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)Find vcm, the linear speed of the center of mass of the chimney just as it hits the ground.

m/s

b) Find vtop, the linear speed of a point on the top of the chimney just as it hits the ground.

m/s

i need explanation step by step

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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