# PHYSICS 1210 Exam 1 University of Wyoming 14 February points

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1 PHYSICS 1210 Em 1 Uniersiy of Wyoming 14 Februry poins This es is open-noe nd closed-book. Clculors re permied bu compuers re no. No collborion, consulion, or communicion wih oher people (oher hn he dminisror) is llowed by ny mens, including bu no limied o erbl, wrien, or elecronic mehods. Shring of merils including clculors is prohibied. If you he quesion bou he es, plese rise your hnd. Plese do no open his es bookle unil eeryone hs receied bookle nd he es dminisror hs indiced for you o begin. While you re wiing, mke sure h your nme is wrien clerly he op of he firs pge. g = 9.80 m/s 2 1 rdin = mi = km 1 m = in = 3.28 f A B = ABcos = A B + A y B y + A z B z = dr d = d d = d 2 r d 2 = 0 + = /2 2 2 = ( 0 ) 0 = ( 0 + ) /2 = 0 + d = 0 + d = 0 + r = r = ( 0 cos 0 ) y = ( 0 sin 0 ) 1/2 g 2 = 0 cos 0 y = 0 sin 0 g R = 2 0 sin(2 0 )/g r = 2 /R r = 4 2 R/T 2 T = 2 R/T P/A = P/B + B/A A

2 Nme: Answer Key 1. (10 poins) If he sclr produc (do produc) of wo ecors is posiie, wh does h ell you bou he ecors? The ngle beween he wo ecors is cue, so hey poin mosly in he sme direcion. 2. (10 poins) A clssme ells you h he formul for he olume of cone of bse rdius r nd heigh h is r 3 h/3. Eplin why h formul cnno be correc. Th formul would gie unis of (disnce) 4. Volume unis mus be (disnce) (15 poins) The digrms o he righ show fie pirs of ccelerion nd elociy ecors. (The oulined rrow is he ccelerion ecor nd he simple rrow is he elociy ecor.) For ech erbl descripion of moion, idenify which numbered pir of ecors corresponds o he moion described.. 3 speeding up wihou chnging direcion 1 b. 1 slowing down wihou chnging direcion 2 c. 5 chnging direcion consn speed 3 d. 2 speeding up while chnging direcion 4 e. 4 slowing down while chnging direcion 5 PHYS Em 1 A 1 of 7

3 4. (10 poins) A sone is hrown ino he ir n ngle boe he horizonl nd feels negligible ir resisnce. Which one grph bes depics he sone s speed s funcion of ime while i is in he ir? 5. (16 poins) Ech of he quesions below conins he sme grph of posiion s funcion of ime nd erbl descripion of some priculr condiions of moion. Mrk on ech grph he specific ime, imes, or ime inerls h he condiions on he grph mch he descripion. If he condiions described re no me ny ime on he grph, indice h.. speeding up b. slowing down PHYS Em 1 A 2 of 7

4 c. < 0 d. = 0 e. > 0 f. = 0 g. < 0 h. > 0 PHYS Em 1 A 3 of 7

5 6. (10 poins) A sled srs from res nd slides down fricionless ir rck consn ccelerion. In 5.0 s, i rels disnce of 50 m down he rck. Wh is is ccelerion? The equion of moion is = 1/2 2. We know = 50 m nd = 5.0 s; so we cn sole for. = 2/ 2 = 2(50 m)/(5.0 s) 2 = 100/25 m/s 2 = 4 m/s A dr is lunched n ngle of below horizonl wih iniil speed 0 ime = 0. The lunch posiion is heigh H boe nd disnce L o he righ of he origin. In describing he siuion, use he coordine sysem in which up is he +y direcion, righ is he + direcion, nd he lunch posiion is (L, H).. (6 r poins) Fill in he ble wih formuls for he - nd y-componens of ccelerion, elociy r, nd posiion r s funcions of ime. Epress hem in erms of only he consns 0,, H, L, nd g, nd he rible. -componen y-componen r 0 g r 0 cos( ) 0 sin( ) g r L + 0 cos( ) H 0 sin( ) 1/2 g 2 b. (8 poins) A wh ime will he dr lnd on he ground heigh y = 0? Epress s formul gin in erms of some or ll of he quniies 0,, H, L, nd g. y = H 0 sin( ) 1/2 g 2 0 = H 0 sin( ) 1/2 g 2 0 = 1/2 g sin( ) H = 0 sin( ) ± ( 0 sin ) 2 + 2gH The posiie soluion is = g 0 sin( ) + ( 0 sin ) 2 + 2gH g PHYS Em 1 A 4 of 7

6 c. (8 poins) A wh horizonl disnce from he origin will he dr lnd on he ground? Epress s formul gin in erms of some or ll of he quniies 0,, H, L, nd g. = L + 0 cos( ) = L + 0 cos( ) = L + 0 cos( ) 0 sin( ) + ( 0 sin ) 2 + 2gH 0 sin( ) + ( 0 sin ) 2 + 2gH Noice h his reduces o he rnge equion if L = 0 nd H = 0. g g d. (3 poins) There should be wo soluions for he ime nd horizonl posiion of he dr reching he ground. Only one is physiclly pproprie. Wh is he mening of he oher soluion? If he equion of moion hd been lid before he lunch, he dr would he reled upwrd, reched he op of is rc, nd hen begun reling downwrd before = 0. The oher soluion would he been when he dr ws reling upwrd ground leel. e. (4 poins) Wh is he minimum speed of he dr during he ime inerl sring immediely fer i is lunched nd ending immediely before i lnds? 0 f. (3 poins) As he dr flls, does he re which is speed chnges increse, decrese, or remin consn? I increses. The re of chnge of speed is he componen of ccelerion prllel o he elociy. Since he elociy becomes more downwrd s he dr flls, nd since he ccelerion is g downwrd, he prllel componen increses wih ime. PHYS Em 1 A 5 of 7

7 8. A bll is dropped from res from he op of building h is m high. A he sme insn, ime = 0, second bll is projeced ericlly upwrd from he ground, such h is speed is zero when i reches heigh of m.. (8 poins) A wh ime do he blls cross? Dropped bll: y D = H 1/2g 2 Projeced bll: y P = 0 1/2 g 2 = H ime H = 0 g = 0 ime H H = 0 /g H = 2 0 /g 1/2 g( 0 /g) 2 = 1/2 2 0 /g When hey cross: 0 = 2gH = (19.6m/s 2 )(176.4 m) y D = y P = 58.8 m/s H 1/2 g 2 = 2gH 1/2g 2 = H/2g = (176.4 m)/(19.6 m/s 2 ) = 9 s = 3.0 s b. (8 poins) A wh heigh do he blls cross? Dropped bll: y D = H 1/2g 2 = m (4.9 m/s 2 )(9 s 2 ) = m 44.1 m = m Projeced bll: y P = 0 1/2 g 2 = (58.8 m/s)(3 s) (4.9 m/s 2 )(9 s 2 ) = m 44.1 m = m c. (6 poins) When hey cross, wh re he speeds of he wo blls? Be sure o gie he speed of ech one. Dropped bll: = g = (9.8 m/s 2 )(3 s) = 29.4 m/s For boh blls, he speed is 29.4 m/s. Projeced bll: = 0 g = 58.8 m/s (9.8 m/s 2 )(3 s) = 58.8 m/s 29.4 m/s = m/s d. (4 poins) Wh is he ccelerion of he blls when hey cross? Be sure o gie he ccelerion of ech one. For boh blls, he ccelerion is g downwrd. PHYS Em 1 A 6 of 7

8 9. In n episode of he Briish eleision show Top Ger, one of he hoss droe cr on helicl ph (like corkscrew) in unnel so h i briefly reled upside down on he roof of he unnel. The rdius of he unnel ws 5.0 meers.. (8 poins) How quickly would he cr need o mke one loop (wh is is period of roion) so h is cenripel ccelerion ws les g? = 4 2 R/T 2 T = 2 R/ = 2 R/g = 2 (5.0 m)/(9.8 m/s 2 ) = 2 ( s) = 4.49 s b. (8 poins) If he cr s ph ws ngled 20 o he rodwy, how fs ws he cr reling o eecue he loop? = 2 R/T / = sin( ) = /sin( ) = 2 R/(T sin ) = = (5 m)(9.8 m/s 2 ) /sin(20 ) = 7/( ) m/s = m/s 2 R 2 R/g sin( ) = Rg /sin( ) PHYS Em 1 A 7 of 7

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