1. The 200-kg lunar lander is descending onto the moon s surface with a velocity of 6 m/s when its retro-engine is fired. If the engine produces a

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2 PROBLEMS. The -kg lunar lander is descending ono he moon s surface wih a eloci of 6 m/s when is rero-engine is fired. If he engine produces a hrus T for 4 s which aries wih he ime as shown and hen cus off, calculae he eloci of he lander when = 5 s, assuming ha i has no e landed. Graiaional acceleraion a he moon s surface is.6 m/s. (3/84)

3 SOLUTIO m = -kg, = 6 m/s, =? when = 5 s, g moon =.6 m/s Fd m m mg(5) (8) (8) m/ s 6 moion mg T

4 PROBLEMS. The 9-kg block is moing o he righ wih a eloci of.6 m/s on a horizonal surface when a force P is applied o i a ime =. Calculae he eloci of he block when =.4 s. The kineic coefficien of fricion is m k =.3. (3/87)

5 SOLUTIO F mg 9(9.8) 88.3 in x direcion Fd m 7. d 36 m.4. m = 9-kg, =.6 m/s, =? when =.4 s. m k =.3 d.3(88.3).4 d 9(.6) 7(.) 36(.) 6.49(.4) m / s moion W=mg x P F f =m k

6 PROBLEMS 3. The 4 gram projecile is fired wih a eloci of 6 m/s and picks up hree washers, each wih a mass of gram. Find he common eloci of he projecile and washers. Deermine also he loss DE of energ during he ineracion. (3/9)

7 PROBLEMS m p = 4 g, = 6 m/s, m w = g. Find he common eloci of he projecile and washers. Deermine he loss DE of energ during he ineracion. Fd G G.43(.).4 m m 9.9 m/ s 6 DE DT DVg DV e T T m.44(9.9).4(6) DE 7.8 kj m J

8 PROBLEMS 4. A ennis plaer srikes he ennis ball wih her racke while he ball is sill rising. The ball speed before impac wih he racke is =5 m/s and afer impac is speed is = m/s, wih direcions as shown in he figure. If he 6-g ball is in conac wih he racke for.5 s, deermine he magniude of he aerage force R exered b he racke on he ball. Find he angle b made b R wih he horizonal. Commen on he reamen of he ball weigh during impac. (3/)

9 SOLUTIO in x direcion F xd R.5R.5R m m.6.7 in direcion F d R R x R x cos.6 5 cos m m.6(9.8).35 b = 5 m/s, = m/s, m = 6-g, =.5 s, deermine R exered b he racke on he ball and b made b R wih he horizonal. Commen on he reamen of he ball weigh during impac. x R R R x R x.5 x an b sin.65 sin R R x b 8.68 R x R x R x W=.59

10 PROBLEMS 5. The 4-kg bo has aken a running jump from he upper surface and lands on his 5-kg skaeboard wih a eloci of 5 m/s in he plane of he figure as shown. If his impac wih he skaeboard has a ime duraion of.5 s, deermine he final speed along he horizonal surface and he oal normal force exered b he surface on he skaeboard wheels during he impac.

11 SOLUTIO mb = 4-kg, m S = 5-kg, = 5 m/s, =.5 s, =?, deermine he normal force exered b he surface on he skaeboard wheels during he impac. (m B +m S )g x Linear momenum is consered in x-direcion m B Bx mssx mb ms 5 cos m / s 4 m B B 4 m S S.5 m 5sin B 44 m or S g d.44 k

12 PROBLEM 6. The small spheres, which hae he masses and inial elociies shown in he figure, srike and become aached o he spiked ends of he rod, which is freel pioed a O and is iniiall a res. Deermine he angular eloci w of he assembl afer impac and calculae he change D E in he ssem energ. eglec he mass of he rod compared wih m. (3/)

13 SOLUTIO m E m m m m m L m T T V V T E L L L k m L k m L L m k L m k L i ml Lj i ml Lj i m Lj i m Lj m r m r H H H H d M m L g e O O O O O D D D D D w w w w x z small spheres srike and become aached o he spiked ends of he rod, which is freel pioed a O and is iniiall a res. Deermine he angular eloci w of he assembl afer impac and calculae he change D E in he ssem energ.

14 PROBLEM 7. A small gram paricle is projeced wih a horizonal eloci of m/s ino he op A of he smooh circular guide fixed in he erical plane. Calculae he ime rae of change H B of angular momenum abou poin B when he parcle passes he boom of he guide a C. (3/5)

15 PROBLEM m = g, A = m/s, Calculae he ime rae of change TA U m C F ma a A C AC A a T mgh gh 3.8 n H B of angular momenum abou poin B when he parcle passes he boom of he guide a C. C AC AC C m C (9.8)(.5) ( m/ s) m/ s n W=.(9.8) = A.(9.8).(55.4) H B M W.79 B 7.6.5i j.59k m C

16 PROBLEM 8. A pendulum consiss of wo 3. kg concenraed masses posiioned as shown on a ligh bu rigid bar. The pendulum is swinging hrough he erical posiion wih a clockwise angular eloci w = 6 rad/s when a 5-g bulle raeling wih eloci =3 m/s in he direcion shown srikes he lower mass and becomes embedded in i. Calculae he angular eloci w which he pendulum has immediael afer impac and find he maximum deflecion q of he pendulum. (3/35)

17 SOLUTIO m mass = 3. kg, w = 6 rad/s (cw), m bulle = 5 g, =3 m/s. Calculae angular eloci w which he pendulum has immediael afer impac and find he maximum Angular momenum is consered during impac; q M Od HO H, O H O H O M O r m r m r. j 3.(.)(6) i.4 j 3.(.4)(6) i.4 j.5(3 cos i 3sin j). cosqj.sin qi 3.(. cosqi. sin qj).4 cosqj.4sin qi 3.5(.4 cosqi.4 sin qj) or.768 k 3.7 k k.8 cos.798k.5 cos qk.5 sin qk in scalar form rad / s deflecion q of he pendulum. sin q cos q.5 sin q cos q ( ccw) qk.8 sin qk.64 w q q O w q

18 SOLUTIO Energ consideraions afer impac; q U DT T T T DT e T (maximum DV g DV deflecion (Daum a O) ) q O q w.558 J w q ΔV g 3.(9.8)(.cosq.) 3.5(9.8)(.4cosq.4) 6.47( cosq ) ( cosq ), cosq.65 q 5. o

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