Concept explainers
The proof of
Answer to Problem 40PQ
The proof of
Explanation of Solution
Write the Lorentz’s transformation equations.
Here,
Differentiate above Lorentz’s equations to find
Case 1:
Write the equation for the velocity of the particle in the unprimed frame.
Substitute equation (IV) and equation (V) in above equation to find
Write the equation for the velocity of the particle in primed frame along
Write the equation for the velocity of the particle in primed frame along
Substitute equation (IX) and (X) in equation (VIII) to find
Case 2:
Write the equation for the velocity of the particle in the primed frame.
Substitute
Write the equation for the velocity of the particle in unprimed frame along
Write the equation for the velocity of the particle in unprimed frame along
Substitute equation (IX) and (X) in equation (VIII) to find
Conclusion:
Therefore, the transformation of a velocity component perpendicular to
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Chapter 39 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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