Question

How fast must an object move before its length appears to be contracted to one-half its proper length?

Answer 1

The object must move with the speed of $\frac{\sqrt{3} }2}$ times to approximately seeing that it is contracted to exactly half of its actual length.

How is this calculated?

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

$\frac{L}{L'} = \sqrt{(1) - (\frac{v}{c})^{2}$

Here, v is the current speed m/s

c is the speed of light in m/s

L' is the length of the object at rest in m

L is the length of the object at the current speed in m

Now we know that

$\frac{L}{L'}= \frac{1}{2}$ and $\frac{v}{c} = r$ then,

$\frac{1}{2} = \sqrt{1 - r^{2} }\\\frac{1}{4} = 1 - r^{2}\\r^{2} = \frac{3}{4}$

Hence, r = $\frac{\sqrt{3} }{2}$

Therefore, the answer is the object must travel at a speed of $\frac{\sqrt{3} }{2}$ times the lightspeed to be contracted to one-half its proper length.

To know more about the Lorentz contraction formula, visit:

brainly.com/question/17407131

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