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1 Page 1 o The brighes sar in he nigh sky is α Canis Majoris, also known as Sirius. I lies 8.8 ligh-years away. Express his disance in meers. ( ligh-year is he disance coered by ligh in one year. Ligh raels in acuum a m/s). a m b m c m d m e m days 4 h 3600 s 3 10 m ligh years m. Le 3iˆ + 5kˆ and iˆ+ ˆj+α kˆ. ind he alue o scalar α ha makes hese wo ecors perpendicular o each oher. a. α 0.3 b. α 0.6 c. α 0.9 d. α 1. e. α year 1 day 1 h 1 s Perpendicular α 0 α 0.6

2 Page o box has an iniial speed 0 up a ricionless incline. The box moes up he incline and hen reurns o is iniial posiion, and coninues o moe down he incline. Which o he ollowing elociy ersus ime graphs corresponds o his moion? C D E The box goes rom posiie elociy o zero elociy (or an insan) and hen o negaie elociy. also, he slope o he () graph should be consan (consan acceleraion).

3 Page 3 o 13 The siuaion below reers o he nex wo quesions: paricle moes along he rajecory shown below a consan speed. The posiions o he paricle a 0 and a 1 s are shown. 1 s 0 4. Which o hese ecors bes describes he direcion o he aerage elociy o he paricle beween 0 and 1 s? a. b. c. d. e. The aerage elociy poins in he same direcion as r: 1 s r 0 5. Which o hese ecors bes describes he direcion o he insananeous acceleraion o he paricle a 0? a. b. c. d. e. The insananeous acceleraion is he cenripeal acceleraion (speed is consan), so is direcion is perpendicular o rajecory (or o he insananeous elociy a ha poin) and poining owards he cener o curaure.

4 Page 4 o 13 The siuaion below reers o he nex wo quesions: You are sanding on he edge o a cli o heigh h. You hrow a ball a an angle θ 30 aboe he horizonal wih an iniial speed 0 54 m/s. Using a sop wach, you deermine ha he ball srikes he ground a he base o he cli 7 s aer release. θ h D 6. Wha is he horizonal disance D coered by he ball? a. D 03 m b. D 8 m c. D 37 m d. D 48 m e. D 564 m D cos θ (54 m/s)cos30 (7 s) 37 m 0x 0 7. wha ime aer he release does he ball reach is maximum heigh? a. 1.9 s b..8 s c. 3.5 s d. 4.1 s e. 4.8 s Condiion or maximum heigh: y a 0 y 0 sinθ g 0 y sin θ (54 m/s)sin 30 g 9.8 m/s 0.8 s

5 Page 5 o 13 The siuaion below reers o he nex wo quesions: ennis ball o weigh W 0.5 N is aached o a massless rope and swung in a erical circle. The rope is L m long. L g 8. Wha is he minimum speed o he ball a he highes poin o he rajecory i he rope is o say sraigh? a. min 1.0 m/s b. min 4.4 m/s c. min 8.8 m/s d. min 19.6 m/s e. min 79.3 m/s This is he ree-body diagram o he ball on op o is rajecory: T W T + mg ma m L The minimum speed is gien by he condiion T 0: mg m L min min Lg 4.4 m/s

6 Page 6 o 13

7 Page 7 o Which o he ollowing is he correc expression or he ension in he sring T when he ball is a he lowes poin? a. b. c. d. e. T 0 T W T W T W 1 + gl T W 1 gl This is he ree-body diagram a he boom o he rajecory: T W T W m L T m + W m + W L gl

8 Page 8 o Two spaceships and moe oward one anoher as shown. ime 0, spaceship launches a shule cra oward spaceship. ime, he shule reaches spaceship. 0 d 0 Shule d Shule The aerage speed o he shule relaie o spaceship is: a. b. c. d. S, S, S, S, d e. None o he aboe d 0 d d0 d + d0 0, he shule is relaie disance zero rom spaceship., is disance o spaceship is d. So he displacemen relaie o is x d. x S, S, d

9 Page 9 o 13 The siuaion below reers o he nex wo quesions: lock 1 wih mass m kg and block wih mass m 1.6 kg si aop a ricionless double inclined plane as shown. The wo blocks are conneced o one anoher hrough a massless sring around an ideal pulley. Direcion o acceleraion N 1 T T N m 1 m W 1 W θ 1 30 θ Wha is he magniude o he acceleraion o he blocks? a. a 0.35 m/s b. a 1.6 m/s c. a.5 m/s d. a 3.0 m/s e. a 3.3 m/s Use he ree-body diagram aboe. I he whole sysem m 1 + m is considered as one, inernal orces can be ignored. The ne orce in he direcion o moion is: mg 1 sinθ1 mg sin θ ( m1+ m) a m1sinθ1 msinθ a g 3.3 m/s m + m 1 1. Now block 1 is coaed wih a rough pain so he ricion orce beween his block and he surace is no negligible (bu no srong enough o preen he blocks rom moing). Compare he ension on he sring beore and aer he coaing. a. The ension says he same. b. The ension increases only on he side o mass 1 (le side). c. The ension decreases only on he side o mass 1 (le side). d. The ension increases on boh ends. e. The ension decreases on boh ends. The sysem has now a smaller acceleraion, so he ne orce on boh blocks needs o be smaller. The orces on block along he incline are he ension and he appropriae componen o he weigh: mg sinθ T ma. or a o be smaller, T mus be larger. nd he change applies o any poin on he sring, since his is a massless sring.

10 Page 10 o 13 The siuaion below reers o he nex wo quesions: box o weigh W 30 N is being pulled across a rough, horizonal surace wih a orce T 10 N exered by a sring ha makes an angle θ 45 wih he horizonal. The box moes a a consan speed 3 m/s across he surace. N T θ W 13. Which o he ollowing expressions is correc or he magniude o he normal orce N exered by he loor on he box? a. b. c. d. e. N W + Tcosθ N W Tcosθ N W + Tsinθ N W Tsinθ N W Newon s second law in he erical direcion, rom he ree-body diagram aboe: N + Tsinθ W ma y 0 N W Tsinθ 14. Wha is he magniude o he ricion orce beween he box and he surace? a. k 3.4 N b. k 5. N c. k 6.9 N d. k 7.1 N e. k 10 N Newon s second law in he horizonal direcion, rom he ree-body diagram aboe: Tcosθ ma 0 k k T cosθ 7.1 N x

11 Page 11 o 13

12 Page 1 o 13 The siuaion below reers o he nex wo quesions: locks and accelerae on a ricionless horizonal surace while being pushed by your hand wih a orce. The mass o block is larger han he mass o block. 15. Compare he acceleraion o each block and he ne orce on each block: a. b. c. d. e. a < a < ne, ne, a a < ne, ne, a a ne, ne, a > a ne, ne, a a > ne, ne, The acceleraion needs o be he same or boh blocks, since hey are moing ogeher. Ne orce is equal o mass imes acceleraion, so a greaer ne orce is required or. 16. The orce exered by block on block is: a. 0 b. c. d. e.,,,, m m + m m m + m mm m + m I is also equal (in magniude) o he orce by on, which is he only orce on block, so,, ne, ma m + m m ( ) (To ind he acceleraion, use he ne orce on he whole sysem: m + m a)

13 Page 13 o Two boxes o masses m and m are sacked as shown in he igure below on op o a horizonal ricionless able. The coeicien o saic ricion beween he wo boxes is µ s. The boom box is being pulled wih a orce. ind he maximum alue o or which he boxes will moe ogeher. ricionless µ s s boom by op m m s op by boom a. b. c. d. e. max max max max max 3µ mg s s µ mg 3 µ smg 1 µ smg 1 µ smg 3 The only horizonal orce on he op box is he saic ricion s, so S by 3ma, so he saic ricion on he op box needs o be 3 Saic ricion has a maximum magniude S ma. The acceleraion is gien µ N µ mg, so he maximum applied orce is: S S S max 3 µ mg S

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