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QUESTION 26.1 Suppose a mass-spring system with the same period as the pendulum is placed in the observer's spaceship. When the spaceship is traveling at a speed of 0.950c relative to an observer on Earth, what is the period of the pendulum as mea- sured by the Earth observer?

QUESTION 26.1 Suppose a mass-spring system with the same period as the pendulum is placed in the observer's spaceship. When the spaceship is traveling at a speed of 0.950c relative to an observer on Earth, what is the period of the pendulum as mea- sured by the Earth observer?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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Answer for Question 26.1. Thank you.

PROBLEM The period of a pendulum is measured to be 3.00 s in the inertial frame of the pendulum at Earth's surface. What is the period as measured by an observer moving at a speed of 0.950c with respect to the pendulum? STRATEGY Here, we're given the period of the clock as measured by an observer in the rest frame of the clock, so that's a proper time interval At,. We want to know how much time passes as measured by an observer in a frame moving relative to the clock, which is At. Substitution into Equation 26.2 then solves the problem. SOLUTION At, 3.00 s Substitute the proper time and relative speed into Equation 26.2: Δι- 9.61 s V1 - v²/c? (0.950c)² REMARKS The moving observer considers the pendulum to be moving, and moving clocks are observed to run more slowly: while the pendulum oscillates once in 3 s for an observer in the rest frame of the clock, it takes nearly 10 s to oscillate once according the moving observer. QUESTION 26.1 Suppose a mass-spring system with the same period as the pendulum is placed in the observer's spaceship. When the spaceship is traveling at a speed of 0.950c relative to an observer on Earth, what is the period of the pendulum as mea- sured by the Earth observer?
Transcribed Image Text:PROBLEM The period of a pendulum is measured to be 3.00 s in the inertial frame of the pendulum at Earth's surface. What is the period as measured by an observer moving at a speed of 0.950c with respect to the pendulum? STRATEGY Here, we're given the period of the clock as measured by an observer in the rest frame of the clock, so that's a proper time interval At,. We want to know how much time passes as measured by an observer in a frame moving relative to the clock, which is At. Substitution into Equation 26.2 then solves the problem. SOLUTION At, 3.00 s Substitute the proper time and relative speed into Equation 26.2: Δι- 9.61 s V1 - v²/c? (0.950c)² REMARKS The moving observer considers the pendulum to be moving, and moving clocks are observed to run more slowly: while the pendulum oscillates once in 3 s for an observer in the rest frame of the clock, it takes nearly 10 s to oscillate once according the moving observer. QUESTION 26.1 Suppose a mass-spring system with the same period as the pendulum is placed in the observer's spaceship. When the spaceship is traveling at a speed of 0.950c relative to an observer on Earth, what is the period of the pendulum as mea- sured by the Earth observer?
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