¿Qué proporción deberían guardar los platos de una prensa hidráulica para que, aplicando 40N de fuerza en el plato menor, podamos levantar un objeto de 80Kg en el plato mayor?

  r₂ = 4.43 r₁

Explanation:

To solve this exercise we must use Pascal's principle that the pressure at a point at a given depth is constant regardless of the body shape.

Let's use index 1 for the smallest plate and index 2 for the largest plate.

          P₁ = P₂

pressure is defined

         P = F / A

         F₁ / A₁ = F₂ / A₂

         A₂ / A₁ = F₂ / F₁

They indicate F1 = 40 N and the mass on the large plate is m₂ = 80kg

therefore the body weight is

          W₂ = F₂ = m₂g

we substitute

          A₂ / A₁ = m₂ g / F₁

          A₂ / A₁ = 80 9.8 / 40

          A₂ / A₁ = 19.6

the dishes are generally circular

          A = π r²

          A₂ / A₁ = π r₂² / π r₁²

          A₂ / A₁ = (r₂ / r₁)²

we substitute

           (r₂ / r₁)² = 19.6

            r₂ / r₁ = √19.6 = 4.43

             r₂ = 4.43 r₁

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