The average lifetime of a pi meson in its own frame of reference (i.e., the prop

Question

The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6 times 10^-8 s. (a) If the meson moves with a speed of 0.93c, what is its mean lifetime as measured by an observer on Earth? Regard the pi meson as a clock measuring its lifetime in its own rest frame. What time interval does this lifetime become in a reference frame in which the pi meson is moving at the specified speed? s (b) What is the average distance it travels before decaying, as measured by an observer on Earth? m (c) What distance would it travel if time dilation did not occur? m

Explanation / Answer

Part A)

Apply t = t'/(1 - v2/c2)

t = (2.6 * 10^-8)/(1 - .93^2)

t = 7.07 * 10^-8 sec

Part B)

Apply d = vt

d = (.93)(3 *10^8)(7.07 * 10^-8)

d = 19.7m

(c) l' = v*T

= (0.93*3*10^8*2.6*10^-8)

= 7.254 s

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