Beer Vector Mechanics for Engineers DYNAMICS 10th Solutions.pdf - Adobe Reader F

Question

Beer Vector Mechanics for Engineers DYNAMICS 10th Solutions.pdf - Adobe Reader File Edit View Window Help a Open | G E. 2 4 B 6 0 | O 0 1061 (1062 of 2493) | O | 130% |- |E G | 9 Y | Tools Fill &L; Sign | Comment PROBLEM 15.46 or loan. 1 and V, only lay 150 mm The plate shown moves in the xy plane. Knowing that (VA);= 250 mm/s. (V, ), =450 mms, and (vc); =-500 mms, determine (a) the angular velocity of the plate, (b) the velocity of Point A. — 150 mm '50 mm SOLUTION Angular velocity: W = ok Relative position vectors: MBIA = (150 mm)i rCIA = (200 mm)i+(150 mm)j Velocity vectors: VA = (250 mmsi+ (Ay j VB = (VBI-(450 mm/s)j NC --(500 mm/s)i +(VC Cyj Unknowns are 0, (VA, (VB), and (vc. Ay Cy

Explanation / Answer

rCB=(150mm)i +(150+50)j
=K
(a) (vC)xi-(500mm/s)j=(vB)xi+(450mm/s)j+ X rC/B

(vC)xi-500j=(vB)xi+450j+K X (150i+200j)

(vC)xi-500j=(vB)xi+450j+150j+200i
coefficient of j -500=450+150
=-6.3rad/s(=6.3)

(b)Velocity of A
rA/B=-(150mm)i + (180mm)j
VA=VB+VA/B=VB+ x rA/B
250i+(vA)yj=(vB)xi-450j+(-6.3k) X (-150i+150j)
250i+(vA)yj=(vB)xi-450j+950j+950i

coefficient of j =(vA)y=-450+950=500
vA=(250mm/s)i+(500mm/s)j

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