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The human head weighs 4.8 kg and its center of mas 1.8 cm in front of the spinal column joint. If the trapezius muscle inserts 1.1 cm behind the spinal cord joint, how much downward force does it need to exert in order to maintain equilibrium

Respuesta :

Answer:

The downward force does it need to exert in order to maintain equilibrium is 76.974 N

Explanation:

The downward force does it need to exert in order to maintain equilibrium is:

[tex]F=\frac{mgL}{x}[/tex]

Where

m = mass of human head = 4.8 kg

g = gravity = 9.8 m/s²

L = center of mass = 1.8 cm = 0.018 m

x = distance = 1.1 cm = 0.011 m

Replacing:

[tex]F=\frac{4.8*9.8*0.018}{0.011} =76.974N[/tex]

The downward force required to exert in order to maintain equilibrium is of 76.97 N.

Given data:

The mass of human head is, m = 4.8 kg.

The position of center of mass is, L = 1.8 cm = 0.018 m.

The distance of muscular joint from the spinal cord is, x = 1.1 cm = 0.011 m.

The standard expression for the downward force needed to exert in order to maintain the equilibrium is given as,

[tex]F = \dfrac{mgL}{x}[/tex]

Here,

g is the gravitational acceleration.

Solving as,

[tex]F = \dfrac{4.8 \times 9.8 \times 0.018}{0.011}\\\\F =76.97 \;\rm N[/tex]

Thus, we can conclude that the downward force required to exert in order to maintain equilibrium is of 76.97 N.

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