Question

A chimney (length 17.6 m, mass 823 kg] cracks at the base and topples. Assume: - the chimney behaves like a thin rod, and does not break apart as it falls. - only gravity (no friction) acts on the chimney as it falls. - the bottom of the chimney pivots, but does not move. Find the linear speed of the center of mass of the chimney, in m/s, just as it hits the ground

Part 2)A chimney (length 11.1 m, mass 852 kg] cracks at the base and topples. Assume: - the chimney behaves like a thin rod, and does not break apart as it falls. - only gravity (no friction) acts on the chimney as it falls. - the bottom of the chimney pivots, but does not move. Find the linear speed of the very top of the chimney, in m/s, just as it hits the ground.

Answer 1

Part 1

The change in potential energy of the centre of mass of the rod will be equal to the change in rotational kinetic energy of the rod.

where is the moment of inertia of a rod pivoted at a point and is equal to .

Substituting the required values, we get

Now that we know the angular velocity, we can find the linear velocity of the required point, which is just the angular velocity times the point's distance from the centre.

Part 2

We know that for a falling rod, the angular velocity is

Substituting our values for this rod, we get

The velocity of the top end will be