COLLEGE PHYSICS
COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 25, Problem 29QAP
To determine

(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)

Expert Solution
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Answer to Problem 29QAP

COLLEGE PHYSICS, Chapter 25, Problem 29QAP , additional homework tip  1

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?
    010.71.40028
    0.11.0050380.81.666667
    0.21.0206210.92.294157
    0.31.0482850.997.088812
    0.41.0910890.99922.36627
    0.51.1547010.999970.71245
    0.61.25

Graph:

From the given values, we can draw graph.

COLLEGE PHYSICS, Chapter 25, Problem 29QAP , additional homework tip  2

Formula used:

Relativistic gamma:

  γ=11v2c2

After rearranging

  (vc)=11γ2

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, γ=1.00999

  (vc)=11γ2=11(1.00999)2=0.14

Conclusion:

Maximum value of v/c for which ? is less than 1% larger than unity (1.0) is 0.14

To determine

(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?

Expert Solution
Check Mark

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:

  γ=11v2c2

  [y(x)=11 x 2diffrentiatingw.r.txgivesslopeoftheequationdydx=x( 1x2) 3 2]

Similarly,

  slope=dγd(vc)=(vc)(1 v2 c2 )32

Calculation:

  slope(atvc=0.1)=(vc)(1 v2 c2 )32=(0.1)(1 0.12)32=0.1015

  slope(atvc=0.5)=(vc)(1 v2 c2 )32=(0.5)(1 (0.5 )2)32=0.7698

  slope(atvc=0.9)=(vc)(1 v2 c2 )32=(0.9)(1 (0.9 )2)32=10.867

  slope(atvc=0.999)=(vc)(1 v2 c2 )32=(0.999)(1 (0.999 )2)32=11177.54

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

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