activity prior to the students. This way the teacher will be able to answer student questions as they arise. Encourage students to read the instructions prior to proceeding to the next page. This will help make the lab easier. While the students are conducting "The Ultimate Kinetic Energy Challenge" the teacher may want to encourage the students to try to determine under what circumstances Newton predicts the speed correctly and under what circumstances Newton predicts the speed incorrectly.

This activity takes 1 classroom period, depending on technical problems and skill of students. It is worthwhile to discuss any possible technical problems with the technical specialist prior to beginning the lab. Such problems may include: whether or not all students have network access, the number of available computers with Internet access, whether or not the local server is up and running on the day you wish to conduct the lab.

A Student Lab packet is provided that includes student instructions, tables, and the questions from the lab. Teachers may wish to use this for classes that need extra support, or for classes with time constraints, or merely to facilitate the ease of conducting the investigation.

Ask the students to share with each other, or to write down, the limits that they found to Newtonian mechanics. Students should have found that the smaller objects with higher energies did not obey the Ek = mv2 equation, while the larger objects with lower energies did. They should also note that 3.0 x 10⁸ m/s is the upper limit on the speed of all the particles. Share with them that this is approximately the speed of light, and that nothing can travel faster than that, no matter how much energy it has. Also tell them that Einstein proposed a theory to explain this phenomena, called the theory of special relativity.

Students can conduct research on how scientific theories have changed over time as people have learned more about our universe. Use this as an introduction to special relativity. Interesting note, Einstein was not awarded a Nobel prize for special relativity, his most famous theory. His Nobel prize was for work in quantum mechanics. For many years after Einstein first proposed special relativity there was no evidence supporting the theory. The first evidence came from solar cosmic rays.