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The weight of a hydraulic barber's chair with a client is 2000 N. When the barber steps on the input piston with a force of 40 N, the output plunger of a hydraulic system begins to lift the chair. Determine the ratio of the radius of the output plunger to the radius of the input piston.

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Nandhitha1098

Answer: The weight of a hydraulic barber's chair with a client is 2000 N. When the barber steps on the input piston with a force of 40 N, the output plunger of a hydraulic system begins to lift the chair. Then the ratio of the radius of the output plunger to the radius of the input piston will be 7.07.

Explanation: To find the answer, we have to know more about the Pascal's law and the hydraulic lift.

What is pascal's law and how it is used in case of hydraulic lift?

  • The law states that, the pressure exerted at any point on an enclosed liquid is transmitted equally in all directions.
  • A hydraulic lift consists of two cylinders connected to each other by pipe.
  • If the force F1 applied on the smaller piston of area A1, the pressure exerted will be,

                            [tex]P_1=\frac{F_1}{A_1}[/tex]

  • By pascal's law, the pressure transmitted to the large piston of large area A2 will be,

                            [tex]P_2=\frac{F_2}{A_2}[/tex]

  • Then,

                          [tex]\frac{F_2}{A_2} =\frac{F_1}{A_1}[/tex]

How to solve the problem?

  • We have to find the ratio of the radius of the output plunger to the radius of the input piston.
  • We have the equation for this as,

                     [tex]\frac{A_{Plunger}}{A_{piston}} =\frac{F_{Plunger}}{F_{piston}}[/tex]

                    [tex]\frac{R_{Plunger}}{R_{piston}}=\sqrt{ \frac{F_{Plunger}}{F_{piston}}}=\sqrt{\frac{2000}{40} } =7.07[/tex]

Thus, we can conclude that, the ratio of the radius of the output plunger to the radius of the input piston will be 7.07.

Learn more about the Pascal's law and the hydraulic lift here:

https://brainly.com/question/28044939

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