(a)
The speed of the first piece inspected by an observer in the lab.
(a)
Answer to Problem 83PQ
The speed of the first piece inspected by an observer in the lab is
Explanation of Solution
Write the expression for the Lorentz constant.
Here, Lorentz constant is
Write the expression for the momentum in fixed frame.
Here, momentum in fixed frame is
Write the expression for the momentum with respect to laboratory frame.
Here, momentum with respect to laboratory frame is
Substitute
Conclusion:
Substitute
Take square both sides.
Further solve the above equation.
Further solve the above equation.
Further solve the above equation.
Therefore, the speed of the first piece inspected by an observer in the lab is
(b)
The speed of the second piece inspected by an observer in the lab.
(b)
Answer to Problem 83PQ
The speed of the second piece inspected by an observer in the lab is
Explanation of Solution
Write the expression for the Lorentz constant.
Here, Lorentz constant is
Write the expression for the momentum in fixed frame.
Here, momentum in fixed frame is
Write the expression for the momentum with respect to laboratory frame.
Here, momentum with respect to laboratory frame is
Substitute
Conclusion:
Substitute
Take square both sides.
Further solve the above equation
Further solve the above equation
Further solve the above equation
Therefore, the speed of the second piece inspected by an observer in the lab is
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Chapter 39 Solutions
Physics for Scientists and Engineers: Foundations and Connections