General Physics, 2nd Edition
General Physics, 2nd Edition
2nd Edition
ISBN: 9780471522782
Author: Morton M. Sternheim
Publisher: WILEY
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Chapter 25, Problem 49E

(a)

To determine

Distance between A and B relative to rocket.

(a)

Expert Solution
Check Mark

Answer to Problem 49E

The distance between A and B is 4m relative to rocket.

Explanation of Solution

Rocket travels past observers A and B on platform at speed 0.6c. Guns that are fired simultaneously strike rocket at points A and B.

Write the expression of distance d between A and B with respect to rocket

  d=d(1u2c2)12        (I)

Here, d is distance between A and B relative to platform and u is speed of rocket relative to platform.

Conclusion:

Substitute 0.6c for u and 5m for d in expression (I).

  d=(5m)(1(0.6c)2c2)12=4m

Thus, observers on rocket measure the distance between observers A and B to be 4m.

(b)

To determine

Time when observer A fires with respect to rocket.

(b)

Expert Solution
Check Mark

Answer to Problem 49E

The observer A fires at time 1.25×108s with respect to rocket.

Explanation of Solution

Observer B fires at time t=0 relative to both the platform and the rocket.

Write the expression of time tA when A fires with respect to rocket

  tA=duc2(1u2c2)12        (II)

Conclusion:

Substitute 0.6c for u, 3×108ms1 for c and 5m for d in expression (II).

  tA=(5m)(0.6(3×108m/s))(3×108m/s)2(1(0.6(3×108m/s))2(3×108m/s)2)12=1.25×108s

Thus, observer A fires at time 1.25×108s with respect to rocket.

(c)

To determine

Distance between points A and B relative to rocket.

(c)

Expert Solution
Check Mark

Answer to Problem 49E

The distance between points A and B relative to rocket is 6.25m.

Explanation of Solution

Write the expression of distance between points A and B relative to rocket

  D=(d+utA)        (III)

Here, D is separation between points A and B according to observers on rocket.

Conclusion:

Substitute 4m for d, 1.25×108s for tA, 0.6c for u and 3×108ms1 for c in expression (III)

  D=((4m)+(0.6(3×108ms))(1.25×108s))=6.25m

Thus, the distance between points A and B relative to rocket is 6.25m.

(d)

To determine

Verification that distance between points A and B relative to platform and the rocket are consistent with formula of length contraction.

(d)

Expert Solution
Check Mark

Answer to Problem 49E

It is verified that distance between points A and B relative to platform and the rocket are consistent with formula of length contraction.

Explanation of Solution

Write the expression of distance between points A and B relative to platform from length contraction formula

  D=D(1u2c2)12        (IV)

Here, D is separation between points A and B with respect to observers on the platform.

Since the distance between points A and B is same as the distance between A and B relative to platform therefore

  D=5m

Conclusion:

Substitute 0.6c for u, 3×108ms1 for c and 6.25m for D in expression (IV)

  D=(6.25m)(1(0.6(3×108ms))2(3×108ms)2)12=5m

Thus, it is verified that distance between points A and B relative to platform and the rocket are consistent with formula of length contraction.

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Length contraction: the real explanation; Author: Fermilab;https://www.youtube.com/watch?v=-Poz_95_0RA;License: Standard YouTube License, CC-BY