Question

A massless, rigid board is placed across two bathroom scales that are separated by a distance of 1.71 m. A person lies on the board. The scale under his head reads 475 N, and the scale under his feet reads 316 N. (a) Find the weight of the person. (b) Locate the center of gravity of the person relative to the scale beneath his head.

Answer 1

Answer:

Let the weight of the person be W and be located at a distance 'a' from the left scale as shown in the figure

Since the body is in equilibrium we can use equations of statics to analyse the problem.

Taking Sum of Moments about A we have

$316\times 1.71-W\times a=0$

Taking Sum of Moments about B we have

$475\times 1.71-W\times (1.71-a)=0$

Solving the above 2 equations for W and 'a' we get

$316\times 1.71=W\times a\\\\475\times 1.71-W\times 1.71=-Wa\\\\\therefore W=\frac{316+475}{1}=791N\\\\\therefore a=\frac{316\times 1.71}{791}=0.683m$