Find Center of Gravity of Person Using Torque

[CACain]

DISCLAIMER: For the sake of academic integrity, I would like to place a warning on this question and say that it is NOT a test question, nor is it a homework question that will receive grading. This is simply a random question out of the textbook to practice torque.

Problem:

A gravity board for locating the center of gravity of a person consists of a horizontal board supported by a fulcrum at one end and by a scale at the other end. A physics student lies horizontally on the board with the top of his head above the fulcrum point. The scale is 2m from the fulcrum. The stuent has a mass of 70kg and when he is on the gravity board, the scale advances 250N. Where is the center of gravity of the student?


Okay, I have the answer to this question because I have a study guide along with the textbook, but I can't follow the steps... Does anyone know of a more logical step progression on how to work this problem?

 

[andrevdh]

First consider the setup without the student. By calculating torques around the fulcrum you will get the scale force in terms of the weight of the board. Use this to eliminate the weight of the board in the second setup - that is by calculating the torques around the fulcrum again (I get 0.73 m).