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

Created by: CK-12

## Ch 1: Units and Problem Solving

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

## Ch 2: Energy Conservation

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

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

## Ch 4: Two-Dimensional and Projectile Motion

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

## Ch 5: Newton’s Laws

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

## Ch 6: Centripetal Forces

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

## Ch 7: Momentum Conservation

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

## Ch 8: Energy & Force

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

## Ch 9: Rotational Motion

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

## Ch 10: Simple Harmonic Motion

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

## Ch 11: Wave Motion and Sound

1. $390 \;\mathrm{Hz}$
1. $4 \;\mathrm{Hz}$
2. It was being driven near its resonant frequency.
3. $8 \;\mathrm{Hz}, 12 \;\mathrm{Hz}$
4. (Note that earthquakes rarely shake at more than $6 \;\mathrm{Hz}$).
2. .
3. .
1. $7$ nodes including the $2$ at the ends
2. $3.6 \;\mathrm{Hz}$
4. $1.7 \;\mathrm{km}$
1. $1.7 \;\mathrm{cm}$
2. $17 \;\mathrm{m}$
1. $4.3 \times 10^{14} \;\mathrm{Hz}$
2. $2.3 \times 10^{-15} \;\mathrm{s} -$ man that electron is moving fast
1. $2.828 \;\mathrm{m}$
2. $3.352 \;\mathrm{m}$
3. $L = 1/4 \ \lambda$ so it would be difficult to receive the longer wavelengths.
5. Very low frequency
6. b. Same as closed at both ends
7. .
8. $1.9 \;\mathrm{Hz}$ or $2.1 \;\mathrm{Hz}$.
9. $0.53 \;\mathrm{m}$
10. $2.2 \;\mathrm{m}, 36 \;\mathrm{Hz}; 1.1 \;\mathrm{m}, 73 \;\mathrm{Hz}; 0.733 \;\mathrm{m}, 110 \;\mathrm{Hz}; 0.55 \;\mathrm{m}, 146 \;\mathrm{Hz}$
11. $430\;\mathrm{Hz}; 1.3 \times 10^3 \;\mathrm{Hz}; 2.1 \times 10^3 \;\mathrm{Hz}; 3.0 \times 10^3 \;\mathrm{Hz};$
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. $80 \;\mathrm{Hz}; 0.6 \;\mathrm{m}$
1. $0.457 \;\mathrm{m}$
2. $0.914 \;\mathrm{m}$
3. $1.37 \;\mathrm{m}$
14. $2230 \;\mathrm{Hz}; 2780 \;\mathrm{Hz}; 2970 \;\mathrm{Hz}$
15. $498 \;\mathrm{Hz}$
16. $150 \;\mathrm{m/s}$

## Ch 12: Electricity

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

## Ch 13: Electric Circuits – Batteries and Resistors

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

## Ch 14: Magnetism

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

## Ch 15: Electric Circuits—Capacitors

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

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

## Ch 17: Light

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

## Ch 18: Fluids

1. $0.84$
2. $1.4 \times 10^5 \;\mathrm{kg}$
1. $90$% of the berg is underwater
2. $57$%
3. b. $5.06 \times 10^{-4} \;\mathrm{N}$ c. $7.05 \;\mathrm{m/s}^2$
4. $4.14 \;\mathrm{m/s}$
5. $40$ coins
6. b. upward c. $4.5 \;\mathrm{m/s}^2$ 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 $10 \;\mathrm{cm}$, the buoyant force is $2.9 \;\mathrm{N}$ d. The bottom of the cup is $3 \;\mathrm{cm}$ in radius
1. $83,000 \;\mathrm{Pa}$
2. $104 \;\mathrm{N}$
3. $110 \;\mathrm{N}$
1. $248 \;\mathrm{kPa}$
2. $591 \;\mathrm{kPa}$
3. $1081 \;\mathrm{kPa}$
8. .
9. $.0081$
1. $12500 \;\mathrm{J/m}^3$
2. $184 \;\mathrm{kPa}$
3. $1.16 \;\mathrm{kW}$
4. $2.56 \;\mathrm{kW}$
5. $11.8 \;\mathrm{A}$
6. \$$12.60$
1. $611 \;\mathrm{kPa}$
2. $6 \;\mathrm{atm}$
10. b. $500,000 \;\mathrm{N}$
1. $27 \;\mathrm{m/s}^2, (2.7 \;\mathrm{g})$ upward
2. $1600 \;\mathrm{N}$
3. $2200 \;\mathrm{N}$
1. $10 \;\mathrm{N}$
2. $10.5 \;\mathrm{N}$
3. $11 \;\mathrm{N}$
4. $11 \;\mathrm{N}$
11. a. “The Thunder Road” b. $2.0 \;\mathrm{m}$ (note: here and below, you may choose differently) c. $33.5 \;\mathrm{m}^3$ e. $3.5 \;\mathrm{million} \;\mathrm{N}$ f. $111 \;\mathrm{MPa}$

## Ch 19: Thermodynamics and Heat Engines

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

## Ch 20: Special and General Relativity

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

## Ch 21: Radioactivity and Nuclear Physics

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

## Ch 22: Standard Model of Particle Physics

1. strange
2. some type of meson
3. Electron, photon, tau$\ldots$
4. Neutron, electron neutrino, $Z^0$
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, $W^+, W^-$, 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 $W^+$ then splits to muon and muon neutrino.
6. Allowed: up quark annihilates with anti-up quark becomes $Z^0$, 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 $W^-$ particle.
13. Allowed: a muon splits into an muon neutrino, an electron and an electron neutrino via a $W^-$ particle.

## Ch 24: Quantum Mechanics

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

Feb 23, 2012

Sep 15, 2014