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Chapter 10: Q21P (page 260)

(II) A hydraulic press for compacting powdered samples has a large cylinder that is 10.0cm in diameter, and a small cylinder with a diameter of 2.0 cm (Fig. 10–51). A lever is attached to the small cylinder as shown. The sample, which is placed on the large cylinder, has an area of 4.0 cm2. What is the pressure on the sample if 320N is applied to the lever?

Short Answer

Expert verified

The pressure on the sample is 40× 106 Pa.

Step by step solution

01

Understanding the Pascal’s Law

In this problem, the pressure at each point on a confined fluid is the same everywhere (Pascal’s Law).

02

Given the data   

The diameter of the large cylinder D=10.0cm.

The force applied on the lever is F =320N.

The diameter of the small cylinder is d=2.0cm.

The area of the sample fluid is A =4.0 cm2.

The length of the lever about point O is 2l.

03

Calculation of Force

The magnitude of the force on the small cylinder is Fs.

For static equilibrium, the total torque about point O is zero. So write

On plugging the values in the above relation.


04

Calculation of pressure

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Most popular questions from this chapter

A beaker of water rests on an electronic balance that reads 975.0 g. A 2.6-cm-diameter solid copper ball attached to a string is submerged in the water, but does not touch the bottom. What are the tension in the string and the new balance reading?

A rowboat floats in a swimming pool, and the level of the water at the edge of the pool is marked. Consider the following situations. (i) The boat is removed from the water. (ii) The boat in the water holds an iron anchor which is removed from the boat and placed on the shore. For each situation, the level of the water will,

(a) Rise.

(b) Fall.

(c) Stay the same.

(III) A patient is to be given a blood transfusion. The blood is to flow through a tube from a raised bottle to a needle inserted in the vein (Fig. 10–55). The inside diameter of the 25-mm-long needle is 0.80 mm, and the required flow rate is \(2.0\;{\rm{c}}{{\rm{m}}^3}\) of blood per minute. How high h should the bottle be placed above the needle? Obtain \(\rho \) and \(\eta \) from the Tables. Assume the blood pressure is 78 torr above atmospheric pressure.

Figure 10-55

A viscometer consists of two concentric cylinders, \({\bf{10}}{\bf{.20}}\;{\bf{cm}}\) and \({\bf{10}}{\bf{.60}}\;{\bf{cm}}\)in diameter. A liquid fills the space between them to a depth of \({\bf{12}}{\bf{.0}}\;{\bf{cm}}\). The outer cylinder is fixed, and a torque of \({\bf{0}}{\bf{.024}}\;{\bf{m}} \cdot {\bf{N}}\) keeps the inner cylinder turning at a steady rotational speed of \({\bf{57}}\;{\bf{rev/min}}\). What is the viscosity of the liquid?

A copper (Cu) weight is placed on top of a 0.40-kg block of wood (\({\bf{density = 0}}{\bf{.60 \times 1}}{{\bf{0}}^{\bf{3}}}\;{\bf{kg/}}{{\bf{m}}^{\bf{3}}}\) ) floating in water, as shown in Fig. 10–58. What is the mass of the copper if the top of the wood block is exactly at the water’s surface?

Figure: 10-58
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