Concept explainers
To Show:The momentum and energy of a particle in frame S’ are related to its momentum and energy in frame S by the transformation equations.
Answer to Problem 55P
Explanation of Solution
Given:
A particle moving with speed u along the y-axis in frame S .
Formula Used:
Relativistic momentum,
Relativistic energy,
Where,
Calculations:
In any inertial frame
As the particle is moving in the y axis
Substitute these values in the transformation equations:
In S’ frame, the momentum components are
The inverse velocity transformations are
Substitute
Thus,
To verify that
Next
Hence
Next, to verify
Finally
The x,y,z and t transformation equations are
The x,y,z and ct transformation equations are
The
Conclusion:
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Chapter 39 Solutions
Physics for Scientists and Engineers
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