The proper length of the ship as measured in the ship's frame Z' is l0. However, from the perspective of the stationary observer in frame Z, the length of the ship appears contracted due to its motion. The length contraction factor γ can be calculated using the formula γ = 1/√(1 - (v^2/c^2)). The actual length of the ship as observed by the stationary observer is given by Length = l0 * γ.
In this scenario, we have an observer stationary in reference frame Z and a spaceship moving in the positive x direction with speed v. The frame of reference associated with the spaceship is Z'. The proper length of the ship, measured in the ship's frame Z', is represented as l0.
1. The concept of length contraction in special relativity states that when an object is moving relative to an observer, its length appears shorter in the direction of motion.
2. In this case, the proper length of the ship (l0) is measured in the ship's frame, Z'. This means that a passenger on the ship measures the back of the ship to be at x' = 0 and the front to be at x' = l0.
3. However, from the perspective of the stationary observer in frame Z, the ship is moving with speed v in the positive x direction. This leads to length contraction, which means the ship will appear shorter in the direction of motion.
4. The length contraction factor, γ, is given by the formula γ = 1/√(1 - (v^2/c^2)), where c is the speed of light.
5. To find the length of the ship as measured by the stationary observer in frame Z, we multiply the proper length l0 by the length contraction factor γ.
- Length = l0 * γ