1) A tall, cylindrical chimney falls over whenits base is ruptured. Treat the ch

Question

1)    A tall, cylindrical chimney falls over whenits base is ruptured. Treat the chimney as a thin rod oflength 55.0 m. At the instant it makes an angle of 35.0°with the vertical as it falls, what is:

a)     The radial acceleration of thetop?

b)    The tangential acceleration of the top?

c)     At what angle is the tangentialacceleration equal to g?

Explanation / Answer

Given that         H = 55.0 m         =35.0o According to conservation of energy we have          KEi + PEi =KEf + PEf ==> mghcom = mgh' + 0.5I2 ==> mgH/2 = mgHcos/2 + 0.5 *(mH2/3)2 ==> angular speed = 3g(1-cos)/H a) radial acceleration ar = 2H b) tangential acceleration = d/dt = 3gsin/ 2H Substitute values. c) g = R = 3gsin / 2     ==> sin = 2 / 3     ==> = 41.19o

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