Question

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?

Answer 1

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

therefore the woman can lift the car

Step-by-step 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