Exam #2 PHYSICS 211 Monday July 6 th, 2009 Please write down your name also on the back page of this exam

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1 Exa #2 PHYSICS 211 Monday July 6 h, 29 NME Please wrie down your nae also on he back pae of his exa 1. The fiure ives how he force varies as a funcion of he posiion. Such force is acin on a paricle, which underoes one-diensional oion. If he paricle beins a res a x=, 1 Find he x coordinae a which he paricle has he reaes kineic enery NSWER x = 3 1B Find he x coordinae a which he paricle has zero speed NSWER x = 6 F 2 N 1 N -1 N x () -2 N 2. = wo sall objecs and B of he sae ass are hrown siulaneously fro he level z= and wih he sae iniial speed of 1 /s (he iniial velociy akes 45 o wih he horizonal.) Objec- ravels free in he air (is rajecory is indicaed in he raph) while objec-b oves alon a fricionless surface of a 45 o rap. B z = h 1 z =

2 2 Le s call h 1 he axiu heih reached by he objec-. Calculae he horizonal coponen of he velociy of he objec- when i passes by he axiu heih h 1. NSWER 7.1 /s 2B Calculae he x-coponen of he velociy of he objec-b when i passes by he heih level z= h 1. NSWER 5 /s 3. = wo sall objecs and B of he sae ass are hrown siulaneously fro he level z= and wih he sae iniial speed of 1 /s (he iniial velociy akes 45 o wih he horizonal.) Objec- ravels free in he air (is rajecory is indicaed in he raph) while objec-b oves alon a fricionless surface of a 45 o rap. B z = h 1 z = 3 How lon does i ake for he objec- o reach he axiu heih h 1? NSWER.7 s 3B How lon does i ake for he objec-b o reach (or pass by) he level of heih z= h 1. NSWER.42 s 4. ball slides couner-clockwise in a fricionless verical circular pah in a unifor raviaional field direced downwards.

3 4 When he block is a he posiion indicaed in he fiure, draw boh all he forces acin on he block, as well as he correspondin vecor velociy. Draw here he forces Draw here he vecor velociy 4B Usin he correspondin raphs iven below, draw he vecor acceleraion when he ball is a he lowes poin of is pah, as well as when he ball is a he hihes poin of is pah. Draw here he vecor acceleraion Draw here he vecor acceleraion lob of slie is launched or dropped fro he ede of a cliff. Circle he raphs ha could possible show how he kineic enery of he lob chanes durin is flih. a ) b ) c ) d ) e) ll he raphs above are incorrec 5B. lob of slie is dropped fro he ede of a cliff. Circle he raphs ha could possible show how he kineic enery of he lob chanes durin is flih. a ) b ) c ) d ) e) ll he raphs above are incorrec

4 6. 6 The oion of a paricle is described by a velociy vs ie raph (as shown in he fiure below. For each of he inervals indicaed in he fiure, indicae wheher he chane in he kineic enery of he paricle (caused by a variable oal force acin on he paricle) is posiive, zero, or neaive. 1 /s v B C 2 /s D F ie - 1 /s E - 2 /s NSWER W( B) Posiive W(B C) Zero W(C D) neaive W(D E) posiive W(E F) neaive 6B. The fiure below shows wo horizonal forces ha ac on a block ha, a =, is slidin o he rih across a fricionless floor. The fiure also shows hree plos of he block s kineic enery versus ie. F 1 F 2 P S U Which of he plos bes corresponds o he followin hree siuaions? i) F1 = F2 NSWER S ii) F1 > F2 NSWER U iii) F1 < F2 NSWER P

5 7 block of ass =.8 slides up a rouh rap. = he block is a (he boo of he rap) and is iniial speed is 5. /s. When he block reaches is hihes posiion 7 wha is he disance i has raveled alon he rap? a) 4.5 b) 3.1 c).5 d) 1. 7 e) N 7B wha is he work done by he raviaional force? a) J b) -12 J c) 3.1 J d) J e) N There is fricion k = s =.35 = x = and iniial speed: v = 5. / s x: posiion : ie = v = 9.8 / s 2 x 3 8 block of ass =.8 slides up a rouh rap. = he block is a (he boo of he rap) and is iniial speed is 5. /s. 8 When he block reaches is hihes posiion wha is he work done by he fricion force? a) J b) -3.3 J c) - 17 J d) J e) N 8B When he ball reurns o is iniial posiion, wha is is speed (in /s)? a) 1.7 b) 5.8 c) 4.3 d) 2.9 e) N = v = 9.8 / s 2 x 3 There is fricion k = s =.35 = x = and iniial speed: v = 5. / s x: posiion : ie Bonus quesion (5 poins) ball is sho fro round level over level round a a cerain iniial speed. The fiure below ives he raner of he ball versus is launch anle. Rank, fro reaes o lowes, he hree leered poins on he plo accordin o:

6 i) The oal flih ie of he ball NSWER: U, S, P ii) The ball s speed a axiu heih NSWER: P, S, U R P S U Soluion corresponds o Y U S P X

7 Helpful forulas verae velociy = x / verae acceleraion = v / insananeous velociy v = d x / d insananeous acceleraion a = d v / d Moion under consan acceleraion a v = v o + a x - x o = v o + (1/2) a 2 v 2 = v 2 o + 2 a (x x o ) Free fall v y = v oy - = 9.8 /s 2 y - y o = v oy - (1/2) 2 x - x o = v ox = 32 f/s 2 v 2 y = v 2 oy - 2 (y y o ) Projecile oion x = x o + (v o Cos ) y = y o + (v o Sin ) (1/2) 2 Rane R= (v 2 o /) Sin 2 Unifor circular oion a = v 2 /R Newon s second law F = a = W oal Work/ineic-enery heore