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# Length Contraction

## As the velocity of an object approaches the speed of light it appears to change length to a stationary observer.

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Practice Length Contraction
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Watch it Shrink!

### How would your family van look if it were moving at the speed of light?

Credit: JLaw45
Source: http://www.flickr.com/photos/27665395@N05/4988574588/sizes/o/in/photolist-8APKqG-aHeyiv-9wNDxc-9uscVx-atekwA-9wNCd2-ceoRx3-89ALsr-8kmc2K-7ZxNhY-8fr6RG-7Zciv2-aHeycZ-aHeysc-dy1UJu-ejjGBY/

What if your family van could move at the speed of light? [Figure1]

Length contraction, another important concept of Einstein’s special relativity (but originally proposed by George FitzGerald and Hendrik Lorentz), claims that an object moving by you at a speed close to that of light would appear to contract, or get smaller in size. It is an interesting idea, but one without concrete evidence. A working experiment that proves length contraction has yet to be carried out.

The “pole and barn” interactive demonstration by Wolfram Mathematica is an effective model of the concept. Click on the link below to access it (Note: requires download of the “Wolfram CDF Player”).

### Creative Applications

1. In the simulation, click on the plus sign next to the “speed” slider as well as the one next to the “time” slider. If you click the play button on the “time” settings and set the speed, the barn or pole (depending on your reference point) should move while retaining its shape, as determined by the speed. Observe what happens if you click the play button for the “speed” settings as well.
2. Read this page on a proposed experiment to prove length contraction. Try to understand its main points and problems.
3. Using the equation  \begin{align*}{L}={L}_0\sqrt{1-\frac{v^2}{c^2}}\end{align*}  try this problem: A train traveling at 80% of the speed of light (c) goes past you as you sit on a bench at the station. If it actually measures 200 meters (L0), how much does it appear to measure after length contraction? (Hint: v = 0.8c)

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