Monday, April 29, 2019

How much time will it take to move an object whose length is equal to one light year?


Suppose there's a stick whose length is one light year and I push it from one side by one centimeter. How much time would it take for its other side to move by one centimeter and why?



Answer



It depends on the material. When you push one end of the stick, you move the atoms at the very end of the stick. Those atoms push the atoms next to them, those atoms push the next atoms, and so on down the stick. This is a sound wave that travels down the stick, so the time you have to wait for the other end to move is the length of the stick divided by the speed of sound in the material of the stick. If the stick is wooden, the speed of sound is about 4000 m/s (compared with 330 m/s in air). It would take $\frac{9.5\cdot10^{15}\,m}{4000\,m/s} = 2.4\cdot10^{12}$ seconds (74 000 years) for the other end of the stick that is a light-year away to move.


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