Length contraction (AQA A-Level Physics): Flashcards

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Length contraction
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Length contraction definition

Objects moving at high speeds appear shorter in direction of motion relative to stationary observer

Proper length (l0)(l_0)

Length measured by observer at rest relative to the object

Length contraction formula

l=l01v2c2l = l_0 \sqrt{1 - \frac{v^2}{c^2}}

Effect as vv approaches cc on contracted length ll

ll decreases, object appears shorter

Dimensions affected by length contraction

Only length in direction of motion, not width or height

Experimental evidence for length contraction

Muon decay experiments

Contracted length in muon example (from 2 km at 0.996c)

180 m

Time for muons to travel contracted 180 m at 0.996c

6.0×1076.0 \times 10^{-7} s

Expected vs observed count rate at Detector 2 (muon exp.)

Expected: 76 s1s^{-1}, Observed: 80 s1s^{-1} (close match)

Applying time dilation & length contraction together

Should not be applied simultaneously in single calculation

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