Modern Physics - Problem Set

Question

1. a tower whose height on the earth is exactly 150 m is lying parallel to the axis of a spacecraft. the spacecraft is moving at 0.60e relative to the earth. what is his height as measured by an observer in the same spacecraft? by an observer on the earth?
2. a stick moving with respect to an observer appears only 2000mm long to her. if the proper length of the stick is 4000mm, what is its relative speed between the two frames?

Answer 1

Hello Phoebe;

We can use the principles of special relativity and, the Lorentz length contraction formula according to which the length of an object in motion appears shorter to an observer at rest relative to that object.

L' = L * √(1 - v²/c²)

L' = 150 * √(1 - (0.6c)²/c²) = L' = 120m

To an observer on Earth, the tower is stationary, and the spacecraft is moving at 0.60c. In this case, the spacecraft is subject to length contraction. Since the tower is parallel to the spacecraft's axis, its height as observed from the spacecraft remains the same as the spacecraft's length

The height of the tower as measured by an observer on Earth (relative to Earth) is reduced to 80% of its proper length because of the spacecraft's length contraction.

That also is 120m.