A hydraulic press for compacting powdered samples has a large cylinder which is 10.0 cm in diameter, and a small cylinder with a diameter of 2.0 cm. A lever is attached to the small cylinder as shown in (Figure 1) . The sample, which is placed on the large cylinder, has an area of 4.0 cm2.

What is the pressure on the sample if F = 350N is applied to the lever?

Pressure is defined as the force applied per unit area of the press. In this case, we are given with a force equivalent to 350 N and an area equal to 4 cm2. 4 cm2 is equal to 0.0004 m2. We divide 350Newton by 0.0004 square meters equal to 875,000 Pascals or 875 kiloPascals.

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johanrusli johanrusli · Answer 2 · 2020-01-31T05:56:32+01:00

The pressure on the sample is 4.375 × 10⁷ Pa

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Further explanation

Let's recall Hydrostatic Pressure formula as follows:

[tex]\boxed{ P = \rho g h}[/tex]

[tex]\boxed{ P = F \div A}[/tex]

where:

P = hydrosatic pressure ( Pa )

ρ = density of fluid ( kg/m³ )

g = gravitational acceleration ( m/s² )

h = height of a column of liquid ( m )

F = force ( N )

A = cross-sectional area ( m² )

Let us now tackle the problem!

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Given:

diameter of large cylinder = D₁ = 10.0 cm

diameter of small cylinder = D₂ = 2.0 cm

area of the sample = A = 4.0 cm² = 4.0 × 10⁻⁴ m²

magnitude of force = F = 350 N

Asked:

pressure on the sample = P = ?

Solution:

Firstly , we will find the force acting on the small cylinder:

[tex]\Sigma \tau = 0[/tex]

[tex]F(2L) - F_2(L) = 0[/tex]

[tex]2FL = F_2L[/tex]

[tex]F_2 = 2F[/tex]

[tex]F_2 = 2(350)[/tex]

[tex]\boxed{F_2 = 700 \texttt{ N}}[/tex]

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Next, we could find the force acting on the large cylinder:

[tex]P_1 = P_2[/tex]

[tex]F_1 \div A_1 = F_2 \div A_2[/tex]

[tex]F_1 = \frac{A_2}{A_1} F_2[/tex]

[tex]F_1 = \frac{\frac{1}{4} \pi (D_2)^2}{\frac{1}{4} \pi (D_1)^2} F_2[/tex]

[tex]F_1 = (\frac{D_2}{D_1})^2 F_2[/tex]

[tex]F_1 = (\frac{10.0}{2.0})^2 \times 700[/tex]

[tex]\boxed{F_1 = 17500 \texttt{ N}}[/tex]

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Finally, we could calculate the pressure on the sample:

[tex]P = F_1 \div A[/tex]

[tex]P = 17500 \div (4 \times 10^{-4})[/tex]

[tex]\boxed{P = 4.375 \times 10^7 \texttt{ Pa}}[/tex]

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Learn more

Buoyant Force : https://brainly.com/question/13922022

Kinetic Energy : https://brainly.com/question/692781

Volume of Gas : https://brainly.com/question/12893622

Impulse : https://brainly.com/question/12855855
Gravity : https://brainly.com/question/1724648

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Answer details

Grade: High School

Subject: Physics

Chapter: Pressure