(a)
Total travel time of the pulse as measured by observers in the S frame.
(a)
Answer to Problem 86AP
The total travel time of the pulse as measured by observers in the S frame is
Explanation of Solution
Let the distance travelled by the light from spacecraft to the mirror be equal to
Write the expression for the distance that the spacecraft travelled forward.
Here,
The spacecraft is travelling towards the mirror. After the reflection of pulse from the mirror it travels back to the approaching spacecraft.
Write the expression for the distance travelled by the pulse after reflection from the mirror.
Here,
Write the expression for the total distance travelled by the light before and after reflection.
Here,
Use expressions (I) and (II) in (III) to find
The light travels at speed of
Write the expression for the total distance travelled by light.
Here,
Left hand side of equations (IV) and (V) are same. Therefore equate the right hand side of these equations.
Solve equation (VI) for
Conclusion:
Therefore, the total travel time of the pulse as measured by observers in the S frame is
(b)
The total travel time of the pulse as measured by observers in the spacecraft.
(b)
Answer to Problem 86AP
The total travel time of the pulse as measured by observers in the spacecraft is
Explanation of Solution
The observer in the spacecraft moving towards the mirror will experience a contraction in length for the distance between the mirror and the spacecraft.
Write the expression for the contracted distance between the mirror and the spacecraft.
Here,
Here both mirror and pulse is moving. The speed of travel of light pulse is
Write the expression for the distance travelled by pulse towards the mirror measured by the observer in spacecraft.
Here,
Write the expression for the distance travelled by mirror towards the spacecraft measured by the observer in spacecraft.
Here,
Write the expression for the total distance travelled by light and mirror.
Here,
Use expressions (IX) and (X) in (XI).
Solve expression (XII) to find
Write the expression for the distance between the mirror and spacecraft when the light strikes mirror.
Here,
The same distance
Write the expression for the distance travelled by light after reflection from the mirror as observed by the observer in spacecraft.
Equate (XV) and (XIV) and solve for
Write the expression to find the total travel time of light.
Here,
Use expressions (XVI) and (XIII) in (XVII).
Use expression (XIII) in (XVIII).
Use expression (VIII) in (XIX).
Conclusion:
Therefore, the total travel time of the pulse as measured by observers in the spacecraft is
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Chapter 39 Solutions
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