Force on one end of Dropped Board

Two men hold the opposite ends of a board a each feels just half the weight of the board. If one drops his end, the other man feels at that instant a weight just one-quarter of the weight of the board. Why is this true? Thanks for any help you can provide.
- Lowell Thelin (age 68)
Clifton, NJ USA

The force can have whatever value that guy chooses to apply. Here we're assuming that he applies just the upward force needed to keep his end from accelerating either up or down. You can easily solve this if you remember that the acceleration of that end consists of two parts:

1. The average acceleration of the board, i.e. the acceleration of the center of mass.

2. The acceleration due to the rotational acceleration of the board around the center of mass, given by the torque divided by the moment of inertia.

Set the sum of them to zero and you get your answer.

Mike W.

(published on 11/09/2014)