Chapter 37: Q1P (page 1145)

The mean lifetime of stationary muons is measured to be $2.2000 μ s$ . The mean lifetime of high-speed muons in a burst of cosmic rays observed from Earth is measured to be $16.000 μ s$ . To five significant figures, what is the speed parameter $β$ of these cosmic-ray muons relative to Earth?

Short Answer

Expert verified

The speed parameter of cosmic ray muons is $0.99050$ .

Step by step solution

Identification of given data

The mean life time for stationary muons is $t_{0} = 2.20 μ s$

The mean life time for high-speed muons is $t = 16 μ s$

The speed parameter in the above problem is found by considering the Lorentz factor as the ration of mean life time for stationary muons to mean life time of high-speed muons.

Determination of speed parameter of cosmic ray muon relative to Earth

The speed parameter of cosmic ray muons is given as:

$β = \sqrt{1 - {(\frac{t_{0}}{t})}^{2}}$

Substitute all the values in equation.

$β = \sqrt{1 - {(\frac{2.20 μ s}{16 μ s})}^{2}} β = 0.99050$

Therefore, the speed parameter of cosmic ray muons is $0.99050$

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The mean lifetime of stationary muons is measured to be $2.2000 μ s$ . The mean lifetime of high-speed muons in a burst of cosmic rays observed from Earth is measured to be $16.000 μ s$ . To five significant figures, what is the speed parameter $β$ of these cosmic-ray muons relative to Earth?

Short Answer

Step by step solution

Identification of given data

Determination of speed parameter of cosmic ray muon relative to Earth

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The mean lifetime of stationary muons is measured to be 2.2000μs. The mean lifetime of high-speed muons in a burst of cosmic rays observed from Earth is measured to be 16.000μs. To five significant figures, what is the speed parameter βof these cosmic-ray muons relative to Earth?

Short Answer

Step by step solution

Identification of given data

Determination of speed parameter of cosmic ray muon relative to Earth

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Rotational Dynamics

Particle Model of Matter

Physics of Motion

Electromagnetism

Translational Dynamics

Atoms and Radioactivity

Study anywhere. Anytime. Across all devices.

The mean lifetime of stationary muons is measured to be $2.2000 μ s$ . The mean lifetime of high-speed muons in a burst of cosmic rays observed from Earth is measured to be $16.000 μ s$ . To five significant figures, what is the speed parameter $β$ of these cosmic-ray muons relative to Earth?