PHYSICS 211 FINAL EXAM 7 June 2004

Transcription

1 PHYSICS FINAL EXAM 7 June 004 Exa is closed book, closed noes. Use only your forula shee. Wrie all work and answers in exa bookles. The backs of pages will no be graded unless you so reques on he fron of he page. Show all your work and explain your reasoning (excep on #). Parial credi will be gien (no on #). No credi will be gien if no work is shown (no on #). If you hae a quesion, raise your hand or coe o he fron.. (35 poins) For each of hese uliple choice quesions, indicae he correc response (A, B, C, or D (where needed)) on he page for proble in your exa bookle. i) A block of ass is sliding on a horizonal, fricionless able and hen encouners a fixed sei-circular wall as shown a righ (looking down on he able). There is fricion beween he wall and he block, so ha he kineic energy of he block is reduced as i raels along he wall. If he iniial elociy is increased, does he loss of kineic energy K of he block increase, decrease, or say he sae? A) Increase. B) Decrease. C) Say he sae. ii) A ension T is applied o he rope while he ass is oing upward wih a decreasing speed. Wha is rue abou he agniude of he ension? A) I is larger han g. B) I is saller han g. C) I is equal o g. iii) Say Sosa can swing his corked ba a 0 ph. Jaie Moyer can hrow a fasball a 80 ph. When Jaie's fasball ees Say's ba in an elasic head-on collision, a wha speed will he ball leae he ba? Assue ha he ass of he ball is negligible copared o ha of he ba. A) 60 ph B) 40 ph C) 300 ph D) 30 ph i) A golf ball (ery ligh) is fired a a bowling ball (ery heay), which is iniially a res. The golf ball bounces back elasically. Afer he collision, he golf ball, copared o he bowling ball, has A) a larger agniude of oenu bu saller kineic energy. B) a larger agniude of oenu and larger kineic energy. C) a saller agniude of oenu and saller kineic energy. D) a saller agniude of oenu bu larger kineic energy. ) A spring-loaded gun shoos arble A horizonally off a able. Marble A lands on he floor a horizonal disance d fro he launch poin. A differen spring-loaded gun shoos arble B erically. Marble B raels up he sae disance d erically before falling back down. Boh springs are hen copressed wice heir original copressions and he experiens are repeaed. Which disance is now greaer: he horizonal disance ha arble A raels before hiing he floor, or he erical disance arble B raels o is axiu heigh? A) Marble A horizonal. B) Marble B erical. C) They rael he sae disance as each oher. i) Two balls are dropped fro a cliff. The second ball is dropped one second afer he firs ball is dropped. As boh fall, does he disance beween he increase, decrease, or say he sae? A) Increase. B) Decrease. C) Reain he sae. ii) A block slides up a rap, oenarily coes o res, and slides back down. There is fricion beween he block and he surface of he rap. Assue ha he rap is so seep ha he block canno reain a res on he rap. Which saeen is rue regarding he ie ha he block akes o go up he rap copared o he ie o coe back down? A) The ie up is longer han he ie down. B) The ie up is shorer han he ie down. C) The ie up is equal o he ie down. T

2 . (30 poins) Two subway sops are separaed by 400. A subway rain acceleraes a 4 /s fro res hrough he firs half of he disance and deceleraes a -4 /s hrough he second half. a) Wha is he rael ie beween he wo sops? b) Wha is he axiu speed? c) Graph x,, and a, each as a funcion of ie, for he coplee rip. 3. (35 poins) A ass on a horizonal able is aached o a hanging ass by a sring hrough a hole in he able, as shown a righ. Express all your answers in ers of he quaniies gien and g. a) If here is fricion beween he able and he ass, wha coefficien of saic fricion is required o keep he syse saionary? Is your alue a axiu or iniu? b) If he able is fricionless and ass oes in a circle of radius R (as shown in figure), wha speed is required o keep a res? 4. (35 poins) Lisa (ass L 60 kg) and Kae (ass K 40 kg) are sanding a he cener of a syeric, saionary railroad car (ass RR 00 kg, lengh L 0 ) ha can roll wihou fricion along a sraigh rack. Lisa runs oward one end of he railroad car wih a speed of 6 /s wih respec o he railroad car and Kae runs oward he oher end wih a speed of /s wih respec o he railroad car. Lisa runs all he way o her end of he car, bu Kae sops afer running a disance of 4 wih respec o he railroad car. b) Wha is he elociy of he railroad car (wih respec o he ground) while Lisa and Kae are running? c) Wha is he elociy of he railroad car (wih respec o he ground) afer boh Lisa and Kae hae sopped running? d) Wha is he displaceen of he railroad car (wih respec o he ground) afer boh Lisa and Kae hae sopped running? 5. (35 poins) A rocke is launched erically fro he surface of plane Claire, which has a ass M 5.0 x 0 kg and a radius R. x 0 5 and does no roae. The rocke reaches a speed of 000 /s in a negligible disance and hen he rocke engines are urned off. Assue G 6.0 x 0 - N /s. a) Wha is he axiu aliude (aboe he surface of he plane) reached by he rocke? b) When he rocke reaches is axiu aliude, he rocke engines are briefly urned on again o gie he rocke a elociy in he horizonal direcion (i.e., perpendicular o he erical pah aken fro Claire). Wha speed is required o pu he rocke ino a circular orbi around Claire? 6. (30 poins) A block of ass kg is pushed up agains a spring (k 8 N/) as shown below. The spring is copressed a disance d 3 before he block is released. The block slides on a fricionless surface and, afer leaing he spring, collides elasically wih anoher block of ass 4 kg ha is iniially a res. The second block hen slides up he fricionless rap. Wha is he heigh h (easured erically fro he boo of he rap) of he second block when i oenarily coes o res on he rap? k

3 PHYSICS FINAL EXAM SOLUTIONS 7 June 004. i) A The loss of kineic energy is gien by -f k d, where f k µ k N and d is he arc lengh of he seicircle. Since he noral force N is he only horizonal force, i us produce he cenripeal acceleraion /r. As increases, he noral force, N /r, will increase, so he fricional force will increase. Thus, for larger, he kineic energy loss will increase. ii) B The ass is oing up, bu wih a decreasing speed, which eans ha he acceleraion is downward. Since he acceleraion is downward, he ne force us be down. Hence, he weigh (down) us be larger han he ension (up). iii) D In elasic collisions he speed of approach of he wo objecs is equal o he speed of recession. The relaie speed of approach here is 00 ph (0 + 80), so he speed of recession will be 00 ph wih respec o he oing ba, which is no slowed down in he collision because of is doinan ass. Hence he speed of he ball is 30 ph (00 +0). i) D Before he collision, he golf ball (and he oal syse) has oenu. Afer he elasic collision, he golf ball will hae oenu approxiaely - and he bowling ball will hae oenu approxiaely (in order o hae oal syse oenu ). The kineic energy of he golf ball will be approxiaely and ha of he bowling ball will be approxiaely 4 MV M M M kineic energy.. Since << M, he bowling ball has less ) B Twice he spring copression iplies four ies he kineic energy and hence wice he iniial elociy. Conseraion of energy ( KEi gh) iplies ha arble B goes four ies as high as originally (4d). Marble A sill akes he sae ie o hi he floor, and since is horizonal elociy is wice he original, i will go wice as far (d). i) A As he balls fall, he speed of he firs ball is always greaer han he speed of he second ball a any gien ie. This speed differenial causes he firs ball o keep increasing is lead oer he second ball. ii) B Since kineic fricion dissipaes energy, he speed of he reurning block a he boo of he rap will be less han he iniial speed up he rap. This eans ha he aerage speed on he way up is larger han on he way down. Since he disances are he sae, he block akes longer o ge down.

4 PHYSICS FINAL EXAM SOLUTIONS 7 June 004. Define a coordinae syse wih he x-axis along he subway line. Le he firs sop be a posiion x 0 0, where he rain sars a ie 0 0. A ie he rain reaches he halfway poin x d/, and a ie i reaches he second sop a he posiion x d. During he firs half of he journey, he acceleraion is a +4 /s, and during he second half of he journey, he acceleraion is a -4 /s -a. Since he rain sars a res and finishes a res, we also know ha 0 0 and 0. a) The firs hing o noice is ha since he acceleraion has he sae agniude on he wo hales of he journey, we expec ha he wo hales ake he sae ie. To show his siply, use he expression for he acceleraion: a a 0 0 a a The equaion of oion for he firs half of he journey can hen be used o find. x x a d x a d a which gies for he oal ie : d 400 a 4 s 0s b) The axiu speed is jus he speed a he idway poin, which can be obained using: + a 0 d a a ad 4 s ( 400) a 40 s c) The graphs for he rip are:

5 PHYSICS FINAL EXAM SOLUTIONS 7 June 004 x 3

6 PHYSICS FINAL EXAM SOLUTIONS 7 June a) The free body diagras for he saic case are shown below: f s N T T g g Since here is no oion of he syse, all acceleraions are zero and he equaions of oion are: T fs 0 T fs N g 0 N g T g 0 T g fs g The saic fricion us obey he equaion fs µ sn, which gies g µ sg µ s So he raio of asses is he iniu alue of µ s needed o keep he blocks saionary. b) When here is no fricion and ass oes in a circle while ass is saionary, he free body diagras are as aboe excep here is no fricional force. The equaions of oion in his case are: T R N g 0 N g T g 0 T g Equaing he wo expressions for he ension, we ge: g R gr gr 4

7 PHYSICS FINAL EXAM SOLUTIONS 7 June a) The syse (Lisa, Kae, & car) is a res and no horizonal forces ac, so he cener of ass of he syse will no oe and horizonal oenu will be consered. The iniial oenu is zero, so he final oenu us also be zero. The equaions we need are conseraion of oenu and he equaions relaing he oion of Lisa (L) and Kae (K) relaie o he car (RR) o heir oion relaie o he ground (G). Le Lisa oe in he posiie direcion, which eans ha Kae oes in he negaie direcion L L/ G K K/ G RR RR/ G + LG / LRR / RRG / K/ G K/ RR+ RR/ G L( L/ RR+ RR/ G)+ K ( K/ RR+ RR/ G)+ RRRR/ G 0 ( + + ) L K RR RR/ G L L/ RR K K/ RR L L/ RR+ K K/ RR 60kg( 6 s) + 40kg( s) RR/ G L + K + RR 60kg + 40kg + 00kg RR 4. s The inus sign eans ha he car oes opposie o he oion of Lisa. b) Afer Lisa and Kae hae sopped running, he car us also sop so ha here is no ne oenu in he syse. This is also clear if we apply he resul fro aboe wih L/RR K/RR 0. RR 0 s c) Pu he origin a he cener of he car where Lisa and Kae sar, so all hree hings sar a x 0. The equaions we need are he posiion of he syse cener of ass (which us be zero) and he equaion relaing he posiions of Lisa (L) and Kae (K) relaie o he car (RR) o heir posiions relaie o he ground (G). LxL/ G+ K xk/ G+ RRxRR/ G xc 0 L + K + RR LxL/ G+ K xk/ G+ RRxRR/ G 0 xl/ G xl/ RR + xrr/ G xk/ G xk/ RR + xrr/ G L( xl/ RR+ xrr/ G) + K ( xk/ RR+ xrr/ G) + RRxRR/ G 0 LxL/ RR+ K xk/ RR 60kg( 0) + 40kg( 4) xrr/ G L + K + RR 60kg + 40kg + 00kg xrr/ G. The inus sign eans ha he car oes opposie o he oion of Lisa. 5

8 PHYSICS FINAL EXAM SOLUTIONS 7 June a) Consere echanical energy as he rocke raels fro he surface (R) o he heigh h aboe he surface. Le he rocke hae ass (which will no be iporan). GM GM + R R+ h GM + GM R h R GM R R+ h GM R R GM h R R 5 R s ( 000 / ) (. 0 ) GM 60 (. 0 N / kg )( 5 0 kg) 5 R. 0 h R h b) A circular orbi requires ha he graiaional force proide he cenripeal force needed o oe in a circle. Le he elociy needed for he circular orbi be V. F a GM V ( R+ h) ( R+ h) V V GM ( R+ h) GM ( R+ h) V 000 / s ( N / kg )( 5 0 kg)

9 PHYSICS FINAL EXAM SOLUTIONS 7 June This proble can be broken ino hree pieces: () he spring expands, conering elasic poenial energy ino kineic energy of block, () he wo blocks collide, consering boh oenu and kineic energy of he wo block syse, and (3) block goes up he rap and sops, conering is kineic energy ino graiaional poenial energy. For sep () we ge: kd i k i d ( i 6 s) For sep () we consere energy and oenu. We are only ineresed in he final elociy of block. i f + f ( i f) f i f f i f + ( ) f ( i f) ( i + f) f ( i + f) f f i f + i i f f f + i d k + + Now apply conseraion of energy up he rap. ( 4 s) f i f gh f f 8 3 h g g d k kd ( kg)( N )( ) + g ( + ) 0 s ( kg + 4kg) h 08. 7