PHYSICS 211 MIDTERM I 21 April 2004

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1 PHYSICS MIDERM I April 004 Exm is closed book, closed notes. Use only your formul sheet. Write ll work nd nswers in exm booklets. he bcks of pges will not be grded unless you so request on the front of the pge. Show ll your work nd explin your resoning (except on #). Prtil credit will be gien (not on #). No credit will be gien if no work is shown (not on #). If you he question, rise your hnd or come to the front.. (0 points) For ech of these multiple choice questions, indicte the correct response (A, B, C, or D (where needed)) on the pge for problem in your exm booklet. i) An pple nd n ornge re thrown stright up into the ir. Ech hs the sme initil elocity, but the ornge is thrown short time fter the pple is thrown. While both re moing upwrds, does the distnce between them increse, decrese, or sty the sme? A) Increse. B) Decrese. C) Sty the sme. ii) he force F is pplied to the box of mss m s shown. Wht is true bout the mgnitude of the norml force on the box (due to the floor)? A) It is lrger thn m B) It is smller thn m C) It is equl to m D) It is independent of the mss of the block. m F iii) hree forces re pplied to the tire s shown t right. As the ngle is decresed from its initil lue of 45, does the mgnitude of the ccelertion of the tire increse, decrese, or sty the sme? here re no forces other thn those shown. A) Increse. B) Decrese. C) Sty the sme. N N N i) wo blocks, with msses m nd m, re connected by string tht psses oer mssless, frictionless pulley. Block hs greter mss thn block. Which sttement is true regrding the tension in the string? A) > m B) < m C) m D) m g < < m m m ) A child sits in wgon tht is moing t constnt speed. he child throws n pple stright upwrd (from her point of iew), while the wgon continues to trel forwrd t constnt speed. Where will the pple lnd? A) Behind the wgon. B) In front of the wgon. C) In the wgon. D) Need more informtion.

2 . (0 points) A speeding cr (constnt elocity ) psses n initilly sttionry motorcycle policemn. At the instnt the cr psses the motorcycle, the policemen ccelertes (constnt ccelertion ) in pursuit of the lwbreker. Express the nswers below in terms of the prmeters,, nd other constnts s needed. ) How much time does it tke for the policemn to ctch up to the speeder? b) How fr does the policemn he to trel to ctch up to the speeder? c) How fst is the policemn treling when he ctches up to the speeder? d) Wht is the policemn's erge speed during the chse? e) Drw single grph depicting the positions of the speeder nd policemn s function of time. 3. (0 points) A bll is thrown from the edge of cliff into the ir s shown t right. he initil speed of the bll is 0 m/s nd the initil upwrd ngle is such tht sin 4/5. he bll hits the flt ground t horizontl distnce of d.8 m from the erticl cliff. Assume g 0 m/s. ) How long does the bll remin in the ir? b) Wht is the mximum height h of the bll boe the ground? c) Wht is the height H of the cliff? H h d.8m 4. (0 points) A dier of mss 40 kg hits the wter with n initil erticl speed of 5 m/s. After penetrting erticlly into the wter distnce of 5 m she finlly comes to rest. ) Wht is the ccelertion of the dier s she moes through the wter, ssuming it remins constnt? b) Wht is the force F exerted by the wter on the dier s she comes to rest? Consider this force s generic force (i.e., you don't need to know wht kind of force it is). c) How long does it tke the dier to come to rest fter first hitting the wter? 5. (0 points) Consider pulley system whose initil stte is shown t right. Ignore the mss of the strings nd pulleys. Ignore friction. Grity (g) points down. Express the nswers below in terms of the msses, g, nd other constnts s needed. () Drw free-body digrm for ech block. (b) Find the ccelertion of the msses. (c) Find the tensions nd in the strings. m m m 3

3 PHYSICS MIDERM I SOLUIONS April 004. i) B As the pple nd ornge rise, the speed of the pple is lwys less thn the speed of the ornge t ny gien time, since the pple strted decelerting sooner. his speed differentil cuses the pple's led oer the ornge to decrese. ii) B If the box is not moing norml to the floor, the erticl forces must sum to zero. he norml force plus the erticl component of F must then equl mg, which mens tht the norml force will be smller thn m If F were strong enough to cuse the box to rise, then the norml force would be zero, which is lso less thn m iii) A At the initil ngle of 45, the digonl forces ech he horizontl components of N, which dd up to exctly cncel the N force. he erticl components of the digonl forces cncel ech other for ll. he initil ccelertion is thus zero, which mens tht the mgnitude cnnot decrese. As is decresed, the horizontl components of the digonl forces get lrger nd their sum becomes bigger thn the N force, giing the tire net ccelertion to the right. hus the mgnitude of the tire's ccelertion increses. i) D Since m > m, mss will fll nd mss will rise. For this to hppen, the tension must be greter thn the weight of mss nd less thn the weight of mss. ) C With respect to the rod or sidewlk, the wgon nd the pple he the sme horizontl elocities when the pple is thrown up. hey mintin these sme horizontl elocities while the pple is in the ir, so tht the pple flls bck into the wgon.

4 PHYSICS MIDERM I SOLUIONS April 004. Define coordinte system with the x-xis long the direction of the speeder nd the origin t the initil loction of the policemn. ) Write the kinemtic equtions nd equte the positions when the policemn ctches up to the speeder: x t x t xf xf tf t f tf ( tf) 0 tf 0, he first solution corresponds to the initil time, so we wnt the second solution: t f b) he distnce cn be found from either position eqution: x f tf x c) Since the initil speed of the policemn is zero, his finl speed is f i + t f t f f d) he erge speed of the policemn is e x f xi x f t t t f i f s it should since both trel the sme distnce in the sme time e e) he grph for the chse nd ctch is: x f x x x t f t

5 PHYSICS MIDERM I SOLUIONS April Put the origin t the bse of the cliff. Let t 0 0 be the time when the bll ws thrown, t be the time when the mximum height is reched, nd t be the time when the bll returns to the ground. ) First determine the components of the initil elocity nd use the x-component to find the time in the ir, since the horizontl speed is constnt. H 0 O h d sin 0 m s( 4 5) 8 m s 0y 0 0x 0cos 0 m s( 3 5) 6 m s d 0xt t d. 8m 6 m s 0x t 38. s b) o find the mximum height h y, find the time to rech tht height (where y 0), then find how fr the bll flls in the remining time. 0y 8ms y 0y gt t s g 08. 0ms y y t t + ( ) g( t t ) y 0 h + 0 g t t h g t t 0m s h 45m c) he height of the cliff H y 0, cn be found by considering the first prt of the trip: + ( y y ) y 0 y y 0 0 y 0 + ( g)( h H) 0 y ( 8ms) H h 45m m m g ( ms) H 4. 8m 3

6 PHYSICS MIDERM I SOLUIONS April Let the -dimensionl coordinte system he its origin t the surfce of the wter so tht y 0 0, 0-5 m/s. he dier comes to rest t y -d -5 m, so we know tht 0. y 0-5m ) o find the ccelertion use: + ( y y ) ( d 0) 0 ( 5ms 5m s ) / d 5 ( m) 0m 5. m s 0 b) First drw free body digrm for the dier, s t right. hen write down the eqution of motion. F mg m F m+ mg m( + g) F 40kg(. 5m s + 0 m s ) F 500N F mg c) he time for the dier to come to rest is found from: + t t 0 0 5ms t ( ) 5. ms t s 4

7 PHYSICS MIDERM I SOLUIONS April ) he three free body digrms re shown below. Since the msses re tied together, they ll ccelerte with the sme ccelertion. Since we don't know the msses, we don't know which wy they will go, so we choose direction nd cll tht positie. N b) he equtions of motion for the msses re (neglecting the erticl motion of m ) m g m m mg m 3 3 Sole these to find : m g+ m c) Now find the tensions: m3g m3 mg m ( mg+ m) m 3 3 mg 3 mg ( m+ m + m3) m m 3 m + m + m g 3 m g+ m m g+ m m3 m m + m + m g 3 m ( m + m + m )+ m m m m + m + m m + m3 m m m mg m g m m g m m m m g g m3 m m + m + m g 3 m ( m + m + m ) m m m m + m + m m+ m m m m mg m g g m 3 m 3 g 5