Simple Nature - Light and Matter

direction it was initially going (it “follows through”).Page 225, problem 41: Q = 1/ √ 2Page 225, problem 43: (a) 7 × 10 −8 radians, or about 4 × 10 −6 degrees.Page 227, problem 51: (a) R = (2v 2 /g) sin θ cos θ(c) 45 ◦Page 227, problem 52: (a) The optimal angle is about 40 ◦ , and the resulting range is about124 meters, which is about the length of a home run. (b) It goes about 9 meters farther. Forcomparison with reality, the stadium’s web site claims a home run goes about 11 meters fartherthere than in a sea-level stadium.Answers for Chapter 5Page 335, problem 7: (c) n ≈ 16Page 336, problem 9: (a) ∼ 2 − 10% (b) 5% (c) The high end for the body’s actual efficiencyis higher than the limit imposed by the laws of thermodynamics. However, the high end ofthe 1-5 watt range quoted in the problem probably includes large people who aren’t just lyingaround. Still, it’s impressive that the human body comes so close to the thermodynamic limit.Page 336, problem 10: (a) Looking up the relevant density for air, and converting everythingto mks, we get a frequency of 730 Hz. This is on the right order of magnitude, which ispromising, considering the crudeness of the approximation. (b) This brings the result down to400 Hz, which is amazingly close to the observed frequency of 300 Hz.Answers for Chapter 6Page 378, problem 9: (b) g/2Page 379, problem 13: Check: The actual length of a flute is about 66 cm from the tip ofthe mouthpiece to the end of the bell.Page 378, problem 8: (a) T = µω 2 r 2Page 380, problem 17: (a) f = 4α/(1 + α) 2 (b) v 2 = √ v 1 v 3Answers for Chapter 10Page 637, problem 22: (a) E = 2kλ/R.Answers for Chapter 11Page 717, problem 5: (a) I = λv.Page 717, problem 6: (b) 2kI 1 I 2 L/c 2 R.Answers for Chapter 12Page 810, problem 61: f/ɛAnswers for Chapter 13Page 901, problem 40: about 10 −10SolutionsSolutions for Chapter 0Page 47, problem 6:134 mg × 10−3 g1 mg × 10−3 kg= 1.34 × 10 −4 kg1 g930 Chapter Appendix 4: Hints and Solutions