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26.1: Appendix A: Answers to Selected Problems (3e)

Difficulty Level: At Grade Created by: CK-12

Ch 1: Units and Problem Solving

    1. A person of height \begin{align*}5 \;\mathrm{ft}\end{align*}. \begin{align*}11 \;\mathrm{in}\end{align*}. is \begin{align*}1.80 \;\mathrm{m}\end{align*} tall
    2. The same person is \begin{align*}180 \;\mathrm{cm}\end{align*}
    1. \begin{align*}3 \;\mathrm{seconds} = 1/1200 \;\mathrm{hours}\end{align*}
    2. \begin{align*}3x10^3 \;\mathrm{ms}\end{align*}
  1. \begin{align*}87.5 \;\mathrm{mi/hr}\end{align*}
  2. c. if the person weighs \begin{align*}150 \;\mathrm{lb}\end{align*}. this is equivalent to \begin{align*}668 \;\mathrm{N}\end{align*}
  3. Pascals (Pa), which equals \begin{align*}\;\mathrm{N/m}^2\end{align*}
  4. \begin{align*}168 \;\mathrm{lb}., 76.2 \;\mathrm{kg}\end{align*}
  5. \begin{align*}5 \;\mathrm{mi/hr/s}\end{align*}
  6. \begin{align*}15.13 \;\mathrm{m}\end{align*}
  7. \begin{align*}11.85 \;\mathrm{m}\end{align*}
  8. \begin{align*}89,300 \;\mathrm{mm}\end{align*}
  9. f. \begin{align*}2025 \;\mathrm{mm}^2\end{align*}
  10. b. \begin{align*}196 \;\mathrm{cm}^2\end{align*}
  11. c. \begin{align*} 250 \;\mathrm{cm}^3\end{align*}
  12. \begin{align*}8:1,\end{align*} each side goes up by \begin{align*}2 \;\mathrm{cm}\end{align*}, so it will change by \begin{align*}2^3\end{align*}
  13. \begin{align*}3.5 \times 10^{51}:1\end{align*}
  14. \begin{align*} 72,000 \;\mathrm{km/h}\end{align*}
  15. \begin{align*} 0.75 \;\mathrm{kg/s}\end{align*}
  16. \begin{align*} 8 \times 2^N \;\mathrm{cm}^3/\;\mathrm{sec}\end{align*}; \begin{align*}N\end{align*} is for each second starting with \begin{align*}0\end{align*} seconds for \begin{align*}8 \;\mathrm{cm}^3\end{align*}
  17. About \begin{align*}12\end{align*} million
  18. About \begin{align*}1 \frac{1}{2}\end{align*} trillion \begin{align*}(1.5 \times 10^{12})\end{align*}
  19. \begin{align*}[\mathrm{a}] = \;\mathrm{N/kg} = \;\mathrm{m/s}^2\end{align*}

Ch 2: Energy Conservation

  1. d
  2. (discuss in class)
    1. \begin{align*}5.0 \times 10^5 \;\mathrm{J}\end{align*}
    2. \begin{align*}3.7 \times 10^5 \;\mathrm{J}\end{align*}
    3. Chemical bonds in the food.
    4. \begin{align*}99 \;\mathrm{m/s}\end{align*}
    1. \begin{align*}5.0 \times 10^5 \;\mathrm{J}\end{align*}
    2. \begin{align*}108 \;\mathrm{m/s}\end{align*}
    1. \begin{align*}450,000 \;\mathrm{J}\end{align*}
    2. \begin{align*}22,500 \;\mathrm{J}\end{align*}
    3. \begin{align*}5,625 \;\mathrm{J}\end{align*}
    4. \begin{align*}21.2 \;\mathrm{m/s}\end{align*}
    5. \begin{align*}9.18 \;\mathrm{m}\end{align*}
  3. .
  4. b. \begin{align*}KE = 504,600 \;\mathrm{J}; U_g = 1,058,400 \;\mathrm{J}; E_{total} = 1,563,000 \;\mathrm{J}\end{align*}
    1. \begin{align*}34 \;\mathrm{m/s \ at \ B}; 28 \;\mathrm{m/s \ at \ D}, 40 \;\mathrm{m/s \ at \ E}, 49 \;\mathrm{m/s \ at \ C \ and \ F}; 0 \;\mathrm{m/s \ at \ H}\end{align*}
    2. \begin{align*}96 \;\mathrm{m}\end{align*}
    1. \begin{align*}1.7 \;\mathrm{J}\end{align*}
    2. \begin{align*}1.3 \;\mathrm{m/s}\end{align*}
    3. \begin{align*}0.4 \;\mathrm{J}, 0.63 \;\mathrm{m/s}\end{align*}
    1. \begin{align*}1.2 \;\mathrm{m/s}^2\end{align*}
    2. \begin{align*}130 \;\mathrm{J}\end{align*}
    1. \begin{align*}6750 \;\mathrm{J}\end{align*}
    2. \begin{align*}2.25 \times 10^5 \;\mathrm{J}\end{align*}
    3. \begin{align*}1.5 \times 10^5 \;\mathrm{J/gallon \ of \ gas}\end{align*}
  5. \begin{align*}0.76 \;\mathrm{m}\end{align*}

Ch 3: One-Dimensional Motion

  1. .
  2. .
  3. .
  4. .
    1. Zyan
    2. Ashaan is accelerating because the distance he travels every 0.1 seconds is increasing, so the speed must be increasing
    3. Ashaan
    4. Zyan
    5. Ashaan
  5. .
  6. .
  7. 6 minutes
  8. d. \begin{align*}20 \;\mathrm{meters}\end{align*} e. \begin{align*}40 \;\mathrm{meters}\end{align*} f. \begin{align*}2.67 \;\mathrm{m/s}\end{align*} g. \begin{align*}6 \;\mathrm{m/s}\end{align*} h. Between \begin{align*}t = 15 \;\mathrm{s}\end{align*} and \begin{align*}t = 20\end{align*} sec because your position goes from \begin{align*}x = 30 \;\mathrm{m}\end{align*} to \begin{align*}x = 20\mathrm{m}\end{align*}. i. You made some sort of turn
    1. \begin{align*}7.7 \;\mathrm{m/s}^2\end{align*}
    2. \begin{align*}47 \;\mathrm{m}, 150 \;\mathrm{feet}\end{align*}
    3. \begin{align*}34 \;\mathrm{m/s}\end{align*}
    1. \begin{align*}1.22 \;\mathrm{m}\end{align*}
    2. \begin{align*}4.9 \;\mathrm{m/s}\end{align*}
    3. \begin{align*}2.46 \;\mathrm{m/s}\end{align*}
    4. \begin{align*}-4.9 \;\mathrm{m/s}\end{align*}
  9. b. 1 second c. at 2 seconds d. \begin{align*}4\mathrm{m}\end{align*}
    1. \begin{align*}250 \;\mathrm{m}\end{align*}
    2. \begin{align*}13 \;\mathrm{m/s}, -13 \;\mathrm{m/s}\end{align*}
    3. \begin{align*}14 \;\mathrm{s}\end{align*} for round trip
  10. Let’s say we can jump \begin{align*}20 \;\mathrm{feet} \ (6.1 \;\mathrm{m})\end{align*} in the air. ☺ Then, on the moon, we can jump \begin{align*}36.5 \;\mathrm{m}\end{align*} straight up.
  11. \begin{align*}-31\mathrm{m/s}^2\end{align*}
    1. \begin{align*}23 \;\mathrm{m/s}\end{align*}
    2. 3.6 seconds
    3. \begin{align*}28 \;\mathrm{m}\end{align*}
    4. \begin{align*}45\mathrm{m}\end{align*}
    1. \begin{align*}25 \;\mathrm{m/s}\end{align*}
    2. \begin{align*}30 \;\mathrm{m}\end{align*}
    3. \begin{align*}2.5 \;\mathrm{m/s}^2\end{align*}
  12. \begin{align*}2 \;\mathrm{m/s}^2\end{align*}
    1. \begin{align*}v_0 = 0\end{align*}
    2. \begin{align*}10 \;\mathrm{m/s}^2\end{align*}
    3. \begin{align*}- 10 \;\mathrm{m/s}^2\end{align*}
    4. \begin{align*}60 \;\mathrm{m}\end{align*}
    1. \begin{align*}0.3 \;\mathrm{m/s}^2\end{align*}
    2. \begin{align*}0.5 \;\mathrm{m/s}\end{align*}

Ch 4: Two-Dimensional and Projectile Motion

  1. .
  2. .
  3. .
  4. .
  5. .
  6. .
    1. \begin{align*}13 \;\mathrm{m}\end{align*}
    2. \begin{align*}41\end{align*} degrees
    3. \begin{align*}v_y = 26 \;\mathrm{m/s}; v_x = 45 \;\mathrm{m/s}\end{align*}
    4. \begin{align*}56\end{align*} degrees, \begin{align*}14 \;\mathrm{m/s}\end{align*}
  7. .
  8. \begin{align*}32 \;\mathrm{m}\end{align*}
    1. \begin{align*}0.5 \;\mathrm{s}\end{align*}
    2. \begin{align*}0.8 \;\mathrm{m/s}\end{align*}
  9. \begin{align*}104 \;\mathrm{m}\end{align*}
  10. \begin{align*}t = 0.60 \;\mathrm{s}, 1.8 \;\mathrm{m}\end{align*} below target
  11. \begin{align*}28 \;\mathrm{m}\end{align*}.
    1. \begin{align*}3.5 \;\mathrm{s}\end{align*}.
    2. \begin{align*}35 \;\mathrm{m}; 15 \;\mathrm{m}\end{align*}
  12. \begin{align*}40 \;\mathrm{m}; 8.5 \;\mathrm{m}\end{align*}
  13. \begin{align*}1.3\end{align*} seconds, \begin{align*}7.1\end{align*} meters
  14. \begin{align*}50 \;\mathrm{m}; v_{0y} = 30 \;\mathrm{m/s}; 50^0\end{align*}; on the way up
  15. \begin{align*}4.4 \;\mathrm{s}\end{align*}
  16. \begin{align*}19^\circ\end{align*}
  17. \begin{align*}0.5 \;\mathrm{s}\end{align*}
  18. \begin{align*}2.3 \;\mathrm{m/s}\end{align*}
  19. \begin{align*}6 \;\mathrm{m}\end{align*}
  20. \begin{align*}1.4\end{align*} seconds
    1. yes
    2. \begin{align*}14 \;\mathrm{m/s}\end{align*} @ \begin{align*}23\end{align*} degrees from horizontal
  21. \begin{align*}22 \;\mathrm{m/s}\end{align*} @ \begin{align*}62\end{align*} degrees

Ch 5: Newton’s Laws

  1. .
  2. .
  3. .
  4. Zero; weight of the hammer minus the air resistance.
  5. \begin{align*}2\end{align*} forces
  6. \begin{align*}1\end{align*} force
  7. No
  8. The towel’s inertia resists the acceleration
    1. Same distance
    2. You go farther
    3. Same amount of force
  9. .
  10. a. \begin{align*}98 \;\mathrm{N}\end{align*} b. \begin{align*}98\;\mathrm{N}\end{align*}
  11. .
  12. \begin{align*}32\;\mathrm{N}\end{align*}
  13. \begin{align*}5.7 \;\mathrm{m/s}^2\end{align*}
  14. .
  15. .
  16. \begin{align*}F_x = 14 \;\mathrm{N}, F_y = 20\;\mathrm{N}\end{align*}
  17. Left picture: \begin{align*}F = 23\mathrm{N} \ 98^\circ\end{align*}, right picture:\begin{align*}F = 54 \;\mathrm{N} \ 5^\circ\end{align*}
  18. \begin{align*}3 \;\mathrm{m/s}^2 \;\mathrm{east}\end{align*}
  19. \begin{align*}4 \;\mathrm{m/s}^2; 22.5^\circ \;\mathrm{NE}\end{align*}
  20. \begin{align*}0.51\end{align*}
  21. \begin{align*}0.2\end{align*}
  22. The rope will not break because his weight of \begin{align*}784\;\mathrm{N}\end{align*} is distributed between the two ropes.
  23. Yes, because his weight of \begin{align*}784\;\mathrm{N}\end{align*} is greater than what the rope can hold.
  24. Mass is \begin{align*}51 \;\mathrm{kg}\end{align*} and weight is \begin{align*}82\;\mathrm{N}\end{align*}
    1. While accelerating down
    2. \begin{align*}686\;\mathrm{N}\end{align*}
    3. \begin{align*}826\;\mathrm{N}\end{align*}
    1. \begin{align*}390\;\mathrm{N}\end{align*}
    2. \begin{align*}490\;\mathrm{N}\end{align*}
  25. \begin{align*}0.33\end{align*}
  26. \begin{align*}3.6 \;\mathrm{kg}\end{align*}
  27. \begin{align*}\mathrm{g} \sin \theta\end{align*}
  28. b.\begin{align*} 20\;\mathrm{N}\end{align*} c. \begin{align*}4.9\;\mathrm{N}\end{align*} d. \begin{align*}1.63 \;\mathrm{kg}\end{align*} e. Eraser would slip down the wall
    1. \begin{align*}1450\;\mathrm{N}\end{align*}
    2. \begin{align*}5600\;\mathrm{N}\end{align*}
    3. \begin{align*}5700\;\mathrm{N}\end{align*}
    4. Friction between the tires and the ground
    5. Fuel, engine, or equal and opposite reaction
  29. b. \begin{align*}210\;\mathrm{N}\end{align*} c. no, the box is flat so the normal force doesn’t change d. \begin{align*}2.8 \;\mathrm{m/s}^2\end{align*} e.\begin{align*} 28 \;\mathrm{m/s}\end{align*} f. no g. \begin{align*}69\;\mathrm{N}\end{align*} h. \begin{align*}57\;\mathrm{N}\end{align*} i. \begin{align*}40\;\mathrm{N}\end{align*} j. \begin{align*}0.33\end{align*} k. \begin{align*}0.09\end{align*}
  30. .
    1. zero
    2. \begin{align*}-kx0\end{align*}
  31. b. \begin{align*}f_1= \mu_km_1\mathrm{g} \cos\theta; f_2 = \mu_km_2\mathrm{g} \cos\theta\end{align*} c. Ma d. \begin{align*}T_A= (m_1 + m_2) (a + \mu \cos\theta)\end{align*} and \begin{align*}T_B = m_2a + \mu m_2 \cos\theta\end{align*} e. Solve by using \begin{align*}d = 1/2at^2\end{align*} and substituting \begin{align*}h\end{align*} for \begin{align*}d\end{align*}
    1. Yes, because it is static and you know the angle and \begin{align*}m_1\end{align*}
    2. Yes, \begin{align*}T_A\end{align*} and the angle gives you \begin{align*}m_1\end{align*} and the angle and \begin{align*}T_C\end{align*} gives you \begin{align*}m_2, m_1 = T_A \cos 25/\mathrm{g}\end{align*} and \begin{align*}m_2 = T_C \cos 30/\mathrm{g}\end{align*}
  32. a. \begin{align*}3\end{align*} seconds d. \begin{align*}90 \;\mathrm{m}\end{align*}
  33. .
  34. .
  35. .
    1. \begin{align*}1.5 \;\mathrm{N}; 2.1 \;\mathrm{N}; 0.71\end{align*}

Ch 6: Centripetal Forces

  1. .
  2. .
  3. .
  4. .
    1. \begin{align*}100 \;\mathrm{N}\end{align*}
    2. \begin{align*}10 \;\mathrm{m/s}^2\end{align*}
    1. \begin{align*}25 \;\mathrm{N}\end{align*} towards her
    2. \begin{align*}25 \;\mathrm{N}\end{align*} towards you
    1. \begin{align*}14.2 \;\mathrm{m/s}^2\end{align*}
    2. \begin{align*}7.1 \times 10^3 \;\mathrm{N}\end{align*}
    3. friction between the tires and the road
  5. \begin{align*}.0034\mathrm{g}\end{align*}
    1. \begin{align*}6.2 \times 10^5\;\mathrm{m/s}^2\end{align*}
    2. The same as a.
  6. \begin{align*}3.56 \times 10^{22}\mathrm{N}\end{align*}
  7. \begin{align*}4.2 \times 10^{-7} \;\mathrm{N}\end{align*}; very small force
  8. \begin{align*}g = 9.8 \;\mathrm{m/s}^2\end{align*}; you’ll get close to this number but not exactly due to some other small effects
    1. \begin{align*}4 \times 10^{26} \;\mathrm{N}\end{align*}
    2. gravity
    3. \begin{align*}2 \times 10^{41} \;\mathrm{kg}\end{align*}
  9. \begin{align*}.006 \;\mathrm{m/s}^2\end{align*}
    1. \begin{align*}.765\end{align*}
    2. \begin{align*}4880 \;\mathrm{N}\end{align*}
    1. \begin{align*}\sim 10^{-8} \;\mathrm{N}\end{align*} very small force
    2. Your pencil does not accelerate toward you because the frictional force on your pencil is much greater than this force.
  10. a. \begin{align*}4.23 \times 10^7\mathrm{m}\end{align*} b. \begin{align*}6.6 \ R_e\end{align*} d. The same, the radius is independent of mass
  11. \begin{align*}1.9 \times 10^7\mathrm{m}\end{align*}
  12. You get two answers for \begin{align*}r\end{align*}, one is outside of the two stars one is between them, that’s the one you want, \begin{align*}1.32 \times 10^{10}\mathrm{m}\end{align*} from the larger star.
  13. .
  14. .
    1. \begin{align*}v = 28\;\mathrm{m/s}\end{align*}
    2. \begin{align*}v-\end{align*}down, \begin{align*}a-\end{align*}right
    3. \begin{align*}f-\end{align*}right
    4. Yes, \begin{align*}640\mathrm{N}\end{align*}

Ch 7: Momentum Conservation

  1. .
  2. .
  3. .
  4. .
  5. .
  6. .
  7. .
  8. \begin{align*}37.5 \;\mathrm{m/s}\end{align*}
  9. \begin{align*}v_1 = 2v_2\end{align*}
    1. \begin{align*}24 \frac{kg-m}{5}\end{align*}
    2. \begin{align*}0.364 \;\mathrm{m/s}\end{align*}
    3. \begin{align*}22 \frac{kg-m}{5}\end{align*}
    4. \begin{align*}109 \;\mathrm{N}\end{align*}
    5. \begin{align*}109 \;\mathrm{N}\end{align*} due to Newton’s third law
  10. \begin{align*}2.0 \;\mathrm{kg}, 125 \;\mathrm{m/s}\end{align*}
  11. \begin{align*}21 \;\mathrm{m/s}\end{align*} to the left
  12. \begin{align*}3250 \;\mathrm{N}\end{align*}
    1. \begin{align*}90 \;\mathrm{sec}\end{align*}
    2. \begin{align*}1.7 \times 10^5 \;\mathrm{sec}\end{align*}
    1. \begin{align*}60 \;\mathrm{m/s}\end{align*}
    2. \begin{align*}.700 \;\mathrm{sec}\end{align*}
    3. yes, \begin{align*}8.16 \;\mathrm{m}\end{align*}
  13. \begin{align*}0.13 \;\mathrm{m/s}\end{align*} to the left
    1. \begin{align*}11000 \;\mathrm{N}\end{align*} to the left
    2. tree experienced same average force of \begin{align*}11000 \;\mathrm{N}\end{align*} but to the right
    3. \begin{align*}2500 \;\mathrm{lb}\end{align*}.
    4. about \begin{align*}2.5\end{align*} “g”s of acceleration
    1. no change
    2. the last two cars
    1. \begin{align*}0.00912 \;\mathrm{s}\end{align*}
    1. \begin{align*}0.0058 \;\mathrm{m/s}^2\end{align*}
    2. \begin{align*}3.5 \;\mathrm{m/s}^2\end{align*}
    1. \begin{align*} 15 \;\mathrm{m/s}\end{align*}
    2. \begin{align*}49^\circ \;\mathrm{S}\end{align*} of \begin{align*}\;\mathrm{E}\end{align*}
  14. b. \begin{align*}4.6 \;\mathrm{m/s} \ 68^\circ\end{align*}

Ch 8: Energy & Force

  1. .
  2. .
  3. .
  4. .
  5. .
    1. \begin{align*}7.18 \times 10^9 \;\mathrm{J}\end{align*}
    2. \begin{align*}204 \;\mathrm{m/s}\end{align*}
    1. \begin{align*}34 \;\mathrm{m/s}\end{align*} @ \begin{align*}B; 28 \;\mathrm{m/s}\end{align*} @ \begin{align*}D; 40 \;\mathrm{m/s}\end{align*} @ \begin{align*}E; 49 \;\mathrm{m/s}\end{align*} @ \begin{align*}C\end{align*} and F; \begin{align*}0 \;\mathrm{m/s}\end{align*} @ \begin{align*}H\end{align*}
    2. \begin{align*}30 \;\mathrm{m}\end{align*}
    3. Yes, it makes the loop
  6. a. \begin{align*}2.3 \;\mathrm{m/s}\end{align*} c. No, the baby will not clear the hill.
    1. \begin{align*}29,500 \;\mathrm{J}\end{align*}
    2. \begin{align*}13 \;\mathrm{m}\end{align*}
  7. .
    1. \begin{align*}86\;\mathrm{m}\end{align*}
    2. \begin{align*}220\;\mathrm{m}\end{align*}
    1. \begin{align*}48.5 \;\mathrm{m/s}\end{align*}
    2. \begin{align*}128 \;\mathrm{N}\end{align*}
  8. \begin{align*}0.32 \;\mathrm{m/s}\end{align*} each
    1. \begin{align*}10 \;\mathrm{m/s}\end{align*}
    2. \begin{align*}52\;\mathrm{m}\end{align*}
    1. \begin{align*}1.1 \times 10^4 \;\mathrm{N/m}\end{align*}
    2. \begin{align*}2\;\mathrm{m}\end{align*} above the spring
  9. \begin{align*}96\end{align*}%
  10. .
    1. \begin{align*}.008\;\mathrm{m}\end{align*}
    2. 5.\begin{align*}12^\circ\end{align*}
  11. \begin{align*}8 \;\mathrm{m/s}\end{align*} same direction as the cue ball and \begin{align*}0 \;\mathrm{m/s}\end{align*}
  12. \begin{align*}\mathrm{v}_{golf} =-24.5 \;\mathrm{m/s}; \mathrm{vpool} = 17.6 \;\mathrm{m/s}\end{align*}
  13. \begin{align*}2.8\;\mathrm{m}\end{align*}
    1. \begin{align*}0.57 \;\mathrm{m/s}\end{align*}
    2. Leonora’s
    3. \begin{align*}617 \;\mathrm{J}\end{align*}
    1. \begin{align*}19.8 \;\mathrm{m/s}\end{align*}
    2. \begin{align*}8.8 \;\mathrm{m/s}\end{align*}
    3. \begin{align*}39.5\;\mathrm{m}\end{align*}
    1. \begin{align*}89 \;\mathrm{kW}\end{align*}
    2. \begin{align*}0.4\end{align*}
    3. \begin{align*}15.1 \;\mathrm{m/s}\end{align*}
  14. \begin{align*}43.8 \;\mathrm{m/s}\end{align*}
  15. .
  16. .
  17. .
    1. \begin{align*}3.15 \times 10^5 \;\mathrm{J}\end{align*}
    2. \begin{align*}18.0 \;\mathrm{m/s}\end{align*}
    3. \begin{align*}2.41\;\mathrm{m}\end{align*}
    4. \begin{align*}7900 \;\mathrm{J}\end{align*}
    1. \begin{align*}v_0 /14\end{align*}
    2. \begin{align*}mv_{0}{^{2}}/8\end{align*}
    3. \begin{align*}7mv_{0}{^{2}}/392\end{align*}
    4. \begin{align*}71\end{align*}%

Ch 9: Rotational Motion

  1. .
    1. \begin{align*}9.74 \times 10^{37} \;\mathrm{kg \ m}2\end{align*}
    2. \begin{align*}1.33 \times 10^{47} \;\mathrm{kg \ m}^2\end{align*}
    3. \begin{align*} 0.5 \;\mathrm{kg \ m}^2\end{align*}
    4. \begin{align*}0.28 \;\mathrm{kg \ m}^2\end{align*}
    5. \begin{align*}0.07 \;\mathrm{kg \ m}^2\end{align*}
  2. a. True, all rotate \begin{align*}2\pi\end{align*} for \begin{align*}86,400 ;\mathrm{sec}\end{align*} which is 24 hours, b. True, \begin{align*}\omega = 2\pi/\mathrm{t}\end{align*} and \begin{align*}t=86,400 \;\mathrm{s}\end{align*} f. True, \begin{align*}L\end{align*} is the same g. \begin{align*}L = I\omega\end{align*} and \begin{align*}I = 2/5 \;\mathrm{mr}^2\end{align*} h. True, \begin{align*}K = \frac{1}{2} I\omega^2\end{align*} & \begin{align*}I = 2/5 \;\mathrm{mr}^2 \;\mathrm{sub-in} \ K = 1/5 \;\mathrm{mr}^2\omega^2\end{align*} i. True, \begin{align*}K = \frac{1}{2} I\omega^2\end{align*} & \begin{align*}I = \;\mathrm{mr}^2 \;\mathrm{sub-in} \ K = \frac{1}{2} mr^2\omega^2\end{align*}
    1. \begin{align*}250 \;\mathrm{rad}\end{align*}
    2. \begin{align*}40 \;\mathrm{rad}\end{align*}
    3. \begin{align*}25 \;\mathrm{rad/s}\end{align*}
    4. Force applied perpendicular to radius allows \begin{align*}\alpha\end{align*}
    5. \begin{align*}0.27 \;\mathrm{kg \ m}^2\end{align*},
    6. \begin{align*}K^5 = 84 \;\mathrm{J}\end{align*} and \begin{align*}K^10 = 340 \;\mathrm{J}\end{align*}
  3. .
  4. Moment of inertia at the end \begin{align*}1/3 \;\mathrm{ML}^2\end{align*} at the center \begin{align*}1/12 \;\mathrm{ML}^2\end{align*}, angular momentum, \begin{align*}L = I\omega\end{align*} and torque, \begin{align*}\tau = I\alpha\end{align*} change the in the same way
  5. .
  6. Lower
  7. Iron ball
    1. \begin{align*}200 \;\mathrm{N}\end{align*} team
    2. \begin{align*}40 \;\mathrm{N}\end{align*}
    3. \begin{align*}0.02 \;\mathrm{rad/s}^2\end{align*}
    4. \begin{align*}25 \;\mathrm{s}\end{align*}
    1. Coin with the hole
    2. Coin with the hole
    1. weight
    2. \begin{align*}19.6 \;\mathrm{N}\end{align*}
    3. plank’s length \begin{align*}(0.8\mathrm{m})\end{align*} left of the pivot
    4. \begin{align*}15.7 \;\mathrm{N \ m}\end{align*},
    5. Ba. weight, Bb. \begin{align*}14.7 \;\mathrm{N}\end{align*}, Bc. plank’s length \begin{align*}(0.3\mathrm{m})\end{align*} left of the pivot, Bd. \begin{align*}4.4 \;\mathrm{N \ m}\end{align*}, Ca. weight, Cb. \begin{align*}13.6\;\mathrm{N}\end{align*}, Cc. plank’s length \begin{align*}(1.00 \;\mathrm{m})\end{align*} right of the pivot, Cd. \begin{align*}13.6 \;\mathrm{N \ m}\end{align*}, f) \begin{align*}6.5 \;\mathrm{N \ m \ CC}\end{align*}, g) no, net torque doesn’t equal zero
    1. \begin{align*}7.27 \times 10^{-6} \;\mathrm{Hz}\end{align*}
    2. \begin{align*}7.27 \;\mathrm{Hz}\end{align*}
    1. \begin{align*}100 \;\mathrm{Hz}\end{align*}
    2. \begin{align*}1.25 \times 10^5 \;\mathrm{J}\end{align*}
    3. \begin{align*}2500 \;\mathrm{J-s}\end{align*}
    4. \begin{align*}12,500 \;\mathrm{m-N}\end{align*}
  8. \begin{align*}28 \;\mathrm{rev/sec}\end{align*}
  9. \begin{align*}2300\;\mathrm{N}\end{align*}
  10. b. \begin{align*}771\;\mathrm{N}, 1030\;\mathrm{N}\end{align*} c. \begin{align*}554 \;\mathrm{kgm}^2\end{align*} d. \begin{align*}4.81\mathrm{rad/sec}^2\end{align*}
    1. \begin{align*}300\;\mathrm{N}\end{align*}
    2. \begin{align*}240N, -22\;\mathrm{N}\end{align*}
    3. \begin{align*}.092\end{align*}
    1. \begin{align*}2280\;\mathrm{N}\end{align*}
    2. \begin{align*}856 \;\mathrm{n}\end{align*} toward beam, \begin{align*}106\;\mathrm{N}\end{align*} down
    3. \begin{align*}425 \;\mathrm{kgm}^2\end{align*}
    4. \begin{align*}3.39 \;\mathrm{rad/sec}^2\end{align*}
    1. \begin{align*}-1.28 \;\mathrm{Nm}\end{align*}
    2. \begin{align*}\;\mathrm{CCW}\end{align*}
  11. a. \begin{align*}1411 \;\mathrm{kg}\end{align*} c. \begin{align*}17410\;\mathrm{N}\end{align*} d. angular acc goes down as arm moves to vertical

Ch 10: Simple Harmonic Motion

    1. Buoyant force and gravity
    2. \begin{align*}T = 6 \;\mathrm{s}, f = 1/6 \;\mathrm{Hz}\end{align*}
    1. \begin{align*}9.8 \times 10^5 \;\mathrm{N/m}\end{align*}
    2. \begin{align*}0.5 \;\mathrm{mm}\end{align*}
    3. \begin{align*}22 \;\mathrm{Hz}\end{align*}, no.
  1. \begin{align*}3.2 \times 10^3 \;\mathrm{N/m}\end{align*}
  2. a. \begin{align*}110 \;\mathrm{N/m}\end{align*} d. \begin{align*}v(t)=(25) \cos(83\mathrm{t})\end{align*}
  3. .
  4. .
    1. \begin{align*}0.0038 \;\mathrm{s}\end{align*}
    2. \begin{align*}0.0038 \;\mathrm{s}\end{align*}
  5. .
  6. .
  7. \begin{align*}4\end{align*} times
  8. \begin{align*}0.04 \;\mathrm{m}\end{align*}
    1. \begin{align*}16 \;\mathrm{Hz}\end{align*}
    2. \begin{align*}16\end{align*} complete cycles but \begin{align*}32\end{align*} times up and down, \begin{align*}315\end{align*} complete cycles but \begin{align*}630\end{align*} times up and down
    3. \begin{align*}0.063 \;\mathrm{s}\end{align*}
    1. \begin{align*}24.8 \;\mathrm{J},165 \;\mathrm{N}, 413 \;\mathrm{m/s}^2\end{align*}
    2. \begin{align*}11.1\mathrm{m/s}, 0, 0\end{align*}
    3. \begin{align*}6.2 \;\mathrm{J}, 18.6 \;\mathrm{J}, 9.49 \;\mathrm{m/s}, 82.5 \;\mathrm{N}, 206 \;\mathrm{m/s}^2\end{align*}
    4. \begin{align*}.169 \;\mathrm{sec}, 5.9 \;\mathrm{Hz}\end{align*}
  9. b. \begin{align*}.245 \;\mathrm{J}\end{align*} c. \begin{align*}1.40\mathrm{m/s}\end{align*} d. \begin{align*}1.00 \;\mathrm{m/s}\end{align*} f. \begin{align*}2.82 \;\mathrm{N}\end{align*} g. \begin{align*}3.10 \;\mathrm{N}\end{align*}

Ch 11: Wave Motion and Sound

  1. \begin{align*}390 \;\mathrm{Hz}\end{align*}
    1. \begin{align*}4 \;\mathrm{Hz}\end{align*}
    2. It was being driven near its resonant frequency.
    3. \begin{align*}8 \;\mathrm{Hz}, 12 \;\mathrm{Hz}\end{align*}
    4. (Note that earthquakes rarely shake at more than \begin{align*}6 \;\mathrm{Hz}\end{align*}).
  2. .
  3. .
    1. \begin{align*}7\end{align*} nodes including the \begin{align*}2\end{align*} at the ends
    2. \begin{align*}3.6 \;\mathrm{Hz}\end{align*}
  4. \begin{align*}1.7 \;\mathrm{km}\end{align*}
    1. \begin{align*}1.7 \;\mathrm{cm}\end{align*}
    2. \begin{align*}17 \;\mathrm{m}\end{align*}
    1. \begin{align*}4.3 \times 10^{14} \;\mathrm{Hz}\end{align*}
    2. \begin{align*}2.3 \times 10^{-15} \;\mathrm{s} -\end{align*} man that electron is moving fast
    1. \begin{align*}2.828 \;\mathrm{m}\end{align*}
    2. \begin{align*}3.352 \;\mathrm{m}\end{align*}
    3. \begin{align*}L = 1/4 \ \lambda\end{align*} so it would be difficult to receive the longer wavelengths.
  5. Very low frequency
  6. b. Same as closed at both ends
  7. .
  8. \begin{align*}1.9 \;\mathrm{Hz}\end{align*} or \begin{align*}2.1 \;\mathrm{Hz}\end{align*}.
  9. \begin{align*}0.53 \;\mathrm{m}\end{align*}
  10. \begin{align*}2.2 \;\mathrm{m}, 36 \;\mathrm{Hz}; 1.1 \;\mathrm{m}, 73 \;\mathrm{Hz}; 0.733 \;\mathrm{m}, 110 \;\mathrm{Hz}; 0.55 \;\mathrm{m}, 146 \;\mathrm{Hz}\end{align*}
  11. \begin{align*}430\;\mathrm{Hz}; 1.3 \times 10^3 \;\mathrm{Hz}; 2.1 \times 10^3 \;\mathrm{Hz}; 3.0 \times 10^3 \;\mathrm{Hz};\end{align*}
    1. The tube closed at one end will have a longer fundamental wavelength and a lower frequency.
    2. If the temperature increases the wavelength will not change, but the frequency will increase accordingly.
  12. struck by bullet first.
  13. \begin{align*}80 \;\mathrm{Hz}; 0.6 \;\mathrm{m}\end{align*}
    1. \begin{align*}0.457 \;\mathrm{m}\end{align*}
    2. \begin{align*}0.914 \;\mathrm{m}\end{align*}
    3. \begin{align*}1.37 \;\mathrm{m}\end{align*}
  14. \begin{align*}2230 \;\mathrm{Hz}; 2780 \;\mathrm{Hz}; 2970 \;\mathrm{Hz}\end{align*}
  15. \begin{align*}498 \;\mathrm{Hz}\end{align*}
  16. \begin{align*}150 \;\mathrm{m/s}\end{align*}

Ch 12: Electricity

  1. .
  2. .
  3. .
  4. .
  5. .
  6. .
  7. .
  8. .
  9. .
  10. .
  11. b. \begin{align*}1350 \;\mathrm{N}\end{align*} c. \begin{align*}1350 \;\mathrm{N}\end{align*}
    1. \begin{align*}1.1 \times 10^9 \;\mathrm{N/C}\end{align*}
    2. \begin{align*}9000 \;\mathrm{N}\end{align*}
  12. \begin{align*}F_g = 1.0 \times 10^{-47} \;\mathrm{N}\end{align*} and \begin{align*}F_e = 2.3 \times 10^{-8} \;\mathrm{N}\end{align*}. The electric force is \begin{align*}39\end{align*} orders of magnitudes bigger.
  13. \begin{align*}1.0 \times 10^{-4} C\end{align*}
  14. .
  15. a. down b. Up \begin{align*}16c, 5.5 \times 10^{11} \;\mathrm{m/s}^2\end{align*} e. \begin{align*}2.9 \times 10^8 \;\mathrm{m/s}^2\end{align*}
    1. Toward the object
    2. \begin{align*}3.6 \times 10^4 \;\mathrm{N/C}\end{align*} to the left with a force of \begin{align*}2.8 \times 10^{-7} \;\mathrm{N}\end{align*}
  16. Twice as close to the smaller charge, so \begin{align*}2 \;\mathrm{m}\end{align*} from \begin{align*}12\mu \mathrm{C}\end{align*} charge and \begin{align*}1 \;\mathrm{m}\end{align*} from \begin{align*}3\mu \mathrm{C}\end{align*} charge.
  17. \begin{align*}0.293 \;\mathrm{N}\end{align*} and at \begin{align*}42.5^\circ\end{align*}
  18. \begin{align*}624 \;\mathrm{N/C}\end{align*} and at an angle of \begin{align*}-22.4^\circ\end{align*} from the \begin{align*}+x-\end{align*}axis.
    1. \begin{align*}7500\mathrm{V}\end{align*}
    2. \begin{align*}1.5 \;\mathrm{m/s}\end{align*}
    1. \begin{align*}6.4 \times 10^{-17}\;\mathrm{N}\end{align*}
    2. \begin{align*}1300\mathrm{V}\end{align*}
    3. \begin{align*}2.1 \times 10 ^{-16} \;\mathrm{J}\end{align*}
    4. \begin{align*}2.2 \times 10^7 \;\mathrm{m/s}\end{align*}
  19. b. \begin{align*}0.25\mathrm{m}\end{align*} c. \begin{align*}F_T = 0.022\;\mathrm{N}\end{align*} d. \begin{align*}0.37 \mu \mathrm{C}\end{align*}

Ch 13: Electric Circuits – Batteries and Resistors

    1. \begin{align*}4.5\mathrm{C}\end{align*}
    2. \begin{align*}2.8 \times 10^{19}\end{align*} electrons
    1. \begin{align*}0.11 \;\mathrm{A}\end{align*}
    2. \begin{align*}1.0 \;\mathrm{W}\end{align*}
    3. \begin{align*}2.5 \times 10^{21}\end{align*} electrons
    4. \begin{align*}3636 \;\mathrm{W}\end{align*}
    1. \begin{align*}192 \ \Omega\end{align*}
    2. \begin{align*}0.42 \;\mathrm{W}\end{align*}
    1. \begin{align*}5.4 \;\mathrm{mV}\end{align*}
    2. \begin{align*}1.4 \times 10^{-8} \;\mathrm{A}\end{align*}
    3. \begin{align*}7.3 \times 10^{-11} \;\mathrm{W}\end{align*}, not a lot
    4. \begin{align*}2.6 \times 10^{-7} \;\mathrm{J}\end{align*}
  1. left = brighter, right = longer
    1. \begin{align*}224 \;\mathrm{V}\end{align*}
    2. \begin{align*}448 \;\mathrm{W}\end{align*}
    3. \begin{align*}400 \;\mathrm{W}\end{align*} by \begin{align*}100 \ \Omega\end{align*} and \begin{align*}48 \;\mathrm{W}\end{align*} by \begin{align*}12 \ \Omega\end{align*}
  2. b. \begin{align*}8.3 \;\mathrm{W}\end{align*}
  3. \begin{align*}0.5\mathrm{A}\end{align*}
  4. .
  5. \begin{align*}0.8\mathrm{A}\end{align*} and the \begin{align*}50 \ \Omega\end{align*} on the left
    1. \begin{align*}0.94 \;\mathrm{A}\end{align*}
    2. \begin{align*}112 \;\mathrm{W}\end{align*}
    3. \begin{align*}0.35 \;\mathrm{A}\end{align*}
    4. \begin{align*}0.94 \;\mathrm{A}\end{align*}
    5. \begin{align*}50, 45, 75 \ \Omega\end{align*}
    6. both \begin{align*}50 \ \Omega\end{align*} resistors are brightest, then \begin{align*}45 \ \Omega\end{align*}, then \begin{align*}75 \ \Omega\end{align*}
    1. \begin{align*}0.76 \;\mathrm{A}\end{align*}
    2. \begin{align*}7.0 \;\mathrm{W}\end{align*}
  6. b. \begin{align*}1000 \;\mathrm{W}\end{align*}
  7. .
    1. \begin{align*}9.1 \ \Omega\end{align*}
    2. \begin{align*}29.1 \ \Omega\end{align*}
    3. \begin{align*}10.8 \ \Omega\end{align*}
    4. \begin{align*} 26.8 \ \Omega\end{align*}
    5. \begin{align*}1.8\mathrm{A}\end{align*}
    6. \begin{align*}21.5\mathrm{V}\end{align*}
    7. \begin{align*}19.4\mathrm{V}\end{align*}
    8. \begin{align*}6.1\mathrm{V}\end{align*}
    9. \begin{align*}0.24\mathrm{A}\end{align*}
    10. \begin{align*}16 \;\mathrm{kW}\end{align*}
    1. \begin{align*}3.66 \ \Omega\end{align*}
    2. \begin{align*}0.36\mathrm{A}\end{align*}
    3. \begin{align*}1.32 \;\mathrm{V}\end{align*}
  8. .
  9. .
  10. .
  11. .
  12. .
  13. .
    1. \begin{align*}10\mathrm{V}\end{align*}

Ch 14: Magnetism

  1. No: if \begin{align*}v = 0\end{align*} then \begin{align*}F = 0\end{align*}; yes: \begin{align*}F = qE\end{align*}
  2. .
  3. .
    1. Into the page
    2. Down the page
    3. Right
  4. Both pointing away from north
  5. .
  6. .
  7. \begin{align*}7.6 \;\mathrm{T}\end{align*}, south
  8. Down the page; \begin{align*}60 \;\mathrm{N}\end{align*}
    1. To the right, \begin{align*}1.88 \times 10^4 \;\mathrm{N}\end{align*}
    2. \begin{align*}91.7 \;\mathrm{m/s}\end{align*}
    3. It should be doubled
  9. East \begin{align*}1.5 \times 10^4 \;\mathrm{A}\end{align*}
  10. \begin{align*}0.00016 \;\mathrm{T}\end{align*}; if CCW motion, B is pointed into the ground.
  11. \begin{align*}1.2 \times 105 \;\mathrm{V}\end{align*}, counterclockwise
    1. \begin{align*}15 \;\mathrm{V}\end{align*}
    2. Counter-clockwise
    1. \begin{align*}2 \times 10^{-5} \;\mathrm{T}\end{align*}
    2. Into the page
    3. \begin{align*}2.8 \;\mathrm{N/m}\end{align*}
    4. CW
    1. \begin{align*}2.42 \times 10^8 \;\mathrm{m/s}\end{align*}
    2. \begin{align*}9.69 \times 10^{-12} \;\mathrm{N}\end{align*}
    3. \begin{align*}.0055 \;\mathrm{m}\end{align*}
  12. E/B
    1. \begin{align*}8 \times 10^{-7} \;\mathrm{T}\end{align*}
    2. \begin{align*}1.3 \times 10^{-6} \;\mathrm{C}\end{align*}
    1. \begin{align*}0 .8 \;\mathrm{V}\end{align*}
    2. CCW
    3. \begin{align*}.064 \;\mathrm{N}\end{align*}
    4. \begin{align*}.16 \;\mathrm{N/C}\end{align*}
    5. \begin{align*}.13 \;\mathrm{w}\end{align*}
  13. a. \begin{align*}1.11 \times 10^8 \;\mathrm{m/s}\end{align*} b. \begin{align*}9.1 \times 10^{-30} \;\mathrm{N} < < 6.4 \times 10^{-14} \;\mathrm{N}\end{align*} d. \begin{align*}.00364 \;\mathrm{T}\end{align*} e. \begin{align*}.173 \;\mathrm{m}\end{align*} f. \begin{align*}7.03 \times 1016 \;\mathrm{m/s}^2\end{align*} g. \begin{align*}3.27^\circ\end{align*}
  14. \begin{align*}19.2 \;\mathrm{V}\end{align*}
    1. \begin{align*}8.39 \times 10^7 \;\mathrm{m/s}\end{align*}
    2. \begin{align*}2.68 \times 10^{-13} \;\mathrm{N}, -y\end{align*}
    3. \begin{align*}2.95 \times 10^17 \;\mathrm{m/s}^2\end{align*}
    4. \begin{align*}.00838 \;\mathrm{m}\end{align*}
    5. \begin{align*}1.68 \times 10^6 \;\mathrm{N/C}\end{align*}
    6. \begin{align*}16,800 \;\mathrm{V}\end{align*}
    1. \begin{align*}1.2 \times 10^{-6} \;\mathrm{T}, +z\end{align*}
    2. \begin{align*}1.5 \times 10^{-17} \;\mathrm{N}, -y\end{align*}
    3. \begin{align*}96 \;\mathrm{N/C}, -y\end{align*}

Ch 15: Electric Circuits—Capacitors

  1. .
    1. \begin{align*}4 \times 10^7 \;\mathrm{V}\end{align*}
    2. \begin{align*}4 \times 10^9 \;\mathrm{J}\end{align*}
  2. .
    1. \begin{align*}100 \;\mathrm{V}\end{align*}
    2. A greater voltage created a stronger electronic field, or because as charges build up they repel each other from the plate.
  3. \begin{align*}21 \;\mathrm{V}, \;\mathrm{V}\end{align*} is squared so it doesn’t act like problem \begin{align*}4\end{align*}
    1. \begin{align*}3.3 \;\mathrm{F}\end{align*}
    2. \begin{align*}54 \ \Omega\end{align*}
    1. \begin{align*}200 \;\mathrm{V}\end{align*}
    2. \begin{align*}5 \times 10^{-9} \;\mathrm{F}\end{align*}
    3. \begin{align*}2.5 \times 10^{-9} \;\mathrm{F}\end{align*}
    1. \begin{align*}6\mathrm{V}\end{align*}
    2. \begin{align*}0.3\mathrm{A}\end{align*}
    3. \begin{align*}18\mathrm{V}\end{align*}
    4. \begin{align*}3.6 \times 10^{-4}\mathrm{C}\end{align*}
    5. \begin{align*}3.2 \times 10^{-3}\mathrm{J}\end{align*}
      1. \begin{align*}80 \mu \mathrm{F}\end{align*}
      2. \begin{align*}40\mu \mathrm{F}\end{align*}
      3. \begin{align*}120 \mu \mathrm{F}\end{align*}
    1. \begin{align*}26.7\mu \mathrm{F}\end{align*}
    2. \begin{align*}166.7\mu \mathrm{F}\end{align*}
    1. \begin{align*}19.0 \times 10^3 \;\mathrm{N/C}\end{align*}
    2. \begin{align*}1.4 \times 10^{-15} \;\mathrm{N}\end{align*}
    3. \begin{align*}1.6 \times 10^{15} \;\mathrm{m/s}^2\end{align*}
    4. \begin{align*}3.3 \times 10^{-11} \;\mathrm{s}\end{align*}
    5. \begin{align*}8.9 \times 10^{-7} \;\mathrm{m}\end{align*}
    6. \begin{align*}5.1 \times 10^{-30}\end{align*}

Ch 16: Electric Circuits—Advanced

    1. \begin{align*}4.9 \times 10^{-5} \;\mathrm{H}\end{align*}
    2. \begin{align*}-9.8 \times 10^{-5} \;\mathrm{V}\end{align*}
  1. Zero
    1. Yes
    2. No
    3. Because they turn current flow on and off.
    1. \begin{align*}0.5 \;\mathrm{V}\end{align*}
    2. \begin{align*}0.05 \;\mathrm{A}\end{align*}
    3. \begin{align*}0.05 \;\mathrm{A}\end{align*}
    4. \begin{align*}5.5 \;\mathrm{V}\end{align*}
    5. \begin{align*}8.25\mathrm{V}\end{align*}
    6. \begin{align*}11 \times\end{align*}
    1. \begin{align*}On\end{align*}
    2. \begin{align*}On\end{align*}
    3. \begin{align*}On, on, off, on, off, off, on, on\end{align*}
  2. 6b. \begin{align*}10.9\mu \;\mathrm{F}\end{align*} c. \begin{align*}195 \ \Omega\end{align*} d. \begin{align*}169 \ \Omega\end{align*} e. \begin{align*}1.39 \;\mathrm{A}\end{align*} f. \begin{align*}-42^\circ\end{align*} g. \begin{align*}115\mathrm{Hz}\end{align*}

Ch 17: Light

  1. .
  2. .
  3. \begin{align*}2200\end{align*} blue wavelengths
  4. \begin{align*}65000 \ x-\end{align*}rays
  5. \begin{align*}6 \times 10^{14} \;\mathrm{Hz}\end{align*} \begin{align*}6. 3.3 \;\mathrm{m}\end{align*}
  6. .
  7. .
  8. b. vacuum & air c. \begin{align*}1.96 \times 10^8 \;\mathrm{m/s}\end{align*}
  9. \begin{align*}6.99 \times 10^{-7}\;\mathrm{m}; 5.26 \times 10^-7\;\mathrm{m}\end{align*}
  10. .
  11. .
  12. Absorbs red and green.
  13. \begin{align*}25^\circ\end{align*}
  14. .
  15. \begin{align*}33.3^\circ\end{align*}
    1. \begin{align*}49.7^\circ\end{align*}
    2. No such angle
    3. \begin{align*}48.8^\circ\end{align*}
  16. b. \begin{align*}11.4\;\mathrm{m}\end{align*} c. \begin{align*}11.5\;\mathrm{m}\end{align*}
  17. \begin{align*}85 \;\mathrm{cm}\end{align*}
  18. c. \begin{align*}+4\end{align*} units e. \begin{align*}-1\end{align*}
    1. \begin{align*}6\end{align*} units
    2. bigger; \begin{align*}M = 3\end{align*}
  19. c. \begin{align*}1.5\end{align*} units d. \begin{align*}2/3\end{align*}
  20. c. \begin{align*}3\end{align*} units e. \begin{align*}- 2/3\end{align*}
  21. c. \begin{align*}5.3\end{align*} units
  22. .
  23. b. \begin{align*}22.5 \;\mathrm{mm}\end{align*}
  24. .
  25. \begin{align*}32\;\mathrm{cm}\end{align*}
    1. \begin{align*}10.2^\circ\end{align*}
    2. \begin{align*}27\;\mathrm{cm}\end{align*}
    3. \begin{align*}20\;\mathrm{cm}\end{align*}
    1. \begin{align*}0.72\;\mathrm{m}\end{align*}
  26. .
  27. \begin{align*}54\;\mathrm{cm}, 44\;\mathrm{cm}, 21\;\mathrm{cm}, 8.8\;\mathrm{cm}\end{align*}
  28. .
  29. \begin{align*}13.5^\circ\end{align*}
  30. \begin{align*}549 \;\mathrm{nm}\end{align*}

Ch 18: Fluids

  1. \begin{align*}0.84\end{align*}
  2. \begin{align*}1.4 \times 10^5 \;\mathrm{kg}\end{align*}
    1. \begin{align*}90\end{align*}% of the berg is underwater
    2. \begin{align*}57\end{align*}%
  3. b. \begin{align*}5.06 \times 10^{-4} \;\mathrm{N}\end{align*} c. \begin{align*}7.05 \;\mathrm{m/s}^2\end{align*}
  4. \begin{align*}4.14 \;\mathrm{m/s}\end{align*}
  5. \begin{align*}40\end{align*} coins
  6. b. upward c. \begin{align*}4.5 \;\mathrm{m/s}^2\end{align*} d. Cooler air outside, so more initial buoyant force e. Thin air at high altitudes weighs almost nothing, so little weight displaced.
  7. a. At a depth of \begin{align*}10 \;\mathrm{cm}\end{align*}, the buoyant force is \begin{align*}2.9 \;\mathrm{N}\end{align*} d. The bottom of the cup is \begin{align*}3 \;\mathrm{cm}\end{align*} in radius
    1. \begin{align*}83,000 \;\mathrm{Pa}\end{align*}
    2. \begin{align*}104 \;\mathrm{N}\end{align*}
    3. \begin{align*}110 \;\mathrm{N}\end{align*}
    1. \begin{align*}248 \;\mathrm{kPa}\end{align*}
    2. \begin{align*}591 \;\mathrm{kPa}\end{align*}
    3. \begin{align*}1081 \;\mathrm{kPa}\end{align*}
  8. .
  9. \begin{align*}.0081\end{align*}
    1. \begin{align*}12500 \;\mathrm{J/m}^3\end{align*}
    2. \begin{align*}184 \;\mathrm{kPa}\end{align*}
    3. \begin{align*}1.16 \;\mathrm{kW}\end{align*}
    4. \begin{align*}2.56 \;\mathrm{kW}\end{align*}
    5. \begin{align*}11.8 \;\mathrm{A}\end{align*}
    6. $\begin{align*}12.60\end{align*}
    1. \begin{align*}611 \;\mathrm{kPa}\end{align*}
    2. \begin{align*}6 \;\mathrm{atm}\end{align*}
  10. b. \begin{align*}500,000 \;\mathrm{N}\end{align*}
    1. \begin{align*}27 \;\mathrm{m/s}^2, (2.7 \;\mathrm{g})\end{align*} upward
    2. \begin{align*}1600 \;\mathrm{N}\end{align*}
    3. \begin{align*}2200 \;\mathrm{N}\end{align*}
    1. \begin{align*}10 \;\mathrm{N}\end{align*}
    2. \begin{align*}10.5 \;\mathrm{N}\end{align*}
    3. \begin{align*}11 \;\mathrm{N}\end{align*}
    4. \begin{align*}11 \;\mathrm{N}\end{align*}
  11. a. “The Thunder Road” b. \begin{align*}2.0 \;\mathrm{m}\end{align*} (note: here and below, you may choose differently) c. \begin{align*}33.5 \;\mathrm{m}^3\end{align*} e. \begin{align*}3.5 \;\mathrm{million} \;\mathrm{N}\end{align*} f. \begin{align*}111 \;\mathrm{MPa}\end{align*}

Ch 19: Thermodynamics and Heat Engines

  1. .
  2. .
  3. .
  4. .
  5. .
  6. .
  7. .
  8. .
  9. .
  10. .
  11. .
  12. .
  13. .
  14. .
  15. .
  16. .
  17. .
  18. \begin{align*}517 \;\mathrm{m/s}\end{align*}
  19. \begin{align*}1.15 \times 10^{12}\;\mathrm{K}\end{align*}
  20. .
  21. \begin{align*}40 \;\mathrm{N}\end{align*}
  22. \begin{align*}\approx \ 10^{28}\end{align*} molecules
    1. \begin{align*}21,000 \;\mathrm{Pa}\end{align*}
    2. Decreases to \begin{align*}61,000 \;\mathrm{Pa}\end{align*}
    3. \begin{align*}5.8 \;\mathrm{km}\end{align*}
    1. No
    2. allowed by highly improbable state. More likely states are more disordered.
  23. a. \begin{align*} 8.34 \times 10^{23}\end{align*} b. \begin{align*}6.64 \times 10^{-27}\;\mathrm{kg}\end{align*} c. \begin{align*}1600 \;\mathrm{m/s}\end{align*} d. \begin{align*}744 \;\mathrm{kPa}\end{align*} e. \begin{align*}4.2 \times 10^{20}\end{align*} or \begin{align*}0.0007 \;\mathrm{moles}\end{align*} g. \begin{align*}0.00785 \;\mathrm{m}^3\end{align*}
    1. \begin{align*}1.9 \;\mathrm{MW}\end{align*}
    2. \begin{align*}0.56 \;\mathrm{MW}\end{align*}
    3. \begin{align*}1.3 \;\mathrm{Mw}\end{align*}
    1. \begin{align*}54\end{align*}%
    2. \begin{align*}240 \;\mathrm{kW}\end{align*}
    3. \begin{align*}890 \;\mathrm{kW}\end{align*}
    4. \begin{align*}590 \;\mathrm{kW}\end{align*}
    5. \begin{align*}630 \;\mathrm{kg}\end{align*}
    1. \begin{align*}98\end{align*}%
    2. \begin{align*}4.0\end{align*}%
    3. \begin{align*}12\end{align*}%
  24. \begin{align*}14800 \;\mathrm{J}\end{align*}
  25. \begin{align*}12,000 \;\mathrm{J}\end{align*}
  26. b. \begin{align*}720 \;\mathrm{K}, 300 \;\mathrm{K}, 600 \;\mathrm{K}\end{align*} c. isochoric; isobaric d. \begin{align*}\;\mathrm{C}\end{align*} to \begin{align*}\;\mathrm{A}; \;\mathrm{B-C}\end{align*} e. \begin{align*}0.018 \;\mathrm{J}\end{align*}
  27. b. \begin{align*}300 \;\mathrm{K}, 1200 \;\mathrm{K}\end{align*}
    1. \begin{align*}1753 \;\mathrm{J}\end{align*}
    2. \begin{align*}-120 \;\mathrm{J}\end{align*}
    3. \begin{align*}80 \;\mathrm{J}\end{align*}
    4. \begin{align*}35 \;\mathrm{J}\end{align*}
    5. \begin{align*}-100 \;\mathrm{J}, 80 \;\mathrm{J}, 80 \;\mathrm{J}\end{align*}

Ch 20: Special and General Relativity

  1. longer
  2. \begin{align*}\gamma = \infty\end{align*}, the universe would be a dot
  3. \begin{align*}76.4 \;\mathrm{m}, 76.4\;\mathrm{m}\end{align*}
  4. .
  5. \begin{align*}\gamma = 1.002\end{align*}
  6. \begin{align*}9.15 \times 10^7\;\mathrm{m/s}\end{align*}
  7. \begin{align*}2.6 \times 10^8\;\mathrm{m/s}\end{align*}
    1. \begin{align*}0.659 \;\mathrm{km}\end{align*}
    2. \begin{align*}22.4\end{align*}
    3. \begin{align*}4.92\times10^{-5}\;\mathrm{m/s}\end{align*}
    4. \begin{align*}14.7 \;\mathrm{km}\end{align*}
  8. \begin{align*}2900\;\mathrm{m}\end{align*}
  9. \begin{align*}1.34 \times 10^{-57}\;\mathrm{m}\end{align*}
  10. \begin{align*} 0.303 \;\mathrm{s}\end{align*}
  11. \begin{align*}2.9 \times 10^{-30}\mathrm{kg}\end{align*}, yes harder to accelerate
    1. f
    2. c
  12. \begin{align*}4.5 \times 10^{16} \;\mathrm{J}; 1.8 \times 10^{13}\end{align*} softballs
    1. \begin{align*}1.568 \times 10^{-13} \;\mathrm{J}\end{align*}
    2. \begin{align*}3.04 \times 10^6 \;\mathrm{J}\end{align*}

Ch 21: Radioactivity and Nuclear Physics

  1. .
  2. .
  3. .
  4. .
  5. .
    1. Substance \begin{align*}A\end{align*} decays faster than \begin{align*}B\end{align*}
    2. Substance \begin{align*}B\end{align*} because there is more material left to decay.
    1. \begin{align*}^{219}{_{88}}\mathrm{Ra} \rightarrow ^{215}{_{86}}\mathrm{Rn} + ^{4}{_{2}}\mathrm{He}\end{align*}
    2. \begin{align*}^{158}{_{63}}\mathrm{Eu} \rightarrow ^{158}{_{64}}\mathrm{Gd} + ^{0}{_{-1}}e^-\end{align*}
    3. \begin{align*}^{53}{_{22}}\mathrm{Ti} \rightarrow ^{53}{_{23}}\mathrm{Va} + ^{0}{_{-1}}e^-\end{align*}
    4. \begin{align*}^{211}{_{83}}\mathrm{Bi} \rightarrow ^{207}{_{81}}\mathrm{Tl} + ^{4}{_{2}}\mathrm{He}\end{align*}
    1. \begin{align*}5 \times 10^{24}\end{align*} atoms
    2. Decay of a lot of atoms in a short period of time
    3. \begin{align*}2.5 \times 10^{24}\end{align*} atoms
    4. \begin{align*}\frac{1}{2}\end{align*}
    5. \begin{align*}26.6\end{align*} minutes
  6. The one with the short half life, because half life is the rate of decay.
    1. Substance \begin{align*}B = 4.6 \;\mathrm{g}\end{align*} and substance \begin{align*}A = 0.035 \;\mathrm{g}\end{align*}
    2. substance \begin{align*}B\end{align*}
  7. \begin{align*}1.2 \;\mathrm{g}\end{align*}
  8. \begin{align*}125 \;\mathrm{g}\end{align*}
  9. \begin{align*}0.46\end{align*} minutes
  10. \begin{align*}t = 144,700\end{align*} years
  11. \begin{align*}0.0155 \;\mathrm{g}\end{align*}
  12. \begin{align*}17\end{align*} years
  13. \begin{align*}49,000\end{align*} years

Ch 22: Standard Model of Particle Physics

  1. strange
  2. some type of meson
  3. Electron, photon, tau\begin{align*}\ldots\end{align*}
  4. Neutron, electron neutrino, \begin{align*}Z^0\end{align*}
  5. Neutron, because it doesn’t have electrical charge
  6. No, because it doesn’t have electrical charge
  7. Two anti-up quarks and an anti-down quark
  8. Lepton number, and energy/mass conservation
  9. Yes, \begin{align*}W^+, W^-\end{align*}, because they both have charge
  10. The weak force because it can interact with both quarks and leptons
  11. Yes; a,b,c,e; no; d,f
  12. The standard model makes verifiable predictions, string theory makes few verifiable predictions.

Ch 23: Feynman Diagrams

  1. Allowed: an electron and anti-electron(positron) annihilate to a photon then become an electron and anti-electron(positron) again.
  2. Not allowed: electrons don’t go backward though time, and charge is not conserved
  3. Not allowed: lepton number is not conserved
    1. Allowed: two electrons exchange a photon
    2. Not allowed: neutrinos do not have charge and therefore cannot exchange a photon.
    1. Allowed: an electron and an up quark exchange a photon
    2. Not allowed: lepton number not conserved
  4. Not allowed: quark number not conserved
  5. Allowed: electron neutrino annihilates with a positron becomes a \begin{align*}W^+\end{align*} then splits to muon and muon neutrino.
  6. Allowed: up quark annihilates with anti-up quark becomes \begin{align*}Z^0\end{align*}, then becomes a strange quark and anti-strange quark
  7. Not allowed: charge not conserved
  8. Allowed: this is a very rare interaction
  9. Not allowed: electrons don’t interact with gluons
  10. Not allowed: neutrinos don’t interact with photons
  11. Allowed: the electron and the positron are exchanging virtual electron/positron pairs
  12. Allowed: this is beta decay, a down quark splits into an up quark an electron and an electron neutrino via a \begin{align*}W^-\end{align*} particle.
  13. Allowed: a muon splits into an muon neutrino, an electron and an electron neutrino via a \begin{align*}W^-\end{align*} particle.

Ch 24: Quantum Mechanics

    1. \begin{align*}6.752 \times 10^{-26} J, 2.253 \times 10^{-34} \;\mathrm{kgm/s}\end{align*}
    2. \begin{align*}5.96 \times 10^{-20} J, 1.99 \times 10^{-28} \;\mathrm{kgm/s}\end{align*}
    3. \begin{align*}4.90 \times 10^{-28} J, 1.63 \times 10^{-36} \;\mathrm{kgm/s}\end{align*}
    1. \begin{align*}1.94 \;\mathrm{eV}, 1.04 \times 10^{-27} \;\mathrm{kgm/s}\end{align*}
    2. \begin{align*}12.7 \;\mathrm{eV}, 6.76 \times 10^{-27} \;\mathrm{kgm/s}\end{align*}
    3. \begin{align*}5.00 \;\mathrm{eV}, 2.67 \times 10^{-21} \;\mathrm{kgm/s}\end{align*}
    1. \begin{align*}.0827 \;\mathrm{nm}\end{align*}
    2. \begin{align*}4.59 \times 10^{-4}\;\mathrm{nm}\end{align*}
    3. \begin{align*}.942 \;\mathrm{nm}\end{align*}
  1. \begin{align*}1.03 \times 10^{-20}\;\mathrm{m}\end{align*}
    1. \begin{align*}36 \;\mathrm{nm}\end{align*}
    2. no
    3. \begin{align*}380 \;\mathrm{nm}, 73 \;\mathrm{nm}, 36 \;\mathrm{nm}, 92 \;\mathrm{nm}, 39 \;\mathrm{nm}\end{align*}
  2. \begin{align*}.80 \;\mathrm{V}\end{align*}
  3. \begin{align*}.564 \;\mathrm{nm}\end{align*}
    1. \begin{align*}.124 \;\mathrm{nm}\end{align*}
    2. \begin{align*}.00120 \;\mathrm{nm}\end{align*}
  4. \begin{align*}24,600 \;\mathrm{m/s}\end{align*}
  5. \begin{align*}1.84 \times 10^8\;\mathrm{m/s}\end{align*}
    1. \begin{align*} .491 \;\mathrm{m/s}\end{align*}
    2. \begin{align*}3.14 10^7\;\mathrm{J}\end{align*}
    3. \begin{align*}64 \;\mathrm{Mw}\end{align*}
    4. \begin{align*}1.55 \;\mathrm{pm}\end{align*}
  6. \begin{align*}3.27 \;\mathrm{eV}\end{align*}
  7. .
  8. b. \begin{align*}15\end{align*} c. \begin{align*}182 \;\mathrm{nm}, 188 \;\mathrm{nm}, 206 \;\mathrm{nm}, 230 \;\mathrm{nm}\end{align*}
  9. \begin{align*}-10.3 \;\mathrm{eV}, -3.82 \;\mathrm{eV}, -2.29 \;\mathrm{eV}, -1.83 \;\mathrm{eV}\end{align*}
    1. \begin{align*}4.19 \times 10^7\;\mathrm{m/s}\end{align*}
    2. \begin{align*}1.70 \times 10^{-11}\;\mathrm{m}\end{align*}
    3. \begin{align*}1.95^\circ\end{align*}
    4. \begin{align*}.068 \;\mathrm{m}\end{align*}
    1. \begin{align*}1.89 \;\mathrm{V}\end{align*}
    2. \begin{align*}1.60 \;\mathrm{A}\end{align*}
    3. \begin{align*}1.25 \ \Omega\end{align*}
    1. \begin{align*}4.40 \times 10^{-24}\;\mathrm{kgm/s}\end{align*}
    2. \begin{align*}1.17 \times 10^{-24}\;\mathrm{kgm/s}\end{align*}
    3. \begin{align*}3.23 \times 10^{-24}\;\mathrm{kgm/s}\end{align*}
    4. \begin{align*}3.76 \times 10^7\;\mathrm{m/s}\end{align*}
    1. \begin{align*}1.1365 \times 10^{-22}\;\mathrm{kgm/s}\end{align*}
    2. \begin{align*}5.860 \;\mathrm{pm}\end{align*}
    3. \begin{align*}^242\;\mathrm{Cu} \rightarrow ^4\mathrm{He} + ^238\mathrm{Pu}\end{align*}
    4. \begin{align*}238.0497 \;\mathrm{amu}\end{align*}
    5. \begin{align*}17.7 \;\mathrm{cm}\end{align*}
    6. \begin{align*}-y\end{align*}
    7. \begin{align*}+y, 34.2 \;\mathrm{N/C}\end{align*}

Ch 25: Global Warming

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