Chapter 30 - Worked Solutions

to selected extension questions from the OUP text Senior Physics - Concepts in Context by Walding, Rapkins and Rossiter

Question 29
Yes (but the difference is very very small).
 
Question 30

 
Question 31
l = 5.80 m; v = 0.760 c
(a) l0 = 8.92 m long; no change to height
(b) t = 20.0 s
t = sv = 20 x 0.6499 = 13 s
(c) v is the same (0.760 c).
 
Question 32
l0 = 4 ly; t0 = 3 y; v = ?

 
Question 33
t0 = 7 y; v = 0.8c; t = ?
(a)

(b) Takes 11.67 y for signal travelling at c to reach Earth,
therefore total time = 9.336y + 11.67y = 21.0 y
 
Question 34
(a) EK = mc2 - m0c2 = c2(m - m0)

= 9 x 1016 (20656 - 20000)
= 5.9 x 1019J
 
(b) EK (classical) = mv2 = x 20000 x (0.25 x 3 x 108)2
= 5.675 x 1019 J
 
D E = 2.75 x 1018 J
% difference = 2.75 x 1018 x 100 / 5.9 x 1019 = 4.7%
 
Question 35

 

v

m (kg)

0.0

1.000

0.1

1.005

0.2

1.021

0.3

1.048

0.4

1.091

0.5

1.155

0.6

1.250

0.7

1.400

0.8

1.667

0.9

2.294

0.95

3.203

0.99

7.089

0.999

22.37

0.9999

70.71

 

 
Question 36
L0 = 6.00; v = 0.18c; your car L = ?

Which is the length you measure his car to be.
 
Your car as measured by him is 6.15 m (ie L = 6.15 m)

Which is what you measure your car to be.
 
Question 37
L0 = 4.225 ly; v = 0.80 c

(a) v = L0/t
t = L0/v = 4.225/0.80 = 5.28 y
 
(b)

(c) L = 2.535 ly

 
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