**Problem 3: Relativistic Length Contraction**A supertrain of proper length 210 m travels at a speed of 0.85c as it passes through a tunnel with a proper length of 90.0 m. How much longer is the tunnel than the train, or vice versa, as seen by an observer at rest with respect to the tunnel?**Solution:**To solve this problem, we need to apply the concept of length contraction from special relativity.The length contraction formula is:\[ L = L_0 \sqrt{1 - \frac{v^2}{c^2}} \]Where:- \( L \) is the contracted length.- \( L_0 \) is the proper length (the length of the object in its rest frame).- \( v \) is the velocity of the object.- \( c \) is the speed of light.**Steps:**1. Calculate the contracted length of the moving train as seen by the stationary observer at the tunnel.2. Compare it to the proper length of the tunnel.**Train Calculation:**- Proper length of the train, \( L_0 = 210 \, \text{m} \).- Velocity, \( v = 0.85c \).\[ L = 210 \, \text{m} \times \sqrt{1 - (0.85)^2} \]3. Calculate the above expression to find the relativistic length of the train.Finally, compare the length of the train with the length of the tunnel to answer how much longer one is than the other.**Answer Box:**- **Length Difference:** ________ meters> **Note:** The detailed explanation here ensures that users can not only compute the solution using special relativity formulas but also understand the application of length contraction in relativistic scenarios.

According to the special theory of relativity, if a body moves with a velocity v , which is nearly…

A supertrain of proper length 210 m travels at a speed of 0.85c as it passes through a tunnel having proper length 0.0 m. How much longer is the tunnel than the train or vice versa as seen by an observer at rest with respect to the innel?

A supertrain of proper length 210 m travels at a speed of 0.85c as it passes through a tunnel having proper length 0.0 m. How much longer is the tunnel than the train or vice versa as seen by an observer at rest with respect to the innel?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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