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Modern Physics
Found in: Page 1
Modern Physics

Modern Physics

Book edition 2nd Edition
Author(s) Randy Harris
Pages 633 pages
ISBN 9780805303087

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Short Answer

A supersonic: - plane travels al 420 m/s. As this plane passes two markers a distance of 4.2km apart on the ground, how will the time interval registered on a very precise clock onboard me plane differ from 10s?

The value of time difference in the plane’s clock is 9.8 ps.

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Write the given data from the question.

Consider a time difference is Δt=10 s.

Consider a speed of the plane is υ=420ms.

Consider a distance is 4200 m.

Determine the formula of time difference in the plane’s clock.

Write the formula of time difference in the plane’s clock.

Δt0=Δt1−υ2c2 …… (1)

Here, Δt is time difference, υ speed of the plane and c speed of light.

Determine the value of time difference in the plane’s clock.

Due to relativistic effects, time relative to an object moves more quickly when it is moving very quickly. The time-dilation equation helps explain this:

Δt=Δt01−υ2c2

Arrive at the following expression for the time difference in the plane's clock using the time-dilation equation:

Δt=Δt01−υ2c2Δt0=Δt1−υ2c2

Calculate the time difference in the clock of the aircraft using the formula for Δt0:

Determine the time difference in the plane’s clock.

Substitute 10 for Δt, 420 for υ and 3×108 for c2 into equation (1).

Δt0=101−42023×1082=9.8×10−12=9.8 ps

According to the findings, the plane's clock would display the time 9.8 ps earlier.

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