GENERAL PHYSICS PH -3A (Dr. S. Mirv) Test 3 (/7/07) ke Smple Test 3 STUDENT NAME: 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.) Imprtnt Frmuls:. Mtin lng stright line with cnstnt ccelertin v ver. speed = [dist. tken]/[time 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 mtin (with psitive directin ) g = 9.80 m/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 mtin (with psitive directin ) v = v = v cs; = v t; m = ( v sin cs)/g = (v sin)/g r in = in ; v = v - gt = v sin - gt; = v t - / gt ; 5. Unirm circulr Mtin =v /r, T=r/v 6. Reltive mtin v P A v P B v B A PA PB 7. Cmpnent methd 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 m=f net ;. Kinetic rictin k = k N; 3. Sttic rictin s = s N; 4. Universl Lw Grvittin: F=GMm/r ; G=6.670 - Nm /kg ; 5. Drg ceicient D C A v 6. Terminl speed v t mg C A 7. Centripetl rce: F c =mv /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 mv. Ttl mechnicl energ: E=K+U. The wrk-energ therem: W=K -K ; W nc =K+U=E -E 3. The principle cnservtin mechnicl energ: when W nc =0, E =E 4. Wrk dne b the grvittinl rce: W m 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 m g ( ) m g ; i 0 n d U 0 ; U ( ) m g i i i i i 8. Elstic ptentil Energ: U ( ) k 9. Ptentil energ curves: du ( ) F ( ) ; K ( ) E m e c U ( ) d 0. Wrk dne n sstem 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 m E d th k W E K U m e c W E E m e c th. Cnservtin energ: W E E E E m e c th r islted sstem (W =0) E E E 0 in t m e c th in t E. Pwer: P vg ; t P de d t ; 3. Center mss: r m r n i i M i 4. Newtns Secnd Lw r sstem prticles: F net M
. Liner Mmentum nd Newtn s Secnd lw r sstem prticles: P M v nd F net dp dt t. Cllisin nd impulse: J F ( t ) d t; J F t; t i vg when strem bdies with mss m nd n n m speed v, cllides with bd whse psitin is ied F vg p m v v t t t Impulse-Liner Mmentum Therem: p p i J 3. Lw Cnservtin Liner mmentum: P P r clsed, islted sstem 4. Inelstic cllisin in ne dimensin: p p p p i i i 5. Mtin the Center Mss: The center mss clsed, islted sstem tw clliding bdies is nt ected b cllisin. 6. Elstic Cllisin in One Dimensin: m m v v ; v m v i i m m m m 7. Cllisin in Tw Dimensins: p p p p ; p p p p i i i i 8. Vrible-mss sstem: 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 m esure) r 0. Angulr Displcement: (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
t ( ) t. ngulr ccelertin: t t ( ) t t. Liner nd ngulr vribles relted: I r d m v r s r ; v r ; t r ; r r ; T r v 3. Rttinl Kinetic Energ nd Rttinl Inerti: K I ; I m iri r bd s sstem discrete prticles; r b d w ith c n tin u u sl d istrib u te d m ss. 4. The prllel es therem: I I M h 5. Trque: rf r F rf sin t 6. Newtn s secnd lw in ngulr rm: 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 m r r t tin g b d ie s v R K I m v 8. Rlling bdies: R g sin I / M R r r llin g sm th l d w n th e r m p 9. Trque s vectr: r F ; rf sin rf r F
. Angulr Mmentum prticle:. Newtn s Secnd lw in Angulr Frm: net l r p m( r v); l rmvsin rp rmv r p r mv 3. Angulr mmentum sstem prticles: dl dt L net et n l i i 4. Angulr Mmentum Rigid Bd: L I 5. Cnservtin Angulr Mmentum: Li L (islted sstem) Fnet 0; net 0 6. Sttic equilibrium: i ll the rces lie in plne F 0; F 0; 0 7. Elstic Mduli: stress=mdulus strin dl dt net, net, net, z F L 8. Tensin nd Cmpressin: E, E is the Yung's mdulus A L F L 9. Shering: G, G is the sher mdulus A L V 0. Hdrulic Stress: p B, B is the bulk mdulus V
+. At the sme instnt tht 0.50-kg bll is drpped rm 5m bve Erth, secnd bll, with mss 0.5 kg, is thrwn stright upwrd rm Erth's surce with n initil speed 5m/s. The mve lng nerb lines nd pss ech ther withut clliding. Wht is the height bve Erth's surce the center mss the tw-bll sstem t the end.0 s? m v =0 =5m v =5 m/s m 5.4m 0.4m t=0 t=.0s ( ) Find inl crdinte the bll ter.0 s. gt 9.8 5 0 t 5 5.4m (b) Find inl crdinte the bll ter.0 s gt 9.8 vt 5 0.4m (c) Find crdinte the center mss tw blls m m (0.5)(5.4) (0.5)(0.4) 7.m m m (0.5 0.5)
. Tw skters with msses 00 kg nd 60 kg, respectivel, stnd 0.0 m prt; ech hlds ne end piece rpe. I the pull themselves lng the rpe until the meet, hw r des ech skter trvel? (Neglect rictin) 00kg 0m 60kg 0 + ( ) Since tw scters represent n islted sstem nd initill theu re t rest their center mss will be t rest nd the will meet t the center mss m m m m (00)(0) (60)(0) 006 0 3.75m 3.8m (b) The 00 kg skter mves 3.75 m (c) The 60 kg skter mves 0-3.75=6.5m=6.m
3. A kg blck wd rests n lng tbletp. A 5 g bullet mving hrizntll with speed 50 m/s is sht int the blck nd sticks in it. The blck then slides 70 cm lng the tble nd stps. () ind the speed the blck just ter impct. (b) ind the rictin rce between blck nd tble. v v 0 =0 m m.7 m () Cnsider inelstic bullet-blck cllisin. At the instnt cllisn bullet-blck sstem is islted, hence, we cn use lw cnservtin liner mmentum t describe the cllisin mv mv 0 0 mv 0mv 0 (0.005)(50) ()(0) ( mm) v; v 0.374 4 0 m/ s ( m m ) (0.005 ) (b) Clculte wrk dne b the net rce n blck-bullet sstem during its mtin lng the tble There re 3 rces cting n ur sstem: Weight, Nrml rectin, nd kineti rictin. Onl kinetic rictin rce will perrm nn zer wrk. W (c) Mtin blck-bullet sstem ter the cllisin cn be described b wrk-energ therem net S ( m m ) v ( m m ) v (0.005 )(0.374) S (.70) Wnet K Ki ks 0 k 50 N k
4. The impct the hed gl club n gl bll cn be pprimtel regrded s n elstic cllisin. The mss the hed the gl club is 0.5 kg. The speed the club bere the cllisin is 46 m/s. The bll cquires speed 70 m/s ter the cllisin. The gl club nd bll re in cntct r but 0.5 ms. ) Wht must be the mss the bll? b) Wht is the verge rce eerted b the club n the bll? () Fr elstic gl club-bll cllisin mc m m mv (0.5)(46) c ci mb v m 0.5 0.047 4.7 0 b c kg 70 v b c b v ci P P P (0.047)(70) 0 ( ) 6600 6.6 0 t t 0.0005 b bi bfvg N N
5.
6. Je is pinting the lr his bsement using pint rller. The rller hs mss.4 kg nd rdius 3.8 cm. In rlling the rller crss the lr Je pplies rce F=6N directed t n ngle 35% s shwn. Ignring the mss the rller hndle, wht is the mgnitude the ngulr ccelertin the rller? F 35 N () nd Newtn lw is: s Fsin m ( b) nd Newtn Lw r rttin but : R I (c) recll the reltinship between nd : R; I ( d) substitute eq.(b) nd (c) in (): Fsin mr; R F sin F sin F sin (6)sin 35 I mr mr mr 3mR 3(.4)(0.038) R rd 67 s s s mg F
7. A hp (I h =MR ), unirm disk (I d =/MR ), nd unirm sphere (I s =/5MR ), ll with the sme mss nd uter rdius, strt with the sme speed nd rll withut sliding up identicl inclines. Rnk the bjects ccrding t hw high the g, lest t gretest. ( )During rlling up the incline mtin the mechnicl energ the hp-erth, disk-erth, nd sphere-erth sstems is cnserved since )rictinl rce des nt trnser n energ t therml energ becuse the bjects d nt slide; ) nrml rce is perpendiculr t the pss; 3) grvittinl rce is cnservtive ne. I Mv 00Mgh ( b) secnd term is the sme r ll ur bjects, is ls the sme, the lrger I the lrger mimum height h reched b the bject. rm lest t gretest in terms height ttined: sphere, disk, hp.
9. A unirm seesw length 6 m hs tw ungsters weights w =700N nd w =400 N sitting n the ends. Find the prper lctin the pivt r the seesw t be just in blnce, i () the weight the seesw cn be ignred (b) the seesw weighs Mg=300N 6 m w Mg ( ) Use nd cnditin equilibrium: WW(6 ) 0; 6W 6(400) W W 700 400.8m w ( b)use nd cnditin equilibrium: WMg(3 ) W(6 ) 0; 6W 3Mg 6(400) 3(300) W W Mg 700 400 300.36m