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This is a Clilstore unit. You can link all words to dictionaries.

Calculating time dilation and lenght contraction

Last lesson we found out about the consequences of assuming that the speed of light is the same in all frames of reference: time dilation and length contraction. We are going to learn now how to calculate the magnitude of these effects.

1. Last lesson we defined the concepts proper and improper time, and proper and improper length. Complete the following sentences:

To determine the magnitude of this effects, the following equations can be used:

Where:

2. Use an plotting tool (such as the one provided on the link below) to plot the values of gamma versus beta. Remember that the range of beta goes from 0 to 1. At which value of beta is improper time doubled and length halved? And tripled?

3. Imagine that a spaceship is flying towards a planet that is 3 light-years away at a speed of two thirds the speed of light. The spaceship only has fuel for 5 years of travel. Will they reach the planet on time?

4. Muons are elementary particles of the family of the electron that have an average lifespan of 2.2 µs at the laboratory. Muons are formed when cosmic rays interact with the higher layers of the atmosphere. If a muon that has been created at an altitude of 10km and is travelling towards the ground at a speed of 0.998c, will it reach the Earth’s surface?

5. Open the “Muons” applet and compare your results with the ones provided by the applet.

Clilstore Graph plotterMuon appletRelativity and electroma

Short url:   https://clilstore.eu/cs/5325