
Concept explainers
To prove: The expression ofenergy as

Explanation of Solution
Given data:
The expression to prove that
The expression to show that
Formula used:
Write the expression for relativistic total energy:
Here,
Write the expression for relativistic momentum
Here,
Write the expression for
Here,
Write the expression for the total energy:
Here,
Explanation:
Recall the expression for
Recall the expression for relativistic total energy:
Substitute
Square both sides
Recall the expression for relativistic momentum p:
Substitute
Square both sides of the above equation
Multiply
Subtract equation (2) from equation (1)
Further solve
Hence, proved.
Now, rewrite the expression for the total energy in relativistic mechanics.
Recall the expression for the total energy:
Equate both the above equations of
Conclusion:
The required expressionsareobtained.
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Chapter 41 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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