# Chapter 30 - Worked Solutions

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

My thanks to Peter Finch from St Joseph's College, Gregory Terrace, for these (pdf) solutions.

Solutions-Ch30-Finch.pdf

The rest are by me, Richard Walding:

Question 29

Yes (but the difference is very very small).

**Question 30**

**Question 31**

l = 5.80 m; v = 0.760 c

(a) l_{0} = 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**

l_{0 }= 4 ly; t_{0} = 3 y; v = ?

**Question 33**

t_{0} = 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) E_{K} = mc^{2} - m_{0}c^{2} = c^{2}(m - m_{0})

= 9 x 10^{16} (20656 - 20000)

= 5.9 x 10^{19}J

(b) E_{K} (classical) = ½ mv^{2} = ½ x 20000 x (0.25 x 3 x 10^{8})^{2
}= 5.675 x 10^{19} J

D
E = 2.75 x 10^{18} J

% difference = 2.75 x 10^{18} x 100 / 5.9 x 10^{19} = 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**

L_{0} = 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**

L_{0} = 4.225 ly; v = 0.80 c

(a) v = L_{0}/t

t = L_{0}/v = 4.225/0.80 = 5.28 y

(b)

(c) L = 2.535 ly

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