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.)

The object must travel at a speed of times the lightspeed () to be contracted to one-fourth its proper length.

The length contraction experimented by the object as it approaches lightspeed (), in meters per second, is described by Lorentz contraction formula:

(1)

Where:

If we know that and , then the value of is:

The object must travel at a speed of times the lightspeed () to be contracted to one-fourth its proper length.

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0.97c

Explanation:

From the relativistic equation for length contraction, we have

=

where

is the final length of the object

is the original length of the object before contraction

β =

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

/ =

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

/ = 1/4

substituting into the equation, we'll have

1/4 =

substituting for β, we'll have

1/4 =

squaring both side of the equation, we'll have

1/16 = 1 -

= 1 - 1/16

= 15/16

square root both sides of the equation, we have

v/c = 0.968

v = 0.97c

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