Question

In a car lift compressed air exerts a force F_(1) on a small piston having a radius of 4.0cm.This pressure is transmitted to a second piston of radius 12cm.(see figure).If the mass of the car to be lifted is 1200kg.Calculate F_(1).What is the pressure necessary to accomplish this task? (g=9.8ms^(-2))​

Answer 1

Answer:

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Answer 2

Given:

Force = F₁

Radius of first piston = 4.0 cm

Radius of second piston = 12 cm

Mass of car = 1200 kg

g = 9.8 ms⁻¹

To find:

F₁ and pressure which is required to accomplish the task

Solution:

Formula used in this question will be as follows-

From pascal's law,

             P₁ = P₂

here P₁ = pressure exerted by the small piston

        P₂ = pressure exerted by the second piston

also,

           $P = \frac{F}{A}$

here, P = pressure

         F = force

        A = area = πr² (r = radius)

So, according to question,

        P₁ = P₂

        $\frac{F_1}{A_1} = \frac{F_2}{A_2}$

        $\frac{F_1}{\pi r_1^2} = \frac{F_2}{\pi r_2^2}$

        $F_1 = \frac{F_2r_1^2}{r_2^2}$

 here, F₁ = force exerted on small piston

          F₂ = force exerted on second piston

           r₁ = radius of small piston

           r₂ = radius of second piston

To find F₂-

      F₂ = m× g

here, m = mass of the car = 1200 kg

          g = 9.8 ms⁻¹

so,

         $F_1 = \frac{1200 \times 9.8 \times (4.0)^2}{(12)^2}$

        F₁ = 1307N

         F₁ = 1.3 × 10³ N

$P_1 = \frac{F_1}{A_1} = \frac{F_1}{\pi r_1^2} = \frac{1307}{\pi \times (4)^2}$

P₁ = 26.02 × 10⁴ Nm⁻²

and,

$P_2 = \frac{F_2}{A_2} = \frac{F_2}{\pi r_2^2}$

$P_2 = \frac{1200 \times 9.8}{\pi \times (12)^2}$

P₂ = 26 × 10⁴ Nm⁻².