Question

An observer measures the length (L), width (w), and height (h) of a box while stationary relative to the box. The observer then travels at near light speeds parallel to the length (L) of the box. If the observer measures the width (w) of the box while moving, the measured value will now be

Answer 1

An observer measures the length (L), width (w), and height (h) of a box while stationary relative to the box. The observer then travels at near light speeds parallel to the length (L) of the box.The measured value will now be less than w(width).

An object's length appears to be shorter than it actually is when moving quickly (relative to the observer) (again, for the observer). The following length contraction equation supports this:

$L = L_{0} \sqrt{1-\frac{v^{2} }{c^{2} } }$

In this case,$L_{0}$ is the object's original length and L is the observed length. The speed of light is equal to c, while v is the relative speed between the object and the observer.

This equation demonstrates that the square root of the equation yields values smaller than 1.0 as the speed between the item and the observer is increased to be nearly that of light. The length that is observed is effectively reduced as a result.

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