solucionario mecanica vectorial para ingenieros - beer & johnston (dinamica) 7ma edicion Cap 15

download solucionario mecanica vectorial para ingenieros - beer  & johnston (dinamica) 7ma edicion Cap 15

of 312

  • date post

    06-May-2015
  • Category

    Technology

  • view

    16.595
  • download

    92

Embed Size (px)

Transcript of solucionario mecanica vectorial para ingenieros - beer & johnston (dinamica) 7ma edicion Cap 15

  • 1.COSMOS: Complete Online Solutions Manual Organization SystemVector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell 2007 The McGraw-Hill Companies.Chapter 15, Solution 1.Angular coordinate: ( )238 6 2 radianst t = Angular velocity: ( )224 12 2 rad/sdt tdt = = Angular acceleration: 248 12 rad/sdtdt = = (a) When the angular acceleration is zero.48 12 0t = 0.250 st =(b) Angular coordinate and angular velocity at t = 0.250 s.( )( ) ( )( )3 28 0.250 6 0.250 2 = 18.25 radians = ( )( ) ( )( )224 0.250 12 0.250 2 = 22.5 rad/s =

2. COSMOS: Complete Online Solutions Manual Organization SystemVector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell 2007 The McGraw-Hill Companies.Chapter 15, Solution 2.30.5 cos4te t =( )3 30.5 3 cos4 4 sin 4t tde t e tdt = = ( )( )2 3 2 3 2 3 2 32 3 2 30.5 9 cos4 12 sin 4 12 sin 4 16 cos40.5 24 sin 4 7 cos4t t t tt tde t e t e t e tdte t e t = = + + = (a) 0,t = ( )0.5 = 0.500 rad =( )( )0.5 3 4.71 = = 4.71rad/s = ( )( )20.5 7 34.5 = = 234.5 rad/s = ( ) 0.125 s, cos4 cos 0, sin 4 sin 12 2b t t t = = = = =30.30786te =( )( )( )0.5 0.30786 0 0 = = 0 =( )( )( )0.5 0.30786 4 1.93437 = = 1.934 rad/s = ( )( )( )20.5 0.30786 24 36.461 = = 236.5 rad/s = 3. COSMOS: Complete Online Solutions Manual Organization SystemVector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell 2007 The McGraw-Hill Companies.Chapter 15, Solution 3.7 /60 sin 4te t =7 /6 7 /607sin 4 4 cos46t tde t e tdt = = + 2 2 27 /6 7 /6 7 /6 2 7 /607 /6 2 2049 28 28sin 4 cos4 cos4 16 sin 436 6 649 2816 sin 4 cos436 3t t t ttde t e t e t e tdte t t = = = + ( )a 0 0.4 rad, = 0.125 st =7 (0.125)/60.63245, 4 , sin 1, cos 02 2 2e t = = = =( )( )( )0.4 0.63245 1 0.25298 radians = = 0.253 rad =( )( ) ( )70.4 0.63245 1 0.92722 rad/s6 = = 0.927 rad/s = ( )( ) ( )2 2490.4 0.63245 16 1 36.551rad/s36 = = 236.6 rad/s = ( )b ,t = 7 /60te = 0 =0 =0 = 4. COSMOS: Complete Online Solutions Manual Organization SystemVector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell 2007 The McGraw-Hill Companies.Chapter 15, Solution 4.Angular coordinate: 1800 rev = 3600 radians =Initial angular velocity: 0 6000 rpm = 200 rad/s =Angular acceleration: constantd ddt d = = =d d =000d d = 2012 = ( )( )( )2220 20017.4533 rad/s2 2 3600 = = = (a) Time required to coast to rest.0 t = +0 0 20017.4533t = =36.0 st =(b) Time to execute the first 900 revolutions.900 rev = 1800 radians =2012t t = +( ) 211800 200 17.45332t t = 272 648 0t t + =( ) ( )( )272 72 4 6482t = 10.54 st = 5. COSMOS: Complete Online Solutions Manual Organization SystemVector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell 2007 The McGraw-Hill Companies.Chapter 15, Solution 5.( )( )1 0 12400 22400 rpm 80 rad/s, 0, 4 s60t = = = = =( )a 211 080, 20 rad/s4t tt = + = = = =( )( )2 21 01 1 1600 20 4 160 rad 80 rev2 2 2t t = + = + = = =1 80 rev =(b) 1 2 2 180 rad/s, 0, 40 st t = = =( ) 22 12 1 2 12 10 80, 2 rad/s40t tt t = + = = = ( ) ( ) ( )( ) ( )( )2 22 1 1 2 1 2 11 180 40 2 402 2t t t t = + = + 16001600 radians 800 rev2= = = 2 1 800 rev = 6. COSMOS: Complete Online Solutions Manual Organization SystemVector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell 2007 The McGraw-Hill Companies.Chapter 15, Solution 6.Angular acceleration: 0.230 t dedt = =Angular velocity: 0 0tdt = + 0.200 30t te dt= + 0.20300.2tte = ( )0.2150 1 t dedt= =When t = 0.5 s, ( )( )( )0.2 0.5150 1 e = 14.27 rad/s =Angular coordinate: 0 0tdt = + ( )0.200 150 1t te dt= + 0.201501500.2ttt e = ( )0.2150 750 1 tt e= When t = 0.5 s, ( )( ) ( )( )( )0.2 0.5150 0.5 750 1 e = 3.63 radians = 7. COSMOS: Complete Online Solutions Manual Organization SystemVector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell 2007 The McGraw-Hill Companies.Chapter 15, Solution 7.( ) 0.5 , 0.5 0.5da d dd = = = 030 0Integrating, 0.5 30 0.5d d = = 6060 radians 9.55 rev= = =29.55 rev =( ) 0.5 2d db dtdt = = Integrating,00 302t ddt= 02 ln30t = = t = ( )c ( )( )0.02 30 0.6 rad/s = =0.60 302t ddt= 0.62 ln 2 ln 5030t = = 7.82 st = 8. COSMOS: Complete Online Solutions Manual Organization SystemVector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell 2007 The McGraw-Hill Companies.Chapter 15, Solution 8.dk k d k dd = = = Integrating,0 612 0d k d = 2 212 60 02 2k = ( )a222129 s6k = = 29.00 sk =312 0d k d = 2 2 212 39 02 2 2 = ( )b ( )( )22 2 2 212 9 3 63 rad /s = = 7.94 rad/s = 9. COSMOS: Complete Online Solutions Manual Organization SystemVector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell 2007 The McGraw-Hill Companies.Chapter 15, Solution 9.( ) ( ) ( )/ 5 in. 31.2 in. 12 in.A O = + +r i j k( ) ( )/ 5 in. 15.6 in.B O = +r i j( ) ( ) ( )2 2 25 31.2 12 33.8 in.OAl = + + =Angular velocity.( )/6.765 31.2 1233.8A OOAl= = + +r i j k( ) ( ) ( )1.0 rad/s 6.24 rad/s 2.4 rad/s= + +i j kVelocity of point B./B B O= v r1.0 6.24 2.4 37.44 12 15.65 15.6 0B = = + i j kv i j k( ) ( ) ( )37.4 in./s 12.00 in./s 15.60 in./sB = + v i j kAcceleration of point B.B B= a v1.0 6.24 2.4 126.1 74.26 245.637.4 12 15.60B = = + i j ka i j k( ) ( ) ( )2 2 2126.1 in./s 74.3 in./s 246 in./sB = +a i j k 10. COSMOS: Complete Online Solutions Manual Organization SystemVector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell 2007 The McGraw-Hill Companies.Chapter 15, Solution 10.( ) ( ) ( )/ 5 in. 31.2 in. 12 in.A O = + +r i j k( ) ( )/ 5 in. 15.6 in.B O = +r i j( ) ( ) ( )2 2 25 31.2 12 33.8 in.OAl = + + =Angular velocity.( )/3.385 31.2 1233.8A OOAl= = + +r i j k( ) ( ) ( )0.5 rad/s 3.12 rad/s 1.2 rad/s= + +i j kVelocity of point B./B B O= v r0.5 3.12 1.2 18.72 6 7.805 15.6 0B = = + i j kv i j k( ) ( ) ( )18.72 in./s 6.00 in./s 7.80 in./sB = + v i j kAngular Acceleration.( )/5.075 31.2 1233.8A OOAl = = + +r i j k( ) ( ) ( )2 2 20.75 rad/s 4.68 rad/s 1.8 rad/s= i j kAcceleration of point B./B B O B= + a r v 0.75 4.68 1.8 0.5 3.12 1.25 15.6 0 18.72 6 7.8B = + i j k i j ka28.08 9 11.7 31.536 18.564 61.406= + +i j k i j k( ) ( ) ( )2 2 23.46 in./s 27.6 in./s 73.1in./sB = +a i j k 11. COSMOS: Complete Online Solutions Manual Organization SystemVector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell 2007 The McGraw-Hill Companies.Chapter 15, Solution 11.( ) ( ) ( ) ( ) ( ) ( )/ 500 mm 225 mm 300 mm 0.5 m 0.225 m 0.3 mB A = + = +r i j k i j k2 2 20.5 0.225 0.3 0.625 mABl = + + =Angular velocity vector.( )/100.5 0.225 0.30.625B AABl= = +r i j k( ) ( ) ( )8 rad/s 3.6 rad/s 4.8 rad/s= +i j k( ) ( )/ 300 mm 0.3 mE B = = r k kVelocity of E./ 8 3.6 4.8 1.08 2.40 0 0.3E E B= = = +i j kv r i j( ) ( )1.080 m/s 2.40 m/sE = +v i jAcceleration of E.8 3.6 4.8 11.52 5.184 23.0881.08 2.4 0E E= = = + +i j ka v i j k( ) ( ) ( )2 2 211.52 m/s 5.18 m/s 23.1m/sE = + +a i j k 12. COSMOS: Complete Online Solutions Manual Organization SystemVector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell 2007 The McGraw-Hill Companies.Chapter 15, Solution 12.( ) ( ) ( ) ( ) ( ) ( )/ 500 mm 225 mm 300 mm 0.5 m 0.225 m 0.3 mB A = + = +r i j k i j k2 2 20.5 0.225 0.3 0.625 mABl = + + =Angular velocity vector.( )/100.5 0.225 0.30.625B AABl= = +r i j k( ) ( ) ( )8 rad/s 3.6 rad/s 4.8 rad/s= +i j kAngular acceleration vector.( )/200.5 0.225 0.30.625B AABl = = +r i j k( ) ( ) ( )2 2 216 rad/s 7.2 rad/s 9.6 rad/s= + i j k.Velocity of C /C C B= v r( ) ( )/ 500 mm 0.5 mC B = = r i i8 3.6 4.8 2.4 1.80.5 0 0C = = i j kv j k( ) ( )2.40 m/s 1.800 m/sC = v j k.Acceleration of C /C C B C= + a r v 16 7.2 9.6 8 3.6 4.80.5 0 0 0 2.4 1.8= + i j k i j k4.8 3.6 18 14.4 19.2= + + + j k i j k18 19.2 15.6= + i j k( ) ( ) ( )2 2 218.00 m/s 19.20 m/s 15.60 m/sC = + a i j k 13. COSMOS: Complete Online Solutions Manual Organization SystemVector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell 2007 The McGraw-Hill Companies.Chapter 15, Solution 13.( ) ( ) ( )/ 200 mm + 120 mm 90 mmA D = +r i j k( ) ( ) ( )2 2 2200 120 90 250 mmDAd = + + =0.8 + 0.48 + 0.36A/DDADAd= = ri j k( )( ) ( ) ( ) ( )75 0.8 + 0.48 + 0.36 60 rad/s + 36 rad/s + 27 rad/sDA= = = i j k i j k 0DAddt= = ( ) ( )200 mm = 0.2 mB/A =r i iVelocity of corner B./ 60 36 27 5.4 7.20.2 0 0B B A= = = i j kv r j k( ) ( )5.40 m/s 7.20 m/sB = v j kAcceleration of corner B./B B A B= + a r v 0 60 36 27 405 432 3240 5.4 7.2= + = +i j ki j k( ) ( ) ( )2 2 2405 m/s 432 m/s 324 m/sB = +a i j k 14. COSMOS: Complete Onl