Two bars of equal proper length Lo approach each other, moving in a longitudinal direction parallel...

Two bars of equal proper length Lo approach each other, moving in a longitudinal direction parallel to a common axis with the same speed v with respect to a reference system of laboratory. What is the length of each of the bars in the reference system? linked with the other bar?

Solutions

Expert Solution

Given,

The two bars having proper length, , approach eachother moving with same speed, , towards eachother in a direction parallel to their common axis.

For an observer attached to the reference system, each bar seems to have a length less than their proper length. This happens due to special theory of relativity and is called length contraction which appears when length measurements relative to a moving frame or when the object is moving relative to the measurement frame.

So, for an observer attached to the reference system relative to which each bar is moving with a velocity v, the length of each of the bars will be

If the observer is attached to one of the bars, then that bar is at rest with respect to the observer so the observer measures its length as .

But, then relative to the observer attached to one of the bar, the other bar is moving with a relative velocity 2v. So, the observer measures the length of the second bar as

Regards

genius_generous answered 1 year ago

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