How fast must an object move before its length appears to be contracted to one-fourth its proper length? (Give your answer in terms of c.)

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How fast must an object move before its length appears to be contracted to one-fourth its proper length? (Give your answer in terms of c.)

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Dulcie 5 years 2021-07-28T03:42:37+00:00 1 Answers 291 views 0

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  1. King
    0
    2021-07-28T03:43:58+00:00
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    Answer:

    0.97c

    Explanation:

    From the relativistic equation for length contraction, we have

    l = l_{0}\sqrt{1 - \beta }

    where

    l is the final length of the object

    l_{0} is the original length of the object before contraction

    β = v^{2} /c^2

    where v is the speed of the object

    c is the speed of light in free space = 3 x 10^8 m/s

    The equation can be re-written as

    l/l_{0} = \sqrt{1 - \beta }

    For the length to contract to one-fourth of the proper length, then

    l/l_{0} = 1/4

    substituting into the equation, we’ll have

    1/4 = \sqrt{1 - \beta }

    substituting for β, we’ll have

    1/4 = \sqrt{1 - v^2/c^2 }

    squaring both side of the equation, we’ll have

    1/16 = 1 – v^2/c^2

    v^2/c^2 = 1 – 1/16

    v^2/c^2 = 15/16

    square root both sides of the equation, we have

    v/c = 0.968

    v = 0.97c

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