A solid brass (bulk modulus 6.7 x 10¹0 N/m²) sphere is subjected to a pressure of 1.0 x 105 Pa due to the earth's atmosphere. On Venus the pressure due to the atmosphere is 9.0 x 106 Pa. By what fraction Ar/ro (including the algebraic sign) does the radius of the sphere change when it is exposed to the Venusian atmosphere? Assume that the change in radius is very small relative to the initial radius. Number i Units

A solid brass (bulk modulus 6.7 x 10¹0 N/m²) sphere is subjected to a pressure of 1.0 x 105 Pa due to the earth's atmosphere. On Venus the pressure due to the atmosphere is 9.0 x 106 Pa. By what fraction Ar/ro (including the algebraic sign) does the radius of the sphere change when it is exposed to the Venusian atmosphere? Assume that the change in radius is very small relative to the initial radius. Number i Units

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter15: Fluid Mechanics

Section: Chapter Questions

Problem 62P: In about 1657, Otto von Guericke, inventor of the air pump, evacuated a sphere made of two brass...

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In about 1657, Otto von Guericke, inventor of the air pump, evacuated a sphere made of two brass hemispheres (Fig. P15.62). Two teams of eight horses each could pull the hemispheres apart only on some trials and then with greatest difficulty, with the resulting sound likened to a cannon firing. Find the force F required to pull the thin-walled evacuated hemispheres apart in terms of R, the radius of the hemispheres; P, the pressure inside the hemispheres; and atmospheric pressure P0. Figure P15.62
A copper rod with length 1.4 m and cross-sectional area 2.0 cm2 is fastened to a steel rod of length L and cross-sectional area 1.0 cm2. The compound structure is pulled on each side by two forces of equal magnitude 6.00 104 N (Fig. P14.57). Find the length L of the steel rod if the elongations (L) of the two rods are equal. Use the values Ysteel = 2.0 1011 Pa and YCu = 1.1 1011 Pa. FIGURE P14.57
A 100-N weight is attached to a free end of a metallic wire that hangs from the ceiling. When a second 100-N weight is added to the wire, it stretches 3.0 mm. The diameter and the length of the wire are 1.0 mm and2.0 m, respectively. What is Young’s modulus of the metal used to manufacture the wire?
Parcels of air (small volumes of air) in a stable atmosphere (where the temperature increases with height) can oscillate up and down, due to the restoring force provided by the buoyancy of the air parcel. The frequency of the oscillations are a measure of the stability of the atmosphere. Assuming that the acceleration of an air parcel can be modeled as 2zt2=g(z)0zz , prove that z=z0etN2 is a solution, where N is known as the Brunt-Väisälä frequency. Note that in a stable atmosphere, the density decreases with height and parcel oscillates up and down.
The temperature of the atmosphere oscillates from a maximum near noontime and a minimum near sunrise. Would you consider the atmosphere to be in stable or unstable equilibrium?
The lintel of prestressed reinforced concrete in Figure P12.27 is 1.50 m long. The concrete encloses one steel reinforcing rod with cross-sectional area 1.50 cm2. The rod joins two strong end plates. The cross-sectional area of the concrete perpendicular to the rod is 50.0 cm2. Youngs modulus for the concrete is 30.0 109 N/m2. After the concrete cures and the original tension T1 in the rod is released, the concrete is to be under compressive stress 8.00 106 N/m2. (a) By what distance will the rod compress the concrete when the original tension in the rod is released? (b) What is the new tension T2 in the rod? (c) The rod will then be how much longer than its unstressed length? (d) When the concrete was poured, the rod should have been stretched by what extension distance from its unstressed length? (e) Find the required original tension T1 in the rod. Figure P12.27
Normal forces of magnitude 1.0106N are applied uniformly to a spherical surface enclosing a volume of a liquid. This causes the radius of the surface to decrease from 50.000 cm to 49.995 cm. What is the bulk modulus of the liquid?
A specimen of oil having an initial volume of 600 cm3 is subjected to a pressure increase of 3.6 * 106 Pa, and the volume is found to decrease by 0.45 cm3. What is the bulk modulus of the material? The compressibility?
In the Challenger Deep of the Marianas Trench, the depth of seawater is 10.9 km and the pressure is 1.16×10^8 Pa, (about 1150 atmospheres). If a cubic meter of water is taken to this depth from the surface (where the normal atmospheric pressure is about 1.0×10^5 Pa), what is the change in its volume? Assume that the bulk modulus for seawater is the same as for freshwater 2.2×10^9 Pa. Report in cubic meters.
How large a pressure must be applied to water if it is to be compressed by 0.1 percent? What is the ratio of this present to atmsopheric pressure (101kPa) ? The bulk modulus of water is 2100M Pa.
An anchor made of cast iron of bulk modulus 60.0 × 109 PA and volume of 0.230 m3, is lowered over the side of a ship to the bottom of the harbor where the pressure is greater than sea level pressure by 1.75 × 106 Pa. •Find the change in the volume of the anchor.
Calculate the volumetric change in a copper cube of side length (40mm) when subjected to a pressure of (20MPa). If you know that the modulus of volumetric elasticity of copper is equal to (125GPa)?