A 900 N man, 165 cm tall lies on a center of gravity reaction board with his fee

Question

A 900 N man, 165 cm tall lies on a center of gravity reaction board with his feet at the left end. The reaction board is 206 cm long, weighs 249.2 N, has a uniform distribution of mass, and is supported at both ends by knife-edges. At the right end the knife-edge rests on a scale which reads 585 N. Assuming the CG of the reaction board is 103 cm from A, what percentage of his height is his center of gravity (measured from his feet)? SHOW ALL STEPS!

Explanation / Answer

let x be the CG of the man from his feet.

Force acting on the reaction board are

1. weight of the man 900 N at x, downward

2. weight of the board 249.2 N at 103 cm from left

3. reaction at right end - 585 N

4. reaction at left end - unknown

Now we take moments of the forces about the left end, CW moments -ve

206*585 - 103*249.2 - 900*x =0

x = 105.38 cm

CG height percentage = 105.38/165 = 63.86

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