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Homework Help: Measuring the velocity of cosmic ray muons

  1. Apr 30, 2012 #1
    1. The problem statement, all variables and given/known data

    I'm participating in a worldwide undergraduate-level experiment to measure cosmic ray muons. I've got the data, and am in the process of writing a paper (called a poster for some reason), which details the experiment, procedure, and results. Right now I'm trying to interpret the data. The mean value for the time is 1.59E-13 Julian days for the data set I'm using. Our detectors were set up 3.14 meters apart, and at an angle of 60 degrees.

    2. Relevant equations

    γ: t=t0/sqrt(1-v^2/c^2)

    3. The attempt at a solution

    First I converted 1.59E-13 Julian days to seconds by multiplying that number by 86,400 and got 1.37376E-8 seconds. Then I took that value and divided the distance between the detectors by it: 3.14m/1.37E-8s=2.286E8 m/s. This is much lower than c, because of time dilation. Then I entered these numbers into γ: t=1.37376E-13/sqrt(1-2.286E8^2/3.0E8^2) and got 2.121E-8 which is *much* lower than c. Muons are supposed to be traveling at around 99% c, so what am I doing wrong? γ is supposed to compensate for time dilation, so I'm thinking I messed up something there. My analysis isn't the problem, because another student independently got the same number for his mean time.

    I'm often stymied by forgetting or messing up something very simple or by writing down the wrong values . . . hope it's that and not something big like a fundamental misunderstanding of what it is we're doing.
  2. jcsd
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