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Consider a simple hydraulic system in an automotive shop. A worker can exert a force of 2000 N on a circular piston with an area of 20 $cm^2$. Another piston is used to raise a car weighing 20000 N. What must the area of the second piston be in order to raise the car?
A. 20 cm^2B. 2000 cm^2C. 2 cm^2D. 200 cm^2

Answer :

valeriagonzalez0213

Answer:

D) A₂ =  200 cm²

Explanation:

Pascal principle

When exerting a pressure on one of the vessels, this will be exerted with equal magnitude in all directions and in each part of the fluid, in this way the fluid will move towards the other container to achieve equilibrium again, that is, to equalize the pressures in both vessels.

The pressures must be the same in vessels 1 and 2, then:

P₁ = P₂ and therefore:

[tex]\frac{F_{1} }{A_{1} } = \frac{F_{2} }{A_{2} }[/tex]   Equation (1)

Data

F₁ = 2000 N

A₁=  20 cm²

F₂= 20000 N

Calculating of the area of the second piston  (A₂)

We replace data in the equation (1)

[tex]\frac{ 2000  }{ 20 } = \frac{20000 }{A_{2} }[/tex]  

100 = 20000/A₂

100 * A₂ = 20000

A₂ =  20000/100

A₂ =  200 cm²

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