Question

This is one problem. To clarify its one problem that has 2 different questions. My teacher just broke it up with each problem having different numbers to make it more annoying than the problem already is. Thank you so much for taking the time to help me out. (it's asking for the time taken because the units are meters/second

A chimney (length 13.2 m, mass 178 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

A chimney (length 20.9 m, mass 712 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

In this case, we can't use energy conservation because we don't know the amount of force that the pivot is exerting on the chimney. Also, the rotational motion is happening solely because of the gravitational force. With this in mind, please follow the discussion in the below images:

Note that the velocities are independent of the mass of the chimneys.