A) At each point along the pipe, the volume of fluid passing by is given by dv dt = Av, thus, the two velocities are: v n. + ρgy 1

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1 1) The horizontal pipe hon in Fig. 1 ha a diameter of 4.8 cm at the ider portion and 3.7 cm at the contriction. Water i floing in the pipe and the dicharge from the pipe i 6.50 x -3 m 3 /. A) Find the flo peed at the ide and narro portion. (8 pt.) B) Find the preure difference beteen thee portion. (6 pt.) C) The difference in height beteen the mercury column in the U-haped tube. The denity of Hg i 13.6 g/cm 3. (6 pt.) A) At each point along the pipe, the volume of fluid paing by i given by dv dt Av, thu, the to velocitie are: v n v 3.7 v 4.8 n 3.59 m/. 6.5x 3 m 3 / 6.04 m/, and π(3.7x m) / 4 B) Uing Bernoulli equation: p ρv 1 + ρgy 1 p + 1 ρv + ρgy, and uing the ame height, the preure difference i jut: 1 ρv 1 1 ρv v 1 (00kg/ m3 )[(6.04m/ ) (3.59m/ ) ] 1.18 x 4 Pa. C) Again, uing Bernoulli equation, but thi time velocitie are zero, thu p ρgh h p ρg 1.18x 4 Pa 8.85 cm. 13.6g/ cm 3 3 kg/ g 9.8m/ 6 m 3 3 / cm

2 ) A 1.-kg monkey rench i pivoted 0.3 m from it center of ma and alloed to ing a a phyical pendulum. The period for mall-angle ocillation i A) What i the moment of inertia of the rench about an axi through the pivot? (6 pt.) B) f the rench i initially diplaced 0.15 radian from it equilibrium poition, hat i the angular peed of the rench a it pae through the equilibrium poition? (6 pt.) C) What i the total energy of the ytem in part B? (6 pt.) A) ω mgd mgdt 4π 1.kg 9.8m/ 0.3m (0.94) 4π 7.9 x - kg m. B) For mall angle, e aume the motion i SHM, thu, Θ(t) Θ o co(ωt +φ ). The initial condition imply that hen Θ(t) 0, the angular velocity ill be given by ωθ o π 0.15rad 1.00 rad/ C) Given that ET+U and i contant, ill calculate at Θ(t) 0, hich give, E 1 dθ dt 1 7.9x kg m (1.00rad / ) 3.95 x - Nm.

3 3) The ound of a hip onar ytem operate at a frequency of 4.0 khz. The peed of ound in ater i 148 m/. The hip i at ret in the ater. A) What i the avelength of the ave emitted by the ource? (6 pt.) B) What i the difference in frequency beteen the directly radiated ave and the ave reflected from a hale traveling directly toard the hip at 4.95m/? (6 pt.) C) The pecific gravity of eaater i 1.03, calculate the Bulk modulu of the eaater. (6 pt.) A) λ v f 148m/ 4x 3 Hz 6.18 cm. B) The hale receive the onar ignal at a frequency of: f 1+ v v f, thi i alo the frequency that the hale remit the ave, hich i detected by the hip no at ' v a frequency of: f f, o the detected frequency, in term of the emitted frequency i jut: v + v f. Thu the frequency difference i jut ' f f f v + v 1 f v 4.95m/ f 4kHz 161 Hz. 148m 4.95m/ C) v B ρ B ρv kg/ m 3 (148m/ ).6 x 9 Pa.

4 4) The lunch hitle of a local mill radiate uniformly in all direction at 0 o C. At a ditance of 50m from the hitle the ound intenity level i 75 db. The frequency i 448 Hz. For 0 o air the denity i 1. kg/m 3, the peed of ound i 344 m/ and the Bulk modulu i 1.4 x 5 Pa. A) What i the preure amplitude at thi ditance? (6 pt.) B) What i the diplacement amplitude? (6 pt.) C) At hat ditance i the ound intenity level 45 db? (6 pt.) A) p max ρv p max ( ρv, and β db log o β ), thu o p max ρv o ( β ) (1.kg/ m 3 )(344m/ )* 1 W / m * x -1 Pa. B) p max BkA A p max Bk p max v Bπf (.61x Pa)(344m/ ) π(1.4x 5 Pa)(448Hz ) 1.39 x -7 m. C) 1 r r r r 75 db 75 db 45 db 1 45 db 75 r 75 o 45 (50m) ( ) 1581 m. o

5 5) (4 pt. for each part.) A) What i required for periodic motion to occur? A retoring force and equilibrium. B) n addition to the requirement of part A) hat ele i required for Simple Harmonic Motion? The retoring force i proportional to diplacement. C) To unique function, g(x,t) and h(x,t) are olution to the ave equation derived in lecture. Will the ne function created by g(x,t)+h(x,t) alo be a olution to thi ave equation? f o, hy? The um g+h atifie the ave equation derived in cla becaue of the principle of linear uperpoition. D) Sound i a longitudinal preure ave traveling through a medium. Do the molecule of the medium move? f o, hat type of motion do they execute? The molecule of the medium execute imple harmonic motion. E) A tring, fixed at both end, vibrate at it 3 rd harmonic frequency. 1) Ho many boundary condition are there? ) Ho many node and antidnode are there? There are boundary condition. There are 4 node and 3 antinode. F) When forced ocillation on a ytem match one of the natural frequencie of the ytem, hat phenomenon occur? Thi i called reonance.