Posted by tara on Thursday, November 17, 2011 at 5:59pm.
T = tension in line
free body of bucket (Positive is down):
mg - T = m a
free body of pulley:
acceleration a = angular acceleration alpha * r
alpha = moment/I
I = (1/2) m r^2 =
moment = T r
so
alpha = 2 T r/ m r^2 = 2 T/m r
a = alpha r = 2 T/m
therefore
mg - T = m a but a = 2 T/m
so
m g - T = 2T
T = m g/3
now go back and get a and alpha etc
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