Question

A hypothetical train moving with a speed of 0.6c passes by the platform of a small station without being slowed down. The observers on the platform note that the length of the train is just equal to the length of the platform which is 200 m. (a) Find the rest length of the train. (b) Find the length of the platform as measured by the observers in the train.

Answer 1

(a) The length L' of the train at a speed 0.6c is 200 m. If the rest length is L,
$L^{\prime }=\sqrt{1-v^2/c^2}$
or, $L=\frac{L^{\prime }}{\sqrt{1-v^2/c^2}}=\frac{200m}{\sqrt{1-(0.6{)}^2}}$
(b) The rest length of the platform is 200 m. For the observers in the train, the platform is moving at a speed of 0.6c. The length as measured by the observers in the train is, therefore,
$L^{\prime }=200m\sqrt{1-(0.6{)}^2}=160m$.