Halliday Fundamental 10th

TARGET DECK Physics::Halliday Fundamental 10th

Ch 10 Rotation

Problem 10.43:: $\frac{1}{3} M (a^{2} + b^{2})$

Problem 10.41::(a) $I = 5 m d^{2} + \frac{8}{3} M d^{2}$
(b) $K = \frac{1}{2} (5 m d^{2} + \frac{8}{3} M d^{2}) ω^{2}$

Problem 10.51::(a)a= $0.060 m / s^{2}$
(b) $T_{2} = m_{2} (g - a)$
(c) $T_{1} = m_{1} (g + a)$
(d) $α = \frac{a}{r}$
(e) $I = \frac{( T _{2} - T _{1} ) R}{α}$

Problem 10.52:: $α = \frac{2 ( R ( F _{1} - F _{2} ) - r F _{3} )}{M R ^{2}}$

Problem 10.53:: $\frac{MR ω}{2 t} + F_{1}$

Problem 10.54::(a) $α = \frac{m g d}{I}$
(b) $α = \frac{m g d + F _{a} h}{I}$

Problem 10.56:: $α = \frac{g ( L _{1} - L _{2} )}{L _{1}^{2} + L _{2}^{2}}$

Problem 10.66:: $m g Δ h = \frac{1}{2} (\frac{2}{3} M + \frac{I _{2}}{r ^{2}} + m) v^{2}$

Problem 10.67:: $4 \frac{6 g}{65 R}$

Problem 10.69:: $πh ρ (\frac{1}{2} r^{4} + \frac{1}{2} R^{4} + r^{2} (r + R)^{2})$

Problem 10.71::(b) $α = \frac{2 θ}{t ^{2}}$
(b) $a = \frac{2 Rθ}{t ^{2}}$
(c) $T_{1} = m (g - a)$
(d) $T_{2} = T_{1} - \frac{I α}{R}$

Problem 10.95:: $\frac{1}{2} M (3 a^{2} + b^{2}) ω^{2}$

Problem 10.98:: $I = \frac{r ( R F _{a pp} - r m ( g + a ))}{a}$

11 Rolling, Torque, And Angular Momentum

Problem 11.9:: $s = \frac{20}{7} (H - h) h$

Problem 11.11::(a) $f_{s} = F - ma (- \overset{x}{^})$
(b) $I = \frac{R ^{2} ( F - ma )}{a}$

Problem 11.13:: $β = \frac{2 h}{r} - 1$

12 Equilibrium and Elasticity

Problem 12.25:: $F = \frac{m g 2 r h - h ^{2}}{r - h}$

Problem 12.63::(a) $\frac{1}{2} L$
(b) $\frac{1}{4} L$
(c) $\frac{1}{6} L$
(d) $\frac{1}{8} L$

Problem 12.65::(a) $T = \frac{L - h}{h} F$
(b)( $T cos θ - F) (\hat{i}) + (T sin θ + F_{g}) (\hat{j})$

Problem 12.69:: $sin (θ_{1} + θ_{2}) = \frac{m g}{2 T} sin θ_{1}$

Problem 12.72:: $T_{ab} = \frac{M g}{t a n θ _{1} c o s θ _{2} - s i n θ _{2}}$

Problem 12.73::(a),(b) $F_{g, x} = \frac{m g \frac{L ^{2} - h ^{2}}{2} - F ( L - d ) \frac{h}{L}}{h}$
(c) $F = \frac{m g \frac{L ^{2} - h ^{2}}{2} + μ _{s} m g h}{r} (r = \frac{L - d}{L} h)$

Problem 12.79:: $b_{1} = \frac{2}{3} L$
$b_{2} = \frac{1}{2} L$
$h = \frac{7}{6} L$

14 Fluids

Problem 14.10:: $d + \frac{F}{ρ g A}$

Problem 14.29:: $\frac{k x}{18 g}$

Problem 14.65:: $V = \frac{2 a ^{2} Δ p}{ρ ( a ^{2} - A ^{2} )}$
$R = A \frac{2 a ^{2} Δ p}{ρ ( a ^{2} - A ^{2} )}$

Problem 14.86::1.25

15 Oscillations

Problem 15.25:: $T = 2 π \frac{F _{g}}{g k}$

Problem 15.41::(a) $I = \frac{1}{2} m r^{2} + m (L + r)^{2} + \frac{1}{3} M L^{2}$
(b) $d = \frac{m ( L + r ) + \frac{1}{2} L M}{m + M}$
(c) $T = 2 π \frac{I}{( m + M ) g d}$

Problem 15.47:: $T = 2 π \frac{\frac{1}{2} m r ^{2} + m d ^{2}}{m g d}$

Problem 15.48::(a) $T = 2 π \frac{\frac{1}{12} ( a ^{2} + b ^{2} ) + r ^{2}}{g r}$
(b) $r = \frac{a ^{2} + b ^{2}}{12}$

Problem 15.53:: $T = 2 π \frac{m}{3 k}$

Problem 15.70:: $ω = \frac{k r ^{2}}{m R ^{2}}$

Problem 15.92:: $T = \frac{\frac{1}{2} M r ^{2} + M ( L + r ) ^{2}}{m g ( L + r )}$

Problem 15.100::(a) $\frac{1}{3} k x^{2}$
(b) $\frac{1}{6} k x^{2}$
(c) $\frac{2}{3} M v_{c m} a_{c m} + k x_{c m} v_{c m}$

19 The Kinetic Theory of Gases

Problem 19.17:: $P^{'} = \frac{P _{A} + 4 P _{B} \frac{T _{A}}{T _{B}}}{1 + \frac{4 T _{A}}{T _{B}}}$

Problem 19.37::(a) $\frac{2}{3}$
(b) $\frac{11}{9}$
(c) $\frac{31}{18}$
(d) $\frac{1}{3}$

Problem 19.44::(a) $\frac{5}{2} (P_{c} V_{b c} - P_{ab} V_{a})$
(b) $Δ Q = 3 P_{c} V_{b c} - 3 P_{ab} V_{a} + \frac{1}{2} P_{ab} V_{b c} - \frac{1}{2} P_{c} V_{a}$
(c) $Δ Q = \frac{5}{2} P_{c} V_{b c} - \frac{7}{2} P_{ab} V_{a} + P_{ab} V_{b c}$

Problem 19.59::-15J

Problem 19.77::(a) $C = \frac{3}{v _{0}^{3}}$
(b) $v_{a vg} = \frac{3}{4} v_{0}$
(c) $\frac{3}{5} v_{0}$

Problem 19.87::-3.0J

Problem 19.89:: $h = \frac{P _{0} + ρ g \frac{L}{2}}{ρ g}$

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