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

Transcription

1

2 PROLEMS. The -kg lunar lander is descending onto the oon s surface with a elocit of 6 /s when its retro-engine is fired. If the engine produces a thrust T for 4 s which aries with the tie as shown and then cuts off, calculate the elocit of the lander when t = 5 s, assuing that it has not et landed. Graitational acceleration at the oon s surface is.6 /s. (3/84)

3 SOLUTIO = -kg, = 6 /s, =? when t = 5 s, g oon =.6 /s Fdt g(5) (8) (8) / s 6 otion g T

4 PROLEMS. The hdraulic braking sste for the truck and trailer is set to produce equal braking forces for the two units. If the brakes are applied uniforl for 5 seconds to bring the rig to a stop fro a speed of 3 k/h down the percent grade, deterine the force P in the coupling between the trailer and the truck. The ass of the truck is Mg and that of the trailer is 7.5 Mg. (3/99)

5 PROLEMS The hdraulic braking sste for the truck and trailer is set to produce equal braking forces for the two units, brakes are applied uniforl for 5 seconds to bring the rig to a stop fro a speed of 3 k/h down the percent grade, deterine the force P in the coupling between the trailer and the truck. truck = Mg, trailer = 7.5 Mg. FD of whole sste Fdt F b 3, (9.8)sin 5.7F F F dt FD of trailer b 3 5P 65, P 33 P 3.3 k( tension) 3 k / h 8.33 / s (9.8)sin 5.73 P b 5 5 trailer W trailer F b tan., 5.7 trailer truck W trailer F b W truck F b P

6 PROLEMS 3. The 4 gra projectile is fired with a elocit of 6 /s and picks up three washers, each with a ass of gra. Find the coon elocit of the projectile and washers. Deterine also the loss DE of energ during the interaction. (3/9)

7 PROLEMS p = 4 g, = 6 /s, w = g. Find the coon elocit of the projectile and washers. Deterine the loss DE of energ during the interaction. t Fdt G G.43(.) / s 6 DE DT DVg DV e T T.44(9.9).4(6) DE 7.8 kj J

8 PROLEMS 4. tennis plaer strikes the tennis ball with her racket while the ball is still rising. The ball speed before ipact with the racket is =5 /s and after ipact its speed is = /s, with directions as shown in the figure. If the 6-g ball is in contact with the racket for.5 s, deterine the agnitude of the aerage force R eerted b the racket on the ball. Find the angle b ade b R with the horizontal. Coent on the treatent of the ball weight during ipact. (3/)

9 SOLUTIO in direction t F dt R.5R.5R in direction t F dt R R t t R cos.6 5 cos.6(9.8) t.35 b = 5 /s, = /s, = 6-g, t =.5 s, deterine R eerted b the racket on the ball and b ade b R with the horizontal. Coent on the treatent of the ball weight during ipact. R R R R tan b sin.65 sin R R b 8.68 R R R W=.59

10 PROLEMS 5. The 4-kg bo has taken a running jup fro the upper surface and lands on his 5-kg skateboard with a elocit of 5 /s in the plane of the figure as shown. If his ipact with the skateboard has a tie duration of.5 s, deterine the final speed along the horizontal surface and the total noral force eerted b the surface on the skateboard wheels during the ipact.

11 SOLUTIO = 4-kg, S = 5-kg, = 5 /s, t =.5 s, =?, deterine the noral force eerted b the surface on the skateboard wheels during the ipact. ( + S )g Linear oentu is consered in -direction SS S 5 cos / s 4 4 S S.5 5sin or S g dt.44 k

12 PROLEMS 6. The siple pendulu of ass and length l is suspended fro the trolle of ass. If the sste is released fro rest at =, deterine the elocit of the trolle when = 9. Friction is negligible. (3/3)

13 PROLEMS pendulu of ass, length l suspended fro trolle of ass. Sste released fro rest at =, deterine elocit of trolle when = 9. l = = 9 W=g T l l F dt, g gl gl gl gl l V T U D D

14 PROLEM 7. sall gra particle is projected with a horizontal elocit of /s into the top of the sooth circular guide fied in the ertical plane. Calculate the tie rate of change H of angular oentu about point when the partcle passes the botto of the guide at C. (3/5)

15 PROLEM = g, = /s, Calculate the tie rate of change T U C F a a C C a T gh gh 3.8 n H of angular oentu about point when the partcle passes the botto of the guide at C. C C C C C (9.8)(.5) ( / s) / s n W=.(9.8) =.(9.8).(55.4) H M W i j.59k C t

16 PROLEM 8. sall. kg particle is gien a speed of /s at point on the horizontal - plane and is guided b the fied cured rail. Friction is negligible. s the particle crosses the -ais at, its elocit is in the - direction and as it crosses the -ais at point, its elocit akes a 6 angle with the -ais. The radius of curature of the path at is 5. Deterine the tie rate of change of the angular oentu H O of the particle about the z-ais through O at both and. (3/3)

17 PROLEM =. kg, = /s (//), = 5. Deterine the tie rate of change of the angular oentu H O of the particle about the z-ais through O at both and. / s b 5 C t t so M O fro Oz H Oz H Oz F M M n Oz Oz a n 6 / s so b H Oz ( in clockwise, z b.8(.5). direction)..8.5

18 PROLEM 9. pendulu consists of two 3. kg concentrated asses positioned as shown on a light but rigid bar. The pendulu is swinging through the ertical position with a clockwise angular elocit w = 6 rad/s when a 5-g bullet traeling with elocit =3 /s in the direction shown strikes the lower ass and becoes ebedded in it. Calculate the angular elocit w which the pendulu has iediatel after ipact and find the aiu deflection of the pendulu. (3/35)

19 SOLUTIO ass = 3. kg, w = 6 rad/s (cw), bullet = 5 g, =3 /s. Calculate angular elocit w which the pendulu has iediatel after ipact and find the aiu ngular oentu is consered during ipact; t M Odt HO H, O H O H O M O r r r. j 3.(.)(6) i.4 j 3.(.4)(6) i.4 j.5(3 cos i 3sin j). cosj.sin i 3.(. cosi. sin j).4 cosj.4sin i 3.5(.4 cosi.4 sin j) or.768 k 3.7 k k.8 cos.798k.5 cos k.5 sin k in scalar for rad / s deflection of the pendulu. sin cos.5 sin cos ( ccw) k.8 sin k.64 w O w

20 SOLUTIO Energ considerations after ipact; U DT T T T DT e T (aiu DV g DV deflection (Datu at O) ) O w.558 J w ΔV g 3.(9.8)(.cos.) 3.5(9.8)(.4cos.4) 6.47( cos ) ( cos ), cos o