7/28/2019 Solucin primer punto parcial dinmica.pdf

1/2

COSMOS: Complete Online Solutions Manual Organization System

Vector 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.

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Geometry. ( ) ( )120 mm 180 mmA = +r j k

Method 1

Let the rigid bodyDCB be a rotating frame of reference.

Its angular velocity is ( ) ( )1 2 1.2 rad/s 1.5 rad/s . = + = i k i k

Its angular acceleration is ( )21 2 1 2 1.8 rad/s . = = =i k j j

Motion of the coinciding pointA in the frame.

( ) ( )

( ) ( ) ( )

1.2 1.5 120 180

144 216 180 180 mm/s 216 mm/s 144 mm/s

A A = = +

= + = +

v r i k j k

k j i i j k

( ) ( )2 2

0 1.8 0 1.2 0 1.5

0 120 180 180 216 144

324 324 442.8 259.2 442.8 mm/s 259.2 mm/s

A A A = +

= +

+

= + =

a r v

i j k i j k

i i j k j k

Motion of point A relative to the frame.

( )/ /60 mm/s , 0A F A Fu= = =v j j a

Velocity of point A. /A A A F= +v v v

180 216 144 60A

= + +v i j k j

( ) ( ) ( )180.0 mm/s 156.0 mm/s 144.0 mm/sA = +v i j k Coriolis acceleration. /2 A F v

( )( ) ( ) ( )2 2/2 2 1.2 1.5 60 180 mm/s 144 mm/sA F = = +v i k j i k

Acceleration of point A. / /2A A A F A F= + + a a a v

442.8 259.2 180 144A

= + +a j k i k

( ) ( ) ( )2 2 2180 mm/s 443 mm/s 115.2 mm/sA = a i j k

7/28/2019 Solucin primer punto parcial dinmica.pdf

2/2

COSMOS: Complete Online Solutions Manual Organization System

Vector 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.

Method 2

Let frame Dxyz, which at instant shown coincides with DXYZ, rotate with an angular velocity

11.2 rad/s.= =i i Then the motion relative to the frame consists of the rotation of body DCB

about the z axis with angular velocity ( )2 1.5 rad/s = k kplus the sliding motion ( )60 mmu= =u i j of the rodAB relative to the bodyDCB.

Motion of the coinciding point in the frame.

( ) ( ) ( )

( ) ( ) ( )2 21.2 120 180 216 mm/s 144 mm/s

1.2 216 144 172.8 mm/s 259.2 mm/s

A A

A A

= = + = +

= = + =

v r i j k j k

a v i j k j k

Motion of point A relative to the frame.

( ) ( ) ( ) ( )

( ) ( )

( ) ( ) ( ) ( ) ( )

( ) ( )

/ 2

/ 2 2 2 2

2 2

1.5 120 180 60 180 mm/s 60 mm/s

2

0 1.5 180 0 2 1.5 60

270 180 180 mm/s 270 mm/s

A F A

A F A A

u

u u

= + = + + = +

= + + +

= + + +

= + =

v k r j k j k j i j

a k r k k r j k j

k i k j

j i i j

&

Velocity of point A./A A A F= +v v v

216 144 180 60A

= + +v j k i j

( ) ( ) ( )180.0 mm/s 156.0 mm/s 144.0 mm/sA = +v i j k Coriolis acceleration. /2 F v

( )( ) ( ) ( )2

/2 2 1.2 180 60 144 mm/s

A F = + =v i i j k

Acceleration of point A./ /

2A A A F A F= + + a a a v

172.8 259.2 180 270 144A

= + +a j k i j k

( ) ( ) ( )2 2 2180.0 mm/s 443 m m/s 115.2 mm/sA = a i j k