A chimney (length L = 52.3 m, mass M = 1570 kg) cracks at the base, and topples.

Question

A chimney (length L = 52.3 m, mass M = 1570 kg) cracks at the base, and topples. Assume:
- the chimney behaves like a thin rod, and it does not break apart as it falls
- only gravity (no friction) acts on the chimney as if falls
- the bottom of the chimney tilts but does not move left or right

a) When the chimney makes an angle of ? = 44.6o with the vertical, find ?, the magnitude of the torque acting on the chimney due to gravity.
1 N-m

b) When the chimney makes an angle of ? = 44.6o with the vertical, find ?, the magnitude of the angular acceleration of the center of mass of the chimney.
2 rad/s2

c) Find vcm, the linear speed of the center of mass of the chimney just as it hits the ground.
3 m/s

d) Find vtop, the linear speed of a point on the top of the chimney just as it hits the ground.
4 m/s

Explanation / Answer

Net torque about the hinge ==I = mglcos/2

I = Ml2/3

=d/d

substituting,

(2l/3)d/d = gcos

integrating from /2 to 0

l2/3 = g

= 3g/l

vcm = l/2 = (3gl)/2

vtop = l = 3gl

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