Inside a spaceship flying past the earth at three-fourths...

Inside a spaceship flying past the earth at three-fourths the speed of light, a pendulum is swinging. (a) If each swing takes 1.80 s as measured by an astronaut performing an experiment inside the spaceship, how long will the swing take as measured by a person at mission control (on earth) who is watching the experiment? (b) If each swing takes 1.80 s as measured by a person at mission control, how long will it take as measured by the astronaut in the spaceship?

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Key Concepts

Special Relativity

Special relativity is a theory of physics that explains how measurements of time, length, and other physical quantities differ for observers in different inertial frames. It provides the foundational framework for understanding phenomena such as time dilation and length contraction for objects moving at a significant fraction of the speed of light.

Time Dilation

Time dilation is the effect predicted by special relativity where a moving clock is observed to tick slower compared to a clock at rest from the perspective of an external observer. This means that time intervals measured in a moving frame (the proper time) appear longer to an observer in a different inertial frame.

Proper Time

Proper time is the time interval measured by an observer who is at rest relative to the event being measured. It is the shortest time interval between events and is used in time dilation calculations as the intrinsic time measured in the rest frame of the event.

Lorentz Factor

The Lorentz factor, typically denoted by ? (gamma), quantifies the amount of time dilation and length contraction experienced by an object moving at a high velocity relative to an observer. It is computed as ? = 1/?(1 - v²/c²), and it scales the proper time to the time measured in another inertial frame.

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