1. The phee P tel in tight line with contnt peed of =100 m/. Fo the intnt hown, detemine the coeponding lue of,,,,, eltie to the fixed Ox coodinte tem. meued + + Poition Velocit e 80 e 45 o 113. 137 d / m co15 96. 593 m / in15 5. 88 m / 5. 88 113. 137 9
The phee P tel in tight line with contnt peed of =100 m/. cceletion ct + 0 0 0 + 5. 9 m / 391 d / 0
. the hdulic clinde otte ound O, the expoed length l of the piton od P i contolled b the ction of oil peue in the clinde. If the clinde otte t the contnt te =60 deg/ nd l i deceing t the contnt te of 150 mm/, clculte the mgnitude of elocit nd cceletion of end B when l =15 mm. Velocit cceletion 548. 31e 0 e e 150e 53. 59e e e 150 = 375 + l when l =15 mm = 500 mm l 150 mm / ( ct ) 0 60 deg/ 0 mm / 150 60 180 53. 59 544. 66 500 548. 31 mm / 0 150 314e 3 548. 31 314 631. 85 mm / 3 d / ( ct ) 500 53. 59 3 mm / 314 mm / 3 mm /
3. t the bottom of loop in the eticl (-) plne t n ltitude of 400 m, the iplne P h hoizontl elocit of 600 km/h nd no hoizontl cceletion. The diu of cutue of the loop i 100 m. Fo the d tcking t O, detemine the ecoded lue of nd fo thi intnt.
166. 67 100 3. 15 m / + cceletion (no hoizontl cceletion) + 1000 tn Poition 400 400 1000 Velocit 166. 67 in 1. 8 61. 896 1077. 03 m 1. 8 600 166. 67 m / 3. 6 co 166. 67 co 1. 8 154. 75 m / o 0575 100 m (diu of cutue in noml & tngentil coodinte) = 1077.03 m (dil ditnce meued fom fixed point (pole) to pticle in pol coodinte) in 3.15in 1.8 8.597 m / co 3.15co 1.8 1.49 m / 8.597 1077.03 0575 1.158 m / 036 m / d / d /
4. The hdulic clinde gie pin contnt elocit = m/ long it xi fo n intel of motion nd, in tun,cue the lotted m to otte bout O. Detemine the lue of,, nd fo the intnt when =30 o.
,, = m/ (ct), detemine when = 30. Pin : (Piton: ectiline motion O: in pol coodinte) Geomet: + b 30 b 180 30 10 30 iocele tingle = 300 mm + b =30 O 300 mm 30 B B Velocit: cceletion: 0 co b co30 1. 73 m / 0 in b in30 1 m / 0 1 3 0 33. 33 3. 3 m / 1 73 3 3. 33 d /. 3. 33 38. 45 d /
5. Pin moe in cicle of 90 mm diu cnk C eole t the contnt te b 6 d /.The lotted link otte bout point O the od ttched to moe in nd out of the lot. Fo the poition b=30 o, detemine,, nd. Cnk C (Pin : Cicul Motion) In Noml nd Tngentil Coodinte: Velocit : mm/ b C 6 90 54 cceletion: b C 0 b : ct b 0 b C 6 90 3. 4 mm / fo t n 90 in Geomet b 30 t n 6. 57 in30 300 90 11. 46 o 30090 O co30 6. 57 mm +t =( ) +n 30 b C
,, fo b=30 o, detemine nd. O (Pin : In Pol Coodinte) + O Velocit : 11.46 o 11.46 o 30 o 30 b + C 54 mm / 3. 4 mm / in 48. 54 4 47 cceletion: co 48. 54 35. 75 mm / mm / 4 47 6. 57 1786 d / co 41. 46 4. 8 mm / in 41. 46 1. 45 mm / 4. 8 6. 57 1. 45 6. 57 1786 31. 507 35. 75 1786 151 d / mm /
6. t time t=0, the bll i thown with n initil peed of 30 m/ t n ngle of 30 o to the hoizontl. Detemine the quntitie,,,, nd, ll eltie to the x- coodinte tem hown, t time t=5.
Detemine the quntitie,,,,, t time t=5. in ctein coodinte x x xo o x t 30co 30 5 x 1. 99 m x x o o t 30 in30 1 gt 1 5 9. 81 5 8. 7 m 30co30 gt 30 in30 9. 81 5 o x 5. 98 m / o 1 095 m / 1. 99 8. 7 15. 4 8. 7 tn 3. 48 1. 99 o m + =8.7 m + //x x =3.48 o x=1.99 m x tn x 7. 87 1. 3 o m /
Detemine the quntitie,,,,, t time t=5. in pol coodinte + 1.3 o + //x =3.48 o Velocit co in 7. 87 co3. 48 1. 3 7. 33 m / 5. 437 15. 4 7. 87 in3. 48 1. 3 5. 437 m / 353 d / cceletion (=9.81 m/ ) in 5. 68 m / co 8. 75 m / 5. 68 15. 4 353 3. 349 m / 8. 75 3. 349 353 15. 4 715 d /
7. When the oke i t the poition d = 7 m, it h elocit of = m/ towd ight which i inceing t te of 6 m/ ech econd. Pin P i foced to moe in the eticl lot of the oke nd the pbolic ufce. Fo the intnt depicted, detemine the elocit nd cceletion of pin P in ) Ctein Coodinte, b) Noml nd Tngentil Coodinte, c) Pol Coodinte.
8. Pticle i moing long pbolic pth. t the intnt when the bci of it poition i x = m, it elocit i 6.45 m/ nd it decee t te of 15 m/ pe econd. Detemine the elocit nd cceletion of the pticle fo thi intnt in ) Ctein coodinte, b) Noml nd tngentil coodinte, c) Pol coodinte. (m) 3 x 16 x = m x (m)
9. The peg moe in the cued lot defined b the eqution = 4in() [m ], nd though the lot in the m. t = 30, the ngul elocit nd ngul cceletion of the m e = d/ nd = 1.5 d/, epectiel. Detemine the mgnitude of the elocit nd cceletion of the peg t thi intnt, ) in pol coodinte, b) in Ctein coodinte, c) in noml nd tngentil coodinte. lo detemine the diu of cutue fo thi intnt.,
1 Pticle P moe long cuiline pth hown in the figue. t the intnt when = m, = 30, the mgnitude of it elocit i 3. m/ nd the elocit ecto mke n ngle of b = 60 with the hoizontl. The -component of the cceletion of pticle P i = 5 m/ ; it - component i = 1.83 m/. Detemine component of the elocit nd cceletion in ) Ctein Coodinte, b) Noml nd Tngentil Coodinte, lo diu of cutue of the pth fo the me intnt, c) Pol Coodinte.
= m, = 30, =3. m/, b = 60 = 5 m/, = 1.83 m/ Velocit +t + + +n 30 o 3. 3. e m / in noml nd tngentil coodinte in Ctein coodinte t 3. co 60i 3. in60 j 1. 6i. 77 j in pol coodinte 3. co30e 3. in30e. 77e 1. 6e
= m, = 30, =3. m/, b = 60 = 5 m/, = 1.83 m/ cceletion co co30 co30 90 1. 83 5 60 1. 83 co co 30 5 co 90 1. 83 30. 73co90 co30co in30 in. 73 co90co in90 in co 30. 73 co 90 // +n //x + 30 o +t + 866co 5in. 73in in 68 co in Ctein coodinte 7. 07 in30 30 o in pol coodinte 1. 83e t 7. 07 coe 7. 07 co t 1. 89e 6. 89e 15 7. 07 m / i 5 j 5i 5 j 60e 7. 07 in 60 n 1. 83e in noml nd tngentil coodinte Rdiu of cutue o 3. n 6. 89 6. 89e e n 1. 5 m
11. The lotted m B otte bout the uppot. Fo the intnt when /6 din, the 3 ngul elocit of the m i d/ nd it ngul cceletion i d/. m B foce pin C to moe while ting inide the chnnel, the ping enue tht the pin doe not looe contct with the chnnel ufce. Fo the poition indicted in the figue detemine the elocit nd cceletion of pin C in Ctein Coodinte. lo detemine the lue of nd.
l 35 m x 35 in 175 m 1. x d dx x 175. 4x 4 b. 78 Velocit: // + 30 o +t b.78 o 30 o //x co 37. d / 35 1. 818 m / in 37. co 37. 1. 448 In Ctein Coodinte: 35 m in 37. 1. 099 m / m / x co. 78 in. 78 1. 676i 7039 j
cceletion: 3 3 17 6 53 0 818 1 53 0 4 4 0 1 1 48 9 448 1 3 0 35 0 3 0 m /... m... dx d dx d m /..... n / / * *
// // + //t +n 30 o +t co 5. 78 co 5. 78 9. 48 b.78 o co co5. 78 in in5. 78 9. 48 1 n b.78 o 30 o //x in n 1 in 6. 17 co co5. 78 in in5. 78 in 9. 48 6. 17 1. 516 6048 co. 31 in x co(. 78 ) 19. 504 m / in(. 78 ) 14. 93 m /. 684 m / 14. 66 o 4. 565 m /. 684 35 6. 138 m /