Lesson: Length Contraction

In this lesson, we will learn how to calculate the change in the length of an object that is moving at a high speed relative to an observer.

Worksheet: 3 Questions

Q1:

The Minkowski diagram shows two inertial reference frames: frame 𝑆 with the axes 𝑥 and 𝑐 𝑡 and frame 𝑆 with the axes 𝑥 and 𝑐 𝑡 . Frame 𝑆 moves at a speed of 0 . 2 𝑐 relative to 𝑆 . The two red lines are the world lines for the ends of a metal rod that is stationary in 𝑆 . The green lines show lines of simultaneity in each reference frame. Five events are shown on the diagram. For which two events would taking the difference in their 𝑥 coordinates give the length of the rod in 𝑆 ?

Q2:

A spaceship that is 300 m long in its rest frame is moving away from Earth at half the speed of light. Does the spaceship appear longer than 300 m, shorter than 300 m, or exactly 300 m long in the rest frame of Earth?

Q3:

The given Minkowski diagram shows three inertial reference frames: frame 𝑆 with the axes 𝑥 and 𝑐 𝑡 , frame 𝑆 with the axes 𝑥 and 𝑐 𝑡 , and frame 𝑆 with axes 𝑥 and 𝑐 𝑡 . Frame 𝑆 moves at a speed of 0 . 3 𝑐 relative to 𝑆 and frame 𝑆 moves at a speed of 0 . 6 𝑐 relative to 𝑆 . The two red lines are the world lines for the ends of a metal rod that is stationary in 𝑆 . The green lines show lines of simultaneity in each reference frame. Six events are shown in the diagram. For which two events would taking the difference in their 𝑥 -coordinates give the length of the rod in 𝑆 ?

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