Exam 14: Fluids and Elasticity

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.

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?

Consider a very small hole in the bottom of a tank in diameter filled with water to a height of Find the speed at which the water exits the tank through the hole.

If you double the pressure on the surface of a can of water, the buoyant force on a stone placed in that water will

A level pipe contains a nonviscous, incompressible fluid with a density 1200 kg/m³ that is flowing steadily. At one position within the pipe, the pressure is 300 kPa and the speed of the flow is 20.0 m/s. At another position, the pressure is 200 kPa. What is the speed of the flow at this second position?

Air is flowing through a rocket nozzle. Inside the rocket the air has a density of 5.25 kg/m³ and a speed of 1.20 m/s. The interior diameter of the rocket is 15.0 cm. At the nozzle exit, the diameter is 2.50 cm and the density is 1.29 kg/m³. What is the speed of the air when it leaves the nozzle?

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

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?

A circular cylinder of height 1.20 m having faces of diameter 0.620 m is immersed in water of density 1.00 × 10³ kg/m³ with its axis vertical so that its faces are parallel to the surface of the water. The upper face is 2.50 m below the surface of the water. The net force on this cylinder is observed to be 1120 N downward. Atmospheric pressure is 1.01 × 10⁵ Pa. What net force does the water exert on the lower face of the cylinder?

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. Find the weight w.

A rock is suspended from a scale reads 20.0 N. A beaker of water (having a density of 1000 kg/m³) is raised up so the rock is totally submerged in the water. The scale now reads 12)5 N. What is the density of the rock?

A horizontal tube consists of a pipe that narrows to a 2.0-cm-diameter throat. In the pipe, the water pressure is twice atmospheric pressure and the water flows with a speed of What is the pressure in the throat, assuming that the water behaves like an ideal fluid? The density of water is 1000 kg/m³, and atmospheric pressure is 1.01 × 10⁵ Pa.

An incompressible fluid flows steadily through a pipe that has a change in diameter. The fluid speed at a location where the pipe diameter is 8.0 cm is 1.28 m/s. What is the fluid speed at a location where the diameter has narrowed to 4.0 cm?

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 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?

In a section of horizontal pipe with a diameter of 3.00 cm the pressure is 5.21 kPa and water is flowing with a speed of 1.50 m/s. The pipe narrows to 2.50 cm. What is the pressure in the narrower region if water behaves like an ideal fluid of density 1000 kg/m³?

The tensile strength (the maximum tensile stress it can support without breaking) for a certain steel wire is 3000 MN/m². What is the maximum load that can be applied to a wire with a diameter of 3.0 mm made of this steel without breaking the wire?

A circular cylinder of height 1.20 m having faces of diameter 0.620 m is immersed in water of density 1.00 × 10³ kg/m³ with its axis vertical so that its faces are parallel to the surface of the water. The upper face is 2.50 m below the surface of the water. The net force on this cylinder is observed to be 1120 N downward. Atmospheric pressure is 1.01 × 10⁵ Pa. What is the weight of the cylinder?

Two compressible solids are formed into spheres of the same size. The bulk modulus of sphere two is twice as large as the bulk modulus of sphere one. You now increase the pressure on both spheres by the same amount. As a result of the increased pressure, how is the change in volume of sphere two related to the change in volume of sphere one ?

You are driving a late model convertible car at the 65 mph speed limit with its soft flexible roof closed up and the windows closed. You observe that the roof