A gravity board is a convenient and quick way to determine the location of the c

Question

A gravity board is a convenient and quick way to determine the location of the center of gravity of a person. It consists of a horizontal board supported by a fulcrum at one end and a scale at the other end. To demonstrate this in class, your physics professor calls on you to lie horizontally on the board with the top of your head directly above the fulcrum point as shown in the figure. The fulcrum is 2.00 m from the scale. In preparation for this experiment, you had accurately weighed yourself and determined your mass to be 90.0 kg. When you are at rest on the gravity board, the scale advances 275 N beyond its reading when the board is there by itself. Use this data to determine the location of your center of gravity relative to the top of your head.

Explanation / Answer

80 x 9.8 = 882 N. The board's mass is cancelled out by the reading being noted before you get on. So, to have 275N on the scale, the weight on the fulcrum must be (882 - 275) = 607N. 607/275 = 2.2073:1. Add the 1 to the 2.2073, = 3.2073. 2m/3.2073 = .623577464 m from the fulcrum to your CM.

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