A person's center of mass is easily found by having the person lie on a reaction board. A horizontal, 3.0-m-long, 6.1kg reaction board is supported only at the ends, with one end resting on a scale and the other on a pivot. A 57kg woman lies on the reaction board with her feet over the pivot. The scale reads 22kg. Assume that the woman doesn't move and a position of her center of mass doesn't change.What is the distance from the woman's feet to her center of mass?

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rejkjavik rejkjavik · Answer 1 · 2019-11-08T08:12:49+01:00

Answer:

X = 0.99 meter

Explanation:

given data:

length board 3 m

mass of board is 6.1 kg

weight of women is 57 kg

scale reading is 22 kg

from figure

[tex]\tau_{pivot } = o[/tex]

[tex]mg\times X + m_s g (L/2) - 22 g L = 0[/tex]

[tex]57\times X + 6.1 g (L/2) - 22 gL[/tex]

Solving for x we get

X = 0.99 meter

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okpalawalter8 okpalawalter8 · Answer 2 · 2022-04-12T13:35:45+02:00

The distance from the woman's feet to her center of mass is mathematically given as

x=0.99m

Question Parameter(s):

A horizontal, 3.0-m-long, 6.1kg reaction board is supported only at the ends.

A 57kg woman lies on the reaction board with her feet over the pivot

Generally, the equation for the torque is mathematically given as

t=o

Therefore

mg* X + m_s g (L/2) - 22 g L =0

57* X + 6.1 g (L/2) - 22 gL=0

x=0.99m

In conclusion, the distance is

x=0.99m