Special Relativity spaceship problem

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SUMMARY

The discussion centers on a special relativity problem involving length contraction as observed from a spaceship traveling at 0.99c relative to Earth. The proper length of the laboratory on Earth is 56.4 meters, measured in its rest frame. The spaceship crew, moving at relativistic speeds, measures the laboratory's length to be shorter due to length contraction. The correct calculation indicates that the crew measures the laboratory's length to be approximately 59.8 meters, which is incorrect; the proper length should be less than 56.4 meters from the spaceship's perspective.

PREREQUISITES
  • Understanding of special relativity concepts, particularly length contraction
  • Familiarity with the formula for length contraction: L = L_0 * sqrt(1 - v^2/c^2)
  • Knowledge of proper length and how it differs from observed length
  • Basic understanding of relativistic speeds (e.g., 0.99c)
NEXT STEPS
  • Study the derivation and implications of the length contraction formula in special relativity
  • Explore examples of relativistic effects in different frames of reference
  • Learn about time dilation and its relationship with length contraction
  • Investigate practical applications of special relativity in modern physics, such as GPS technology
USEFUL FOR

This discussion is beneficial for students and enthusiasts of physics, particularly those studying special relativity and its implications in high-speed scenarios. It is also useful for educators seeking to clarify concepts related to length contraction and proper length.

Taylor_1989
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Homework Statement


You are on Earth as a spaceship flies past at a speed of 0.99c relative to the earth. A high-intensity signal light on the ship blinks on and off, each pulse lasting 2.2 × 10^(−6) s, as measured on the spacecraft .

Your laboratory on Earth has a length of 56.4m. How long does the spaceship crew measure it to be?

Homework Equations


length contraction

The Attempt at a Solution


So I am viewing the question like this. If I am standing on the spaceship as this is my frame of ref; right? The the proper length would be unknown as proper length is only measure when me for example is at rest, so I the thought that if I am at rest on the ship the Earth is moving 0.99c relative to me, therefore I transposed the length contraction formula to get my ans.

L_0= proper length
L= length on Earth

so If I use the length contraction formula to solve for L_0 I would get what the i view it on the space ship, is this correct?

my ans was 59.8m from space ship.

Very new to special relativity so still getting my head round it.
 
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You have it backwards. The proper length of the lab is the length measured in its rest frame, which is the Earth's frame. The spaceship crew will measure that length to be less.
 
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