Matilda Fox
2022-07-17
Answered

A 164-cm-tall person lies on a light (massless) board which is supported by two scales, one under the top of her head and one beneath the bottom of her feet. The two scales read, respectively, 35.1 and 31.6 kg. What distance is the center of gravity of this person form the bottom of her feet?

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Franklin Frey

Answered 2022-07-18
Author has **15** answers

given,

height of the person = 164 cm

reading of the scale = 35.1 Kg

and reading on another scale = 31.6 Kg

center of gravity of person = ?

Let x be the distance of the center of gravity of person from 35.1 Kg

$35.1\times x=31.6\times (164-x)\phantom{\rule{0ex}{0ex}}35.1\text{}x=5182.4-31.6\text{}x\phantom{\rule{0ex}{0ex}}66.7\text{}x=5182.4\phantom{\rule{0ex}{0ex}}x=\frac{5182.4}{66.7}\phantom{\rule{0ex}{0ex}}x=77.7\text{}m$

distance of center of mass from 31.6 Kg

x' = 164 - 77.7

x' = 86.3 m

height of the person = 164 cm

reading of the scale = 35.1 Kg

and reading on another scale = 31.6 Kg

center of gravity of person = ?

Let x be the distance of the center of gravity of person from 35.1 Kg

$35.1\times x=31.6\times (164-x)\phantom{\rule{0ex}{0ex}}35.1\text{}x=5182.4-31.6\text{}x\phantom{\rule{0ex}{0ex}}66.7\text{}x=5182.4\phantom{\rule{0ex}{0ex}}x=\frac{5182.4}{66.7}\phantom{\rule{0ex}{0ex}}x=77.7\text{}m$

distance of center of mass from 31.6 Kg

x' = 164 - 77.7

x' = 86.3 m

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