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A muon travels at a speed of 0.95c relative to an observer - AQA - A-Level Physics - Question 4 - 2020 - Paper 7

Question 4

A muon travels at a speed of 0.95c relative to an observer. The muon travels a distance of 2.5 × 10^3 m between two points in the frame of reference of the observer... show full transcript

Worked Solution & Example Answer:A muon travels at a speed of 0.95c relative to an observer - AQA - A-Level Physics - Question 4 - 2020 - Paper 7

Step 1

Calculate proper length using Lorentz contraction

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Answer

In the frame of reference of the observer, the proper length (L₀) is given as:

$L₀ = 2500 \, m$

Using the Lorentz contraction formula:

$L = L₀ \sqrt{1 - v^2 / c^2}$

where $v = 0.95c$ , we substitute this into the formula.

Step 2

Substituting values to find the contracted length

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Answer

Calculating the contraction factor:

$L = 2500 \, m \times \sqrt{1 - (0.95c)^2 / c^2} = 2500 \, m \times \sqrt{1 - 0.9025} = 2500 \, m \times \sqrt{0.0975}$

$L \approx 2500 \, m \times 0.31225 \approx 780.6 \, m$

Thus, the distance between the two points in the frame of reference of the muon is approximately 781 m.

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