GENERAL PHYSICS PH -D (Dr. S. Mirv) Test 4 (Sple) STUDENT NAME: Ke STUDENT id #: ------------------------------------------------------------------------------------------------------------------------------------------- ALL QUESTIONS ARE WORTH 0 POINTS. WORK OUT FIVE PROBLEMS. NOTE: Clerl write ut slutins nd nswers (circle the nswers) b sectin r ech prt (., b., c., etc.) Iprtnt Fruls:. Mtin lng stright line with cnstnt ccelertin v ver. speed = [dist. tken]/[tie trv.]=s/t; v ver.vel. = /t; v ins =d/t; ver. = v ver. vel. /t; = dv/t; v = v + t; = /(v +v)t; = v t + / t ; v = v + (i =0 t t =0). Free ll tin (with psitive directin ) g = 9.80 /s ; = v ver. t v ver. = (v+v )/; v = v - gt; = v t - / g t ; v = v g (i =0 t t =0) 3. Mtin in plne v = v cs; v = v sin; = v t+ / t ; = v t + / t ; v = v + t; v = v + t; 4. Prjectile tin (with psitive directin ) v = v = v cs; = v t; = ( v sin cs)/g = (v sin)/g r in = in ; v = v - gt = v sin - gt; = v t - / gt ; 5. Unir circulr Mtin =v /r, T=r/v 6. Reltive tin v P A v P B v B A PA PB 7. Cpnent ethd vectr dditin
A = A + A ; A = A + A nd A = A + A ; A A A ; = tn - A /A ; The sclr prduct A b = b c s b ( ˆ ˆ ˆ) ( ˆ ˆ ˆ i j zk b i b j b zk ) b = b b zb z The vectr prduct b ( ˆ ˆ ˆ) ( ˆ ˆ ˆ i j zk b i b j b zk ) iˆ ˆj kˆ z ˆ ˆ z ˆ b b z i j k b b z b b b z b b b b z ( b b ) iˆ ( b b ) ˆj ( b b ) kˆ z z z z. Secnd Newtn s Lw =F net ;. Kinetic rictin k = k N; 3. Sttic rictin s = s N; 4. Universl Lw Grvittin: F=GM/r ; G=6.670 - N /kg ; 5. Drg ceicient D C A v 6. Terinl speed v t g C A 7. Centripetl rce: F c =v /r 8. Speed the stellite in circulr rbit: v =GM E /r 9. The wrk dne b cnstnt rce cting n n bject: W F d cs F d 0. Kinetic energ: K v. Ttl echnicl energ: E=K+U. The wrk-energ there: W=K -K ; W nc =K+U=E -E 3. The principle cnservtin echnicl energ: when W nc =0, E =E 4. Wrk dne b the grvittinl rce: W g d cs g
. Wrk dne in Liting nd Lwering the bject: K K K W W ; i K K ; W W i g i g. Spring Frce: F k (H k's lw ) 3. Wrk dne b spring rce: W k k ; i 0 nd ; W k s i i s 4. Wrk dne b vrible rce: W F ( ) d W d W 5. Pwer: P vg ; P ; P F v cs F v t d t 6. Ptentil energ: U W ; U F ( ) d 7. Grvittinl Ptentil Energ: U g ( ) g ; i 0 n d U 0 ; U ( ) g i i i i i 8. Elstic ptentil Energ: U ( ) k 9. Ptentil energ curves: du ( ) F ( ) ; K ( ) E e c U ( ) d 0. Wrk dne n sste b n eternl rce: F ric ti n is n t in v lv e d W h e n k in e tic ric ti n rc e c ts w ith in th e s ste E d th k W E K U e c W E E e c th. Cnservtin energ: W E E E E e c th r islted sste (W =0) E E E 0 in t e c th in t E. Pwer: P vg ; t P de d t ; 3. Center ss: r r n c i i M i 4. Newtns Secnd Lw r sste prticles: F net M c 3
. Liner Mentu nd Newtn s Secnd lw r sste prticles: P M v nd F c net dp dt t. Cllisin nd ipulse: J F ( t ) d t; J F t; t i vg when stre bdies with ss nd n n speed v, cllides with bd whse psitin is ied F vg p v v t t t Ipulse-Liner Mentu There: p p i J 3. Lw Cnservtin Liner entu: P P r clsed, islted sste 4. Inelstic cllisin in ne diensin: p p p p i i i 5. Mtin the Center Mss: The center ss clsed, islted sste tw clliding bdies is nt ected b cllisin. 6. Elstic Cllisin in One Diensin: v v ; v v i i 7. Cllisin in Tw Diensins: p p p p ; p p p p i i i i 8. Vrible-ss sste: Rv rel v v v M (irst rcket equtin) i r e l M i ln (secnd rcket equtin) M S 9. Angulr Psitin: (rdin esure) r 0. Angulr Displceent: (p sitiv e r c u n terclc k w ise r ttin ) d. Angulr velcit nd speed: vg ; (p sitive r c u n tercl ck w ise rtti n ) t d t. Angulr ccelertin: vg ; t d d t 4
t ( ) t. ngulr ccelertin: t t ( ) t t. Liner nd ngulr vribles relted: I r d v r s r ; v r ; t r ; r r ; T r v 3. Rttinl Kinetic Energ nd Rttinl Inerti: K I ; I iri r bd s sste discrete prticles; r b d w ith c n tin u u sl d istrib u te d ss. 4. The prllel es there: I I c M h 5. Trque: rf r F rf sin t 6. Newtn s secnd lw in ngulr r: net I 7. Wrk nd Rttinl Kinetic Energ: W d ; W ( ) r cnst; i i dw P K K K I I W dt ; i i w rk e n e rg th e re r r t tin g b d ie s v c R K I c v 8. Rlling bdies: c R g sin c I / M R c c r r llin g s th l d w n th e r p 9. Trque s vectr: r F ; rf sin rf r F 5
l r p ( r v ) ;. Angulr Mentu prticle: l r v sin r p r v r p r v dl. Newtn s Secnd lw in Angulr Fr: net dt n L l i i 3. Angulr entu sste prticles: dl net et dt 4. Angulr Mentu Rigid Bd: L I 5. Cnservtin Angulr Mentu: L L (is l te d s ste ) 6. Sttic equilibriu: 7. Elstic Mduli: stress= dulus strin i F net 0; net 0 i ll the rces lie in plne F 0; F 0; 0 F L 8. Tensin nd Cpressin: E, E is the Y ung's dulus A L F L 9. Shering: G, G is the sher dulus A L V 0. Hdrulic Stress: p B, B is th e b u lk d u lu s V net, net, net, z. Siple hrnic tin: t v t t cs( ); sin( ); cs( ) k. The Liner Oscilltr:, T k 3. Pendulus: T T I k, trsin pendulu L g, si ple pendulu T I, phsicl pendulu g h 6
. Dped Hrnic Mtin: bt k b ( t ) e c s ( ' t ), ', E ( t ) k e 4 bt. Sinusidl wves: (, t ) sin( k t ), k,, v T k T 3. Wve speed n stretched string: v 4. Averge pwer trnsitted b sinusidl wve n stretched string: P vg v 5. Intererence wves: '(, t ) [ c s ] s in ( k t ) 6. Stnding wves: '(, t ) [ s in k ] c s t v v 7. Resnnce: n, r n,,3,... L B 8. Sund wves: v, L ( ) r 0,,,3..., cnstructive intererence 9. Intererence: L ( ) r 0,,,3..., destructive intererence 0. Sund Intensit: P P s I, I v s, I A 4 r. Sund level in decibels: I ( 0 db ) l g, I 0 W / I. Stnding wve ptterns in pipes: v n v L, n,,3,..., r pipe pened r bth ends v n v 4 L, n,3,5,..., r pipe clsed t ne end nd pened t the ther 3. Bets: bet 7
vr. The Dppler eect: ' ( ) v sund;(v s =33/s); ' v E v s vs vr ' generl Dppler Eect v v s E, v R the speed the receiver; v s the speed the s + r receiver pprching sttinr eitter, - r receiver ving w r the sttinr eitter;, v E the speed the eitter, v s the speed the sund, - r eitter pprching sttinr receiver, + r eitter ving w r the sttinr receiver; 8
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. Yur grndther clck s pendulu hs length 0.9930. i the clck lses hl inute per d, hw shuld u djust the length the pendulu? L Fr siple pendulu T g Suppse clck's pendulu scilltes "n" ties in d. nt (4 3600 30) 86370s ter the djustent the pendulu's length nt (4 3600) 86400s Tke rti T T L g L L L g 86400 0.9930 L 0.9937 86370 86400 86370 4 L L 0.9937 0.9930 7 0 0
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