Measuring the velocity of cosmic ray muons

[Millenniumf]

Homework Statement

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.

Homework Equations

γ: t=t0/sqrt(1-v^2/c^2)
V=d/t

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.

 

[mark726]

Dear forum participant,

Thank you for sharing your progress and concerns with us. It seems like you are on the right track with your analysis, but there are a few things that may need to be addressed.

First, make sure that your units are consistent. In your attempt at a solution, you have used meters for distance and seconds for time, but in your equations you have used Julian days and meters for distance. This could lead to incorrect calculations.

Second, it is important to double check your calculations and make sure you are using the correct values for the speed of light and the distance between the detectors.

Finally, it may be helpful to discuss your results with your peers or a mentor to see if they have any insights or suggestions for your analysis. Sometimes a fresh pair of eyes can catch any mistakes or help identify areas for improvement.

Keep up the good work and don't be discouraged by any setbacks. Science is all about learning from our mistakes and constantly improving our understanding. Good luck with your paper!