Concept explainers
(a)
A graph of ? versus v/c and determine the maximum value of v/c for which ? is less than 1% larger than unity (1.0)
Answer to Problem 29QAP
And, maximum value of v/c for which ? is less than 1% larger than unity (1.0) is 0.14
Explanation of Solution
Given:
v/c | ? | v/c | ? |
0 | 1 | 0.7 | 1.40028 |
0.1 | 1.005038 | 0.8 | 1.666667 |
0.2 | 1.020621 | 0.9 | 2.294157 |
0.3 | 1.048285 | 0.99 | 7.088812 |
0.4 | 1.091089 | 0.999 | 22.36627 |
0.5 | 1.154701 | 0.9999 | 70.71245 |
0.6 | 1.25 |
Graph:
From the given values, we can draw graph.
Formula used:
Relativistic gamma:
After rearranging
Calculation:
Maximum value of v/c for which ? is less than 1% larger than unity (1.0)
So, 0.00999 < 0.01 (1 % of unity)
At,
Conclusion:
Maximum value of v/c for which ? is less than 1% larger than unity (1.0) is 0.14
(b)
What numerical value does the slope of your graph take at v/c = 0.1, v/c = 0.5, v/c = 0.9, v/c = 0.999?
Answer to Problem 29QAP
At v/c = 0.1, slope = 0.101
At v/c = 0.5, slope = 0.768
At v/c = 0.9, slope = 10.867
At v/c = 0.999, slope = 11177.54
Explanation of Solution
Formula used:
Relativistic gamma:
Similarly,
Calculation:
Conclusion:
Thus, at v/c = 0.1, slope = 0.101
At v/c = 0.5, slope = 0.768
At v/c = 0.9, slope = 10.867
At v/c = 0.999, slope = 11177.54
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Chapter 25 Solutions
COLLEGE PHYSICS,VOLUME 1
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