Question

A person’s center of mass is easily found by having the person lie on a reaction board. A horizontal, 2.5-m-long, 6.1 kg reaction board is supported only at the ends, with one end resting on a scale and the other on a pivot. A 60 kg woman lies on the reaction board with her feet over the pivot. The scale reads 25 kg. What is the distance from the woman’s feet to her center of mass?

Short answer

Woman’s feet to centre of mass is at 91.5 cm .

Step-by-step solution

Given information

The mas of reaction board 6.1 kg

Length = 2.5 m

Mass of woman = 60 kg

Her feet on pivot, the reading of scale is 25 kg

Explanation

Lets understand with a diagram and solve the problem

For a system to be in equilibrium , clock-wise and anticlockwise torque should be same.

This means

$N\times 2.5m=W_{\text{board}}\times \frac{2.5}{2}m+W_{\text{woman}}\times xm$

We have to use weight by multiplying mass with g

$25\times g\times 2.5=6.1\times g\times \frac{2.5}{2}+60\times g\times x$

Cancel g and solve for x, we get

x=0.915 m = 91.5 cm.