Question

Two pistons of a hydraulic lift have radii of 2. 67 cm and 20. 0 cm, respectively. The downward force on the 2. 67-cm piston that is required to lift a mass of 2000 kg supported by the 20-cm piston is

Answer 1

The downward force on the 2. 67-cm piston that is required to lift a mass of 2000 kg supported by the 20-cm piston is 350 N.

What is pascal law?

Pressure applied to a closed system of fluid will be transfer at each point of the fluid and the boundaries of the system.

Let suppose at the two point of such system the input force apllied is F₁ and output force we get is F₂. The area of this points is A₁ and A₂ respectively. As the pressure at both point is same. Then by the pascal law,

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

In case of radius,

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

Two pistons of a hydraulic lift have radii of 2. 67 cm and 20. 0 cm, respectively. Thus,

$r_1=2.67\rm\; cm$

$r_2=20.0\rm\; cm$

The downward force on the 2. 67-cm piston that is required to lift a mass of 2000 kg supported by the 20-cm piston is The force applied on second piston is,

$F_2=mg\\F_2=2000\times9.81\\F_2=19620 \rm\; N$

Put the values in the above formula,

$\dfrac{F_1}{2.67^2}=\dfrac{19620}{20^2}\\F_1=\dfrac{19620\times2.67^2}{20^2}\\F_1\approx 350\rm\; N$

Thus, the downward force on the 2. 67-cm piston that is required to lift a mass of 2000 kg supported by the 20-cm piston is 350 N.

Learn more about the pascal law here;

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