Chapter 2

#6: (a) Distance = 14.1 m, Displacement = 9.0 m
      (b) Increases
      (c) Decreases
      (d) Distance = 28.3 m, Displacement = 0.

#18) v_avg = 64 km/hr

#104)(a) 1.87 m/s
      (b) 1.01 m/s

A) v_A = 2.5 m/s,v_B = 4.0 m/s, v_C = 3.25 m/s

C) v_A = 2.5 m/s,v_B = 1.67 m/s, v_C = 2.0 m/s
      [{v_A + v_B}/2 = 2.08 m/s]

D) 66.0 km/hr

E) After t = 0 B is ahead.
      They meet at t = 50 s, x = 7,750 m.
      A does not catch up in 1500 m, so B wins.

Chapter 3

#66) 1.68 km, 61 deg. S of W.

#72) 3.73 m/s²

A) A+B: Around 3.8, 10 deg. E of N
      A-B: Around 2.5, 20 deg. W of N
      A-2B: Around 1.5, 45 deg. W of N

B) a ~ 5.1 m/s²

C) (i) 2.8 m/s², 225 deg.

      (ii) 2.0 m/s², 270 deg.

      (iii) 0.

D) t = 2, x = 7.7, y = 6.71, r = 10.1, beta = 41 deg.
t = 4, x = 12.4, y = 8.42, r = 15.0, beta = 34 deg.

Chapter 4

A) R = 21.8 m

Chapter 5

#4) 40.6 kg

#40) 1.9 m/s², up; velocity not determined.

Chapter 6

A) x = 10 deg., sinx/x = .9950
x = 5 deg., sinx/x = .9987
x = 2 deg., sinx/x = .9997
x = 1 deg., sinx/x = 1.0000

C) a = 2.17 m/s²; T = 21.4 N

Chapter 8

#4) minus 1100 J, independent of mass

#30) 3,220 N/m; 0.4 m/s

#36) v = {[2(m₂-m₁)gh]/[m₂+m₁]}^1/2

       v= 1.10 m/s

#58) 10.3 degrees

#96) h > (5/2)r

A) 0.88 m/s

B) 0.92 m/s

Chapter 9

#4) v = -0.69 m/s; KE = 0.40 J

#30) 2.93 m/s

#34) 0.035 m

#42) left to right: (1/3)v₀, (4/9)v₀, (16/9)v₀

#46) 0.58 m

#50) y_cm = -(1/10)L

C) v₁ = 2.5 m/s; v₂ = 12.5 m/s; f₁ = 0.062; f₂ = 0.938

D) 2.40 s after the first collision

E)    (a) v = 2.70 m/s; angle = -14.8 degrees

       (b) 48%

F)    (a) 0.94 m/s, to the right

       (b) fraction = 0.67

G)    (a) 1.05 m/s; 18 degrees below positive x axis.

       (b) fraction = 0.63

Chapter 10

#8) 7.27 X 10^-5 rad/s

#30) 1.44 X 10^-4 m/s

#70) 2.1 kg

#110) (a) 357 N; (b) 918 N; (c) 638 N

A) 0.105 rad/s; 1.75 X 10^-3 rad/s

B) 0.01 kg

C) v = 1.60 m/s; a = 1.48 m/s²

D) 0.441 m/s

E) 463 m/s

F) 2.99 X 10⁴ m/s

G) Diagram (a)

Chapter 11

#26) 42.0 kg; 0.74 m

#28) (a) 2.3 m; (b) 1.56 m; (c) no change

A)    (a) 9.38 X 10⁴¹ kg-m²/s
       (b) 1.93 X 10⁴³ kg-m²/s
      (c) ratio = 21

B) 1.94 rev/s

C) Fraction of KE lost = 50%

D) All KE lost

F) angular freq. = 8.6 rad/s; freq. = 1.4 rev/s

Chapter 12

Note: Answers in the textbook for problems 9, 15 and 35 are not correct.

#9) 4.79 X 10²⁰ N; 24.4 degrees

#15) 2.64 X 10³ km

#35) (a) satellite 2; (b) 5.59 X 10³ m/s; (c) 4.56 X 10³ m/s

A) 726 N

B) 9.08 m/s²

C) 1.62 m/s²

D) 0.037 m/s²

F) v_esc = [2Gm_moon/r_moon]^1/2; 2.36 X 10³ m/s

G) v_orbit = 7.90 X 10³ m/s; 1.4 hours

H) mass = 6.02 X 10²⁴ kg

I) 500 km

J) 5.73 X 10³ m/s

K) R = 2GM/c²

L) 14.7 km; density = 7.5 X 10¹⁷ kg/m³

M) 1.8 X 10³⁹ kg; 10⁹ stars

O) r = 4.22 X 10⁷ m; r/R_E = 6.6

Chapter 13

B) -.26, -.48, -.65, -.76
-.64, -.23, +.27, +.66, +.63

C) x: .2, 0, -.2, 0, .2, 0
v: 0, -1.05, 0, +1.05, 0, -1.05

F) 0.39 s

G) T = 2(pi)[m/(k₁ + k₂)]^1/2

H) x: 3.66 m, -4.95 m, -4.94 m
t: 1.04 s

I) v_avg = -.08 m/s; k = 1.97 N/m; v_inst = -0.126 m/s

J) v = 0.155 m/s for x = +1 and -1; x = +0.0205 m

K) T = 5070 s = 1.41 hours

Chapter 14

#14) 0.19 s

#44) 14.6 m/s

Chapter 15

#8) 1.53 X 10⁶ Pa

#48) 20% under water

D) cylinder moves up

E) 4.0 cm

F) density = 15,000 kg/m³

Chapter 16

#36) 120 degrees Celsius

#38) 24.0 degrees C.

#76) a) Probably aluminum (c = 892 J/kg-K)
      b) 54.4 J/s

#88) 3 seconds before 10 AM

A) 12 cm, 1 degree = 1 mm

Chapter 17

#58) 2.2 kg

#60) a) No ice remains, final temp. = 30 deg.
      b) Mass is doubled.

#6) 14%

#14) a) 3.9 X 10²⁴
      b) 1.26; cubed root of 2

#20) 160 kPa

#26) 20 K

#28)a) 4.0 X 10⁶ Pa
      b) 1.18 X 10^-20 J
      c) Pressure is half; kinetic energy the same.

A) p = 13.5 kPa; pressure multiplied by 4

B) 14.7 kPa

C) p =(1/3)(N_A/V) [n_Am_Av_A² + n_Bm_Bv_B²]

D) a) 0.833
      b) 1.12
      c) 1.00

E) "p" = (1/2)[N/(area)]mv²

F) 0.8 moles, 25.6 g

G) density of steam = 0.589 kg/m³; ice/steam = 1,562; s/a = 11.6

H) 1.91

I) N = 336; speed of pellets decreases because of gravity

Chapter 18

#8) a) 468 K; b) decreases

#52) a) 0.88
      b) 300 J
      c) 8.3

#66) 1.12 X 10⁴ J/K

#70) 1.12 X 10³ J/K

#72) 2.6 J/K

A) 12.8 deg. C

B) 231 J/kg-C

C) 75 deg. C

D) 13.3 deg. C

E) 20 g

F) 724 J/kg-C

G) 356 J/kg-C

H) a) L = 0.622 m; W_f = -1.92m; mu = 0.411
      b) Q = 0; W = 0; change in macro energy = -1.92m; change in micro energy = +1.92m; change in temp. = 0.00192 deg. C

I) W_P = 50 J; Q = 0; change in macro energy = +22.5 J; change in micro energy = + 27.5 J

J) 2.6 J/K {Assumption: Cube is 3 cm on a side.}

K) 4.0 J/K {Assumptions: Coffee is 95 deg. C, milk is 4.4 deg. C (40 deg. F); coffee is 8 ounces, milk is 1 ounce.}

L) Q₁ = 10⁴ J; Q₂ = 3.15 X 10⁴ J
eff = 14%