A04. Find the location of the center of gravity of the man lying on the board in

Question

A04. Find the location of the center of gravity of the man lying on the board in the diagram below, showing carefully how you arrived at your answer and expressing your answer as a distance measured from the point where his heels are in contact with the board. His heels are in contact with the board directly above the right hand scale, and his head is in contact with the board directly above the left hand scale. Both scales are set to zero before he gets on the board, and it is known that the center of gravity of the board lies halfway between the two scales. The distance between the two scales is 180cm.

Explanation / Answer

Distance btw the two scales = 180 cm
Let the Center of Gravity is at Distance x from the the Heels.

Now, Torque/Moment about the Center of Gravity = 0
So,
400 * x + 445 * (180 - x) = 0
Solving for x
x = 94.8 cm
Location of the center of gravity of the man, 94.8 cm from his heels.

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