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3 years ago

An 81.5-kg man stands on a horizontal surface.

Physics

1 answer:

OLga [1]3 years ago

7 0

Answer:

a)V= 0.0827 m³

b)P=181.11 x 10² N/m²

Explanation:

Given that

m = 81.5 kg

Density ,ρ = 985 kg/m³

As we know that

Mass = Volume x Density

81.5 = V x 985

V= 0.0827 m³

The force exerted by weight = m g

F= m g= 81.5 x 10 = 815 N ( Take ,g= 10 m/s²)

Area ,A= 4.5 x 10⁻² m²

The Pressure P

$P=\dfrac{F}{A}$

$P = \dfrac{815}{4.5\times 10^{-2}}\ N/m^2$

P=181.11 x 10² N/m²

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To find the acceleration of the system you can assume that the forces are applied in a xy plane, where force toward north are directed in the +y direction, and forces to the east in the +x direction. BY taking into account the components of the acceleration for each axis you obtain the following systems of equations:

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you simplify the equations an replace the values of the mass in order to obtain the acceleration components:

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then, the acceleration of the system has a magnitude of 1.855m/s^2 and a direction of 9.71\° to the east-north

The fifth force must cancel both x an y components of the previous net force, that is:

$0.06N-0.06Nsin(45\°)+F_y=0\\\\F_y=-0.017N\\\\0.08N-0.02N+0.06cos(45\°)+F_x=0\\\\F_x=-0.102N\\\\\phi=tan^{-1}(\frac{-0.017}{-0.102N})=9.46\°$

$F=\sqrt{(0.102)^2+(0.017)^2}N=0.103N$

the, the force needed to reach the equilibrium has a magnitude of 0.103N and a direction of 9.46° to the west-south

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