Warm-Up Exercise 37

Due 12:15 pm, Tue 20 Nov 2012

Physics 123, Fall 2012

Reading assignment: 39.1-39.3

TheGalilean velocity transformation equation, Eqn 39.2 (8th edition), is simple--much simpler than its name implies. It's also sometimes called the "classical velocity addition" formula. It's "obviously" true. Use it to answer this question: A pickup truck is traveling forward at 5 m/s. A man standing in the back of the truck throws a ball forward at 10 m/s (relative to himself). How fast will someone on the ground measure the ball to be traveling?  What is the faulty  assumption on which the equation relies?

15 m/s. The faulty assumption is that all observers will agree on what time it is at any given instant: t' = t for all observers.

Explain in your own words (in language that your non-physics-major roommates could understand) how the Galilean velocity transformation equation and the 2nd postulate of special relativity are at odds with each another.

Einstein said (2nd postulate) that all observers will measure a given light wave to travel at 3x10^8 m/s, regardless of the observers' own velocities. This contradicts the normal velocity addition formula, because if the truck is traveling at (for example) 0.5c, and the man turns on a flashlight with photons traveling at c, then someone on the ground would measure the photons' speed to be 1.5c. That's too fast! And impossible, according to Einstein.

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