A rod of length L0 moves with a speed v along the horizontal direction. The rod makes an angle of θ0 with respect to the x′-axis. (a) Show that the length of the rod as measured by a stationary observer is given by
(a)
To show that the length of the rod as measured by a stationary observer is given by
Answer to Problem 14P
The length of the rod as measured by a stationary observer is given by
Explanation of Solution
The rod of length
The horizontal component of the rod is given by,
Here,
The horizontal component of the rod as measured by the stationary observer is,
Here,
The vertical component of the rod is given by,
Here,
The vertical component of the rod as measured by the stationary observer is,
Here,
Conclusion:
The length of the rod as measured by a stationary observer is
Therefore, the length of the rod as measured by a stationary observer is given by
(b)
To show that the angle the rod makes with the x axis is
Answer to Problem 14P
The angle the rod makes with the x axis is
Explanation of Solution
The angle the rod makes with the x axis is,
Conclusion:
Therefore, the angle the rod makes with the x axis is
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Chapter 1 Solutions
Modern Physics
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