Exam 15: Fluids and Elasticity

On planet X, the absolute pressure at a depth of 2.00 m below the surface of a liquid nitrogen lake is 5.00 × 10⁵ N/m². At a depth 5.00 m below the surface, the absolute pressure is 8.00 × 10⁵ N/m². The density of liquid nitrogen is 808 kg/m³. (a) What is the atmospheric pressure on planet X? (b) What is the acceleration due to gravity on planet X?

The two water reservoirs shown in the figure are open to the atmosphere, and the water has density 1000 kg/m³. The manometer contains incompressible mercury with a density of 13,600 kg/m³. What is the difference in elevation h if the manometer reading m is 25.0 cm?

A steel lift column in a service station is a solid cylinder 4.0 m long and 0.20 m in diameter. Young's modulus for this steel is 20 × 10¹⁰ N/m². By what distance does the column compress when a 5000-kg truck is on it?

At a certain depth in the ocean, the absolute pressure is p. If you go to twice that depth (treating the water as incompressible)

Water, of density 1000 kg/m³, is flowing in a drainage channel of rectangular cross-section. The width of the channel is 15 m, the depth of the water is 8.0 m and the speed of the flow is 2.5 m/s. At what rate is water flowing in this channel?

When the pressure applied to an unknown liquid is increased from 1.0 × 10⁷ N/m² to 5.5 × 10⁷ N/m², the volume of the liquid decreases by 0.70%. Calculate the bulk modulus of the liquid.

A very light 1.00-m wire consists of two segments of equal length, one of steel (Young's modulus is 2.00 × 10¹¹ N/m²) and one of brass (Young's modulus is 9.0 × 10¹⁰ N/m²). The steel segment is 1.50 mm in diameter, and the brass segment has twice this diameter. When a weight w is hung from the ceiling by this wire, the steel segment stretches by 1.10 mm. By what distance does the brass segment stretch?

A barge is 15.0 m wide and 75.0 m long and has vertical sides. The bottom of the hull is 1.20 m below the water surface. What is the weight of the barge and its cargo, if it is floating in fresh water of density 1000 kg/m³?

A cable is 100 m long, has a cross-sectional area of 1.0 mm², and is made of a material having a Young's modulus of 1.0 × 10¹¹ N/m². If a 1000-N force is applied to stretch the cable, how far does it stretch?

A cup of water containing an ice cube at 0°C is filled to the brim. The tip of the ice cube sticks out of the surface. As the ice melts, you observe that

What is the maximum length of a metal cable that can hang vertically supported from one end of the cable? The Young's modulus of this metal is 2.10 × 10¹¹ N/m², its tensile strength (the maximum tensile stress it can support without breaking) is 7.40 × 10⁸ N/m², and its density is 7.60 × 10³ kg/m³.

As shown in the figure, a container has a vertical tube, whose inner radius is 32.00 mm, connected to it at its side. An unknown liquid reaches level A in the container and level B in the tube-level A being 5.0 cm higher than level B. The liquid supports a 20.0-cm high column of oil, between levels B and C, whose density is 460 kg/m³. What is the density of the unknown liquid?

Fluid fills the container shown in the figure. At which of the indicated points is the pressure greatest?

Salt water is more dense than fresh water. A ship floats in both fresh water and salt water. Compared to the fresh water, the volume of salt water displaced by the ship is

An aluminum wire and a steel wire, each of length 2.0 m, are hung from the ceiling. A 5.0-kg mass is suspended from the lower end of each wire. The aluminum wire has a diameter of 2.2 mm. What must be the diameter of the steel wire if it is to stretch the same distance as the aluminum wire, so that the two wires maintain equal lengths after the masses are attached? Young's modulus for aluminum is 0.70 × 10¹¹ N/m² and for steel it is 2.0 × 10¹¹ N/m².

A solid steel sphere with a radius of 2.0 m falls off a ship and sinks to a depth where the pressure is 15 MN/m². The bulk modulus for this steel is 1.6 × 10¹¹ N/m². What is the change in the radius of the sphere?

A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with incompressible oil and capped at both ends with tight-fitting pistons. The wider arm of the U-tube has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm. The car rests on the piston on the wider arm of the U-tube. The pistons are initially at the same level. What is the initial force that must be applied to the smaller piston in order to start lifting the car? (For purposes of this problem, you can neglect the weight of the pistons.)

A sphere is constructed of two concentric parts. The inner part is a solid sphere of radius 10.0 cm made of a material with density 4000 kg/m³. The outer part is a spherical shell with inner radius 10.0 cm and outer radius 20.0 cm. The material in the outer shell has a density 9000 kg/m³. (a) What is the mass of the sphere? (b) What is the average density of this sphere?

Incompressible water flows out of a large reservoir through a pipe that opens to the atmosphere 5.70 m below the level of the water in the reservoir. What is the speed of the water as it comes out of the pipe?

A 0.600-mm diameter wire stretches 0.500% of its length when it is stretched with a tension of 20.0 N. What is the Young's modulus of this wire?