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A light plank rests on two scales that read Fg1 = 420 N and Fg2 = 300 N. The scales are separated by a distance of 2.00 m. How far from the woman's feet is her center of gravity?

Respuesta :

Answer:

1.167 m

Explanation:

given,

Scale reading on both the side

side 1,  F g₁ = 420 N

side 2, F g₂ = 300 N

distance between the scale = 2 m

the woman's feet is her center of gravity  = ?

Let x be the distance of center of gravity from Fg₁

now, Taking moment about center of gravity

Fg₁ × x = Fg₂ x (2 - x)

420 × x = 300 × (2 - x)

420 x = 600 - 300 x

720 x = 600

x = 0.833 m

distance of the center of gravity from the feet

    = 2 - 0.833

    = 1.167 m

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The distance that should be far from the woman's feet is her center of gravity is 1.167 m

Calculation of the distance:

Since Scale reading on both the side

So,

side 1,  F g₁ = 420 N

side 2, F g₂ = 300 N

distance between the scale = 2 m

Here we assume x be the distance with respect to the center of gravity

So,

Fg₁ × x = Fg₂ x (2 - x)420 × x = 300 × (2 - x)

420 x = 600 - 300 x

720 x = 600

x = 0.833 m

Now the distance should be

= 2 - 0.833

= 1.167 m

hence, The distance that should be far from the woman's feet is her center of gravity is 1.167 m

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