2. A simple hydraulic lift is made by fitting a piston attached to a handle into a 3.0-cm diameter cylinder. The cylinder is connected to a larger cylinder with a 24-cm diameter. If a 50-kg woman puts all her weight on the handle of the smaller piston, what weight could the other piston lift? Could the woman lift a large car with a weight of 1.6104 N?

mparing this value with the weight of the vehicle we see    W₂> 1.6 10⁴ N

therefore the woman can lift the car

Explanation:

For this exercise on Pascal's principle, we use that the pressure in every incompressible liquid is the same

         P₁ = P₂

   the press is defined by

         P = F / A

for the woman's side

  the area of a circle is

         A = π D₁² / 4

         P₁ = W (4 /π d₁²)

for the car side

         A₂ =π d₂²

        P₂ = W₂ (4 /π d₂²)

we substitute in the first equation

         W (4 /π d₁²) = W₂ 4 /π d₂²)

          W / d₁² = W₂ / D₂²

           W₂ = (d₂ / d₁)² W

the weight of the woman is

           W = mg

we calculate

          W₂ = (24/3)₂ 50 9.8

          W₂ = 3,136 10⁴ N

when comparing this value with the weight of the vehicle we see

          W₂> 1.6 10⁴ N

therefore the woman can lift the car

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the maxium height is 34m/s