Bernoulli s Equation. Pressure in a fluid. Atmospheric Pressure kpa 14.7 psi. Poiseuille s Equation : = ;<= A? B ) Uniform Circular Motion

Transcription

1 EF 5 Fial Exam, Fall, 4 Page of Te equatio seets may be emoved we te test begis Guidelies: ssume 3 sigifiat figues fo all give umbes uless otewise stated Sow all of you wok o wok, o edit Wite you fial aswe i te box povided - ilude uits fo all aswes If you fiis wit less ta 5 miutes emaiig, emai seated util te ed of te exam ad all exams ae olleted. Stess ad Stai Stess Stai Fato of Safety (FS)! Desity of Wate 6.4 lb/ft 3 kg/m 3 Beoulli s Equatio " $ + $ & '( $ & +') $ " & + $ & '( & & +') & Cotiuity ( $ + $ ( & + & Lift '-+( & Pessue i a fluid " ').+" # Buoyat foe ') tmospei Pessue.3 kpa 4.7 psi Uivesal Law of Gavitatio N B < B ) O < B $$ RSB O T B Keple s Tid Law U B (&;)B V W NX Satellites ( Y N Z < Z [\ ( ]^_ Y &N Z < Z Covesios ft gal m 3 L Fluids p pessue eigt ρ mass desity v veloity K empiial ostat aea d dept " # pessue o top of fluid Mass desity ' 3 Weigt desity Stokes Law! 6789( Poiseuille s Equatio : ;< B ) DE 8 F. K Pa s Uifom Ciula Motio ( t9 u v wb < 9t& (ay uve) Speifi gavity (elative desity) m s o m opq s opq Costat aeleatio ~ ~ # +( # + $ & u& ( ( # +u ~ wb w B &V ` &; a 9 b 6.38 e m g b 5.97 &j kg Ellipse eetiity: x < yz{ < y } &V semi-majo axis: u < yz{[ < y } &

2 EF 5 Fial Exam, Fall, 4 Page of Hamoi Motio ω agula fequey amplitude k stiffess m mass δ pase agle x iitial displaemet v iitial veloity T peiod f fequey x( t) si a si v( t) ω Wave Equatio v wave veloity amplitude k wave umbe ω agula fequey λ wavelegt f fequey z( x, t) si kx v λf π k λ ( ωt + δ ) ( ωt) a os( ωt) os( ωt + δ ) ( ωt) aω si( ωt) si( ωt + δ ) ( ωt) a ω os( ωt) + a ω os a( t) ω a ω si ω k m + a a a δ ta a v a ω π T f ω T ω πf a x ( ωt) v is positive if sig of ω is egative Paallel xis Teoem I I m + M Pedulums Simple: Pysial: ω ω g l Mg I Speed of Soud i i ( 33+.6T ) m s v / T i C Beat Fequey: f f Natual Fequeies: λ wavelegt L Legt amoi T tesio µ mass pe uit legt f fequey v wave veloity i medium Stig L λ v T f λ L µ i Colums 4L L ope pipe: losed pipe: λ, 3, 5 Wave Speed Cables, Ropes, et. T tesio µ mass pe uit legt E modulus of elastiity ρ mass desity Tasvese: Logitudial: λ,, 3 v v T µ E ρ Soud Level I efeee itesity, x - W/m I itesity I β ( i db) log I Dopple Sift f fequey f sifted fequey v veloity of medium v S veloity of soue v L veloity of listee v + vl f f v + vs Positive is fom listee to soue. Wave Eegy, Powe, Itesity E eegy I itesity P powe P - aveage powe E π µ vtf P P P 4π µ vf P I 4π π µ vf Ligt Waves I I Law of Refletio os Idex of Refatio Law of Refatio si θ si a a Ligt Wavelegt b θ ( kx ωt) θ θ b a v λ λ Total Iteal Refletio si θ it b a

3 EF 5 Fial Exam, Fall, 4 Page 3 of Temal Expasio Liea l αl T Liea, Stesses σ αe T Volumeti V βv T Ideal Gas Law pv RT R 8.34 J/(mol-K) vogado s Numbe: 6.x 3 Stadad Pessue ad Temp 73K. atm (.3kPa) st Law of Temodyamis U iteal eegy W wok doe by temal system eat flow ito temal system U W + B B Moleula Temal Pysis m mass of a moleule M moleula mass umbe of moles N umbe of moleules k Boltzma ostat J/ K U N m v 3 U RT 3RT 3kT v ms M m Covesios al 4.86 J BTU 55 J p.77 BTU/se L m 3 m 3 L Wok of Temal Systems W V V pdv Isobai (ostat pessue) W p( V B V ) p T Isooi (ostat volume) W v T Isotemal (ostat temp) V W RT l V W diabati ( ) W p V p γ Effiiey Geeal W η ( V ) Otto Cyle ompessio atio η γ Caot Cyle T T η T T Etopy B d S T T S ml T S T Ideal Gas TB VB S Cv l + R l T V B B Heat eat speifi eat κ temal odutivity R temal esistae Heat Capaity m T Temal Codutivity t T T T T κ L R Temal Resistae L R κ Temal Resistae, Seies R eff R + R Temal Resistae, Paallel R eff + R + R Refigeatos Geeal K oeffiiet of pefomae H eat uet P powe iput W + K Caot K W Caot H P T T T Wate Popeties al/(g- C) 4.86J/(g- C) L f 79.6 al/g L v 54 al/g ρ g/m 3 kg/l kg/m lb/ft 3 L f Latet eat of fusio L v Latet eat of vapoizatio EER 3.43 K

4 EF 5 Fial Exam, Fall, 4 Page 4 of Costats m e 9.9x -3 kg m p.673x -7 kg m.675x -7 kg Nm C k 9x 9 # C Nm o F m e C (eleto age) ev.6-9 J (eleto volt) Coulomb s Law (eletostati foe) qq F k qq F 4πε Eleti Field poit age - uit veto fom age to a loatio F q E ˆ q 4 πε Potetial eegy - poit ages qiq j U 4πε Potetial U V q i< j ij Potetial of a set of poit ages qi V 4 πε i i Potetial diffeee betwee two paallel plates V a V b Ed Capaitae C V ab F C V Capaitae paallel plates ε C i a vauum d Capaitae eegy stoage U CV V C Capaitos i seies + + C C C C eq Capaitos i paallel C + C + C... C eq 3 + Resistos i seies R + R + R R eq Resistos i paallel R eq R Cuet d I dt R R 3 C se Voltage, Resistae, Cuet, Powe VI R ρl PI V R Kioff s Rules V fo a losed loop I fo a jutio R-C iuit time ostat RC τ Magetism V s N T gauss m m 7 T m µ 4π Mageti foe o movig aged patile F q( v B) Mageti field of a movig aged patile µ ˆ qv B 4 π Mageti field of a staigt wie µ I B π Mageti field alog te axis of a looped wie µ NIa B x ( x + a ) 3 / a adius of te loop x distae fom te ete of te loop to poit of iteest o te axis. I uet i te wies N umbe of loops Eleti Flux Φ ƒ.+ q ˆ

5 EF 5 Fial Exam, Fall, 4 Page 5 of Remove te equatio seets, leavig te exam questios stapled togete. CLERLY PRINT te ifomatio below. Name: EF 5 Setio:. ( pt) boat is floatig o a lake wit its uge steel ao i te wate. Te boat oists te ao ito te boat to set sail. Wat appes to te wate level i te lake (wit espet to te soe)? a. ises b. dops. emais te same d. depeds o te size of te steel. ( pt) Suppose you sake te ed of a steted stig to podue a wave. Wi of te followig will iease te speed of te wave? a. move you am up ad dow faste b. move you am a geate distae up ad dow. iease te tesio i te stig d. iease te mass pe uit legt of te stig 3. ( pt) Wi of te followig takes te most time? a. Raise kg of ie fom - C to C b. Covet kg of ie to wate at C. Raise kg of wate fom C to C d. Covet kg of wate to steam at C e. all times ae equal 4. ( pt) Two oppe wies of equal diamete but diffeet legts ae joied ed to ed ad oeted to a battey. Te uet flowig toug te oeted wies is: a. geate i te loge wie b. geate i te sote wie. te same i bot wies 5. (8 pts) -ft-log, 38 lb ladde leas agaist a fitioless wall as sow. Fo µ s.7 ad θ5, detemie te miimum oizotal foe at te base of te ladde i additio to fitio equied to keep te ladde fom slidig. sepaate, omplete FBD is equied fo full edit. θ

6 EF 5 Fial Exam, Fall, 4 Page 6 of 6. (8 pts) 4 lb otaie floats i wate wit 7% of te volume of te otaie above wate. Detemie te foe equied to submege te otaie. 7. (8 pts) O te d floo (elevatio 8m) of Bow Residee Hall, wate flows toug a 3m diamete pipe at a speed of 4. m/s ad te pessue i te pipe is 6 kpa. Te pipe aows to m diamete pipe o te 6 t floo (elevatio 8m). Detemie te pessue at tis poit.

7 EF 5 Fial Exam, Fall, 4 Page 7 of 8. (8 pts).6 kg soote is oeted to a ideal spig (k54 N/m ad is osillatig o a oizotal, fitioless sufae. It is give a iitial displaemet of +7 m ad a ukow iitial veloity. fte 6. seods its veloity is +5m/s. Wat was te soote s iitial veloity? 9. (8 pts) Kevi is stadig 3m away fom a 8W speake ad 3m away fom a W speake. Wat is te soud level (i db) Kevi eas? 3m 3m Kevi. (8 pts) ed a ad a gee a ae blowig idetial os. Te ed a is at est ad te gee a is movig towad te ed a at m/s. Te dive i te ed a eas a beat fequey of 3 Hz. Wat is te fequey of te o? ssume speed of soud i ai is 343 m/s.

8 EF 5 Fial Exam, Fall, 4 Page 8 of. (8 pts) Te Salvo Cyle is sow. Detemie te pessue at B so tat 3 kj of wok will be doe duig ea yle. ssume te gas is a ideal diatomi gas wit γ.4. P B P B 5 kpa C.3 m 3.5 m 3 V. (8 pts) Calulate te age i etopy of.5 kg of liquid wate at C we it is foze to a tempeatue of -3 C. ie.5 al/g C

9 EF 5 Fial Exam, Fall, 4 Page 9 of 3. (8 pts) 45 mf apaito as eoug stoed eegy to eat 3g of wate fom C to 3 C. Wat is te potetial diffeee aoss te plates of te apaito? 4. (8 pts) aged, 7x -6 kg dust patile ags as sow i a uifom eleti field, E 35 N/C. Detemie te age o te dust patile. sepaate, omplete FBD is equied fo full edit. 8 q

10 EF 5 Fial Exam, Fall, 4 Page of 5. (8 pts) eleto wit a veloity of 5.x Œ m/s moves toug a mageti field of ( )µt. Detemie te aeleatio of te eleto ( otatio). 6. (8 pts) Te powe dissipated by te iuit sow is 9 W. Detemie te ukow esistae R. 8 Ω V 6 Ω R