In a machine shop, a hydraulic lift is used to raise heavy equipment for repairs. The system has a small piston with a cross-sectional area of 0.075 m2 and a large piston with a cross-sectional area of 0.237 m2 . An engine weighing 3400 N rests on the large piston. What force must be applied to the small piston in order to lift the engine? Answer in units of N.

Respuesta :

Answer:

[tex]F_s=1075.9493\ N[/tex]

Explanation:

Given:

  • area of piston on the smaller side of hydraulic lift, [tex]a_s=0.075\ m^2[/tex]
  • area of piston on the larger side of hydraulic lift, [tex]a_l=0.237\ m^2[/tex]
  • Weight of the engine on the larger side, [tex]W_l=3400\ N[/tex]

Now, using Pascal's law which state that the pressure change in at any point in a confined continuum of an incompressible fluid is transmitted throughout the fluid at its each point.

[tex]P_s=P_l[/tex]

[tex]\frac{F_s}{a_s}=\frac{W_l}{a_l}[/tex]

[tex]\frac{F_s}{0.075} =\frac{3400}{0.237}[/tex]

[tex]F_s=1075.9493\ N[/tex] is the required effort force.

Answer:

   F = 1076 N

Explanation:

given,

small piston area, a = 0.075 m²

large piston area, A = 0.237 m²

weight on the large piston, W = 3400 N

force applied on the second piston, F = ?

using pascal law for the force calculation

[tex]\dfrac{F}{W}=\dfrac{a}{A}[/tex]

[tex]\dfrac{F}{3400}=\dfrac{0.075}{0.237}[/tex]

   F = 0.3165 x 3400

   F = 1076 N

The force applied to the small piston in order to lift the engine is equal to 1076 N.