91962_02_s13_p0177-0284
6/8/09
10:50 AM
Page 251
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13–94. If the position of the 3-kg collar C on the smooth rod AB is held # at r = 720 mm, determine the constant angular velocity u at which the mechanism is rotating about the vertical axis. The spring has an unstretched length of 400 mm. Neglect the mass of the rod and the size of the collar.
u r
B A 300 mm
Free-Body Diagram: The free-body diagram of the collar is shown in Fig. (a). The force in the spring is given by Fsp = ks = 200 a 20.722 + 0.32 - 0.4b = 76 N. Here, ar is assumed to be directed towards the positive r axis. Equations of Motion: By referring to Fig. (a), + ©F = ma ; : r r
-76 a
12 b = 3ar 13
ar = -23.38 m>s2
# $ Kinematics: Since r = 0.72 m is constant, r = r = 0. # $ ar = r - ru2 # -23.38 = 0 - 0.72u2 # u = 5.70 rad>s
Ans.
251
C
k ⫽ 200 N/m