Question

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?

Answer 1

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.

Answer 2

The pressure on the sample is 4.375 × 10⁷ Pa

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Further explanation

Let's recall Hydrostatic Pressure formula as follows:

$\boxed{ P = \rho g h}$

$\boxed{ P = F \div A}$

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:

$\Sigma \tau = 0$

$F(2L) - F_2(L) = 0$

$2FL = F_2L$

$F_2 = 2F$

$F_2 = 2(350)$

$\boxed{F_2 = 700 \texttt{ N}}$

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

$P_1 = P_2$

$F_1 \div A_1 = F_2 \div A_2$

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

$F_1 = \frac{\frac{1}{4} \pi (D_2)^2}{\frac{1}{4} \pi (D_1)^2} F_2$

$F_1 = (\frac{D_2}{D_1})^2 F_2$

$F_1 = (\frac{10.0}{2.0})^2 \times 700$

$\boxed{F_1 = 17500 \texttt{ N}}$

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Finally, we could calculate the pressure on the sample:

$P = F_1 \div A$

$P = 17500 \div (4 \times 10^{-4})$

$\boxed{P = 4.375 \times 10^7 \texttt{ Pa}}$

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Learn more

• Buoyant Force : brainly.com/question/13922022

• Kinetic Energy : brainly.com/question/692781

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

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

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Answer details

Grade: High School

Subject: Physics

Chapter: Pressure