An airplane has a length of 60 m when measured at rest. When...

Name: Problem 71, Chapter 37: University Physics with Modern Physics
Uploaded: 2020-11-21T20:53:59-08:00
Duration: 1 min 32 s
Channel: Shoukat Ali
Description: An airplane has a length of 60 m when measured at rest. When the airplane is moving at 180 m/s (400 mph) in the alternate universe, how long would the plane appear to be to a stationary observer? (a) 24 m; (b) 36 m; (c) 48 m; (d) 60 m; (e) 75 m.

An airplane has a length of 60 m when measured at rest. When the airplane is moving at 180 m/s (400 mph) in the alternate universe, how long would the plane appear to be to a stationary observer? (a) 24 m; (b) 36 m; (c) 48 m; (d) 60 m; (e) 75 m.

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Key Concepts

Length Contraction

Length contraction is a key prediction of Einstein's special relativity. It states that the length of an object moving relative to an observer will appear shorter along the direction of motion than its proper length, which is the length measured when the object is at rest. The formula for this contraction is L = L??(1 - v²/c²), where L? is the proper length, v is the object's speed relative to the observer, and c is the speed of light.

Lorentz Factor

The Lorentz factor, commonly denoted by ?, is a critical component in special relativity that quantifies the effects of time dilation and length contraction. Defined as ? = 1/?(1 - v²/c²), it becomes significantly greater than one only when the object's speed v approaches the speed of light c. This factor is used to scale measurements between different inertial frames.

Relativistic Speeds

Relativistic speeds refer to velocities close to the speed of light. At these high speeds, the effects of special relativity, such as length contraction and time dilation, are pronounced. However, at everyday speeds, such as 180 m/s, the value of v²/c² is extremely small, making relativistic effects negligible and measurements close to their classical (non-relativistic) values.

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