Question

En la figura los émbolos son de masa despreciable y están en reposo, como se ve en la figura, siendo M=300 kg. Determine: a) la presión generada por el bloque de masa M sobre el embolo. b) La presión manométrica en un punto a 50 cm de profundidad en el embolo más grande. c) La fuerza F para que el sistema esté en equilibrio. Area del emb. grande= 1,2 m2; A del emb.pequeño=20 cm2; P liquido=600kg/m2

Answer 1

The image mentioned is in the attachment

Answer: a) P = 2450 Pa;

b) P = 2940 Pa;

c) F = 4.9 N

Explanation:

a) Pressure is a force applied to a surface of an object or fluid per unit area.

The image shows a block applying pressure on the large side of the piston. The force applied is due to gravitation, so:

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

P = $\frac{m.g}{A}$

P = $\frac{300.9.8}{1.2}$

P = 2450 Pa

The pressure generated by the block is P = 2450 Pa.

b) A static liquid can also exert pressure and can be calculated as:

$P_{staticfluid} =$ρ.g.h

where

ρ is the density of the fluid

h is the depth of the fluid

g is acceleration of gravity

$P_{staticfluid} =$ 600.9.8.0.5

$P_{staticfluid} =$ 2940 Pa

The pressure in the fluid at 50 cm deep is $P_{staticfluid} =$ 2940 Pa.

c) For the system to be in equilibrium both pressures, pressure on the left side and pressure on the right side, have to be the same:

$P_{s} = P_{b}$

$\frac{F}{A_s}$ = $\frac{F_b}{A_b}$

F = $\frac{F_b}{A_b}.A_s$

Adjusting the units, $A_{s}$ = 0.002 m².

F = $\frac{300.9.8.0.002}{1.2}$

F = 4.9 N

The force necessary to be equilibrium is F = 4.9 N.