In order to fit a 50.0 -foot-long stretch limousine into a...

Name: Problem 68, Chapter 35: University Physics with Modern Physics
Uploaded: 2021-05-19T09:36:21-08:00
Duration: 1 min 1 s
Channel: Narayan Hari
Description: In order to fit a 50.0 -foot-long stretch limousine into a 35.0 -footlong garage, how fast would the limousine driver have to be moving, in the garage's reference frame? Comment on what happens to the garage in the limousine's reference frame.

In order to fit a 50.0 -foot-long stretch limousine into a 35.0 -footlong garage, how fast would the limousine driver have to be moving, in the garage's reference frame? Comment on what happens to the garage in the limousine's reference frame.

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Key Concepts

Relativistic Speeds and the Lorentz Factor

At speeds close to the speed of light, relativistic effects become significant. The Lorentz factor (?) quantifies how much time dilates and lengths contract for a moving object. For example, in order to reduce the proper length of an object (like a limousine) to a shorter length as observed in another inertial frame (like a garage), the relative speed must be high enough so that ? provides a sufficient contraction factor.

Length Contraction

This is a phenomenon predicted by special relativity where an object in motion relative to an observer appears shorter along the direction of motion. The degree of contraction is determined by the Lorentz factor, which depends on the relative velocity between the observer and the moving object.

Reference Frames

Reference frames are coordinate systems or perspectives from which observations are made. In the context of relativity, an object's measured length depends on whether the observer is in the same inertial frame as the object or in a different one, leading to different measurements such as the length contraction experienced by the moving limousine.

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