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engineering
mechanical engineering

Questions and Answers of Mechanical Engineering

Determine the mass products of inertia Ixy, Iyz, and Izx of the cast aluminum machine component shown. (The density of aluminum is 2700 kg/m3.)
A section of sheet steel 3 mm thick is cut and bent into the machine component shown. Knowing that the density of the steel is 7860 kg/m3, determine the mass products of inertia Ixy, Iyz, and Izx of
A section of sheet steel 3 mm thick is cut and bent into the machine component shown. Knowing that the density of the steel l is 7860 kg/m3, determine the mass products of inertia Ixy, I yz, and Izx
A section of sheet steel 3 mm thick is cut and bent into the machine component shown. Knowing that the density of the steel l is 7860 kg/m3, determine the mass products of inertia Ixy, Iyz, and Izx
A section of sheet steel 0.08 in. thick is cut and bent into the machine component shown. Knowing that the specific weight of steel is 490 lb/ft3, determine the mass products of inertia a Ixy, Iyz,
Brass wire with a weight per unit length w is used to form the wire figure.
Brass wire with a weight per unit length w is used to form the figure shown. Determine the mass products of inertia a Ixy, Iyz, and Izx of the wire figure.
The figure shown is formed of 0.075-in.-diameter aluminum wire. Knowing that the specific weight of aluminum is 0.10 lb/in3, determine the mass products of inertia Ixy, Iyz , and Izx of the wire
A homogeneous wire with a mass per unit length of 1.8 kg/m is used to form the figure shown. Determine the mass products of inertia Ixy, Iyz, and Izx of the wire figure.
Complete the derivation of Eqs (9.47), which express the parallel-axis theorem for mass products of inertia.
For the homogeneous tetrahedron of mass m shown,(a) Determine by direct integration the mass product of inertia a Izx,(b) Deduce Iyz and Ixy from the results obtained in part a.
The homogeneous circular cylinder shown has a mass m. Determine the mass moment of inertia of the cylinder with respect to the line joining the origin O and point A which is located on the perimeter
The homogeneous circular cone shown has a mass m. Determine the mass moment of inertia of the cone with respect to the line joining the origin O and point A.
Shown is the machine element of Prob. 9.143. Determine its mass moment of inertia with respect to the line joining the origin O and point A.
Determine the mass moment of inertia of the steel machine element of Probs. 9.147 and 9.151 with respect to the axis through the origin which forms equal angles with the x, y, and z axes.
The thin bent plate shown is of uniform density and weight W. Determine its mass moment of inertia with respect to the line joining the origin O and point A.
A piece of sheet metal of thickness t and density ρ is cut and bent into the shape shown. Determine its mass moment of inertia with respect to a line joining points A and B.
Determine the mass moment of inertia of the machine component of Probs. 9.138 and 9.157 with respect to the axis through the origin defined by the unit vector λ = (−4i + 8j + k)/9.
For the wire figure of the problem indicated, determine the mass moment of inertia of the figure with respect to the axis through the origin defined by the unit vector Î» =
For the wire figure of the problem indicated, determine the mass moment of inertia of the figure with respect to the axis through the origin defined by the unit vector λ =
For the wire figure of the problem indicated, determine the mass moment of inertia of the figure with respect to the axis through the origin defined by the unit vector λ = (−3i −
For the rectangular prism shown, determine the values of the ratios b/a and c/a so that the ellipsoid of inertia of the prism is a sphere when computed(a) At point A,(b) At point B.
For the right circular cone of Sample Prob. 9.11, determine the value of the ratio a/h for which the ellipsoid of inertia of the cone is a sphere when calculated(a). At the apex of the cone,(b). At
For the homogeneous circular cylinder of radius a and length L shown, determine the value of the ratio a/L for which the ellipsoid of inertia of the cylinder is a sphere when computed(a) At the
Given an arbitrary body and three rectangular axes x, y, and z, prove that the mass moment of inertia of the body with respect to any one of the three axes cannot be larger than the sum of the mass
Consider a cube of mass m and side a. (a) Show that the ellipsoid of inertia at the center of the cube is a sphere, and use this property to determine the mass moment of inertia of the cube with
Given a homogeneous body of mass m and arbitrary shape and three rectangular axes x, y, and z with origin at O, prove that the sum Ix +Iy + Iz of the mass moments of inertia of the body cannot be
The homogeneous circular cylinder shown has a mass m, and the diameter OB of its top surface forms 45° angles with the x and z axes.(a) Determine the principal mass moments of inertia of the
For the component described in the problem indicated, determine(a) The principal mass moments of inertia at the origin,(b) The principal axes of inertia at the origin. Sketch the body and show the
For the component described in the problem indicated, determine(a) The principal mass moments of inertia at the origin,(b) The principal axes of inertia at the origin. Sketch the body and show the
For the component described in the problem indicated, determine(a) The principal mass moments of inertia at the origin,(b) The principal axes of inertia at the origin. Sketch the body and show the
For the component described in the problem indicated, determine (a) The principal mass moments of inertia at the origin, (b) The principal axes of inertia at the origin. Sketch the body and show the
For the component described in the problem indicated, determine(a) The principal mass moments of inertia at the origin,(b) The principal axes of inertia at the origin. Sketch the body and show the
Determine by direct integration the moment of inertia of the shaded area with respect to the y axis.
Determine by direct integration the moment of inertia of the shaded area with respect to the x axis.
Determine the moment of inertia and the radius of gyration of the shaded area with respect to the x axis.
Determine the moment of inertia and the radius of gyration of the shaded area with respect to the y axis.
Determine the polar moment of inertia of the area shown with respect to(a) Point O,(b) The centroid of the area.
To form a reinforced box section, two rolled W sections and two plates are welded together. Determine the moments of inertia and the radii of gyration of the combined section with respect to the
Two L3 Ã— 3 Ã— ¼-in. angles are welded to a C10 Ã— 20 channel. Determine the moments of inertia of the combined section with respect to centroidal axes
For the 2-kg connecting rod shown, it has been experimentally determined that the mass moments of inertia of the rod with respect to the centerline axes of the bearings AA€² and
Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes.
Using Mohr€™s circle, determine the orientation of the principal centroidal axes and the corresponding values of the moments of inertia.
Determine by direct integration the mass moment of inertia with respect to the z axis of the right circular cylinder shown assuming that it has a uniform density and a mass m.
Determine the mass products of inertia Ixy, Iyz, and Izx of the steel machine element shown. (The specific weight of steel is 0.284 lb / in3)
The thermal conductivity of a sheet of rigid, extruded insulation is reported to be k = 0.029 W/m. K. The measured temperature difference across a 20-mm-thick sheet of the material is T1 - T2 =
A concrete wall, which has a surface area of 20 m2 and is 0.30 m thick, separates conditioned room air from ambient air. The temperature of the inner surface of the wall is maintained at 25°C, and
The concrete slab of a basement is 11 m long, 8 m wide and 0.20 m thick. During the winter, temperatures are nominally 17°C and 10oC at the top and bottom surfaces, respectively. If the concrete has
The heat flux through a wood slab 50 mm thick, whose inner and outer surface temperatures are 40 and 20°C, respectively, has been determined to be 40W/m z. What is the thermal conductivity of the
The inner and outer surface temperatures of a glass window 5 mm thick are 15 and 5°e. What is the heat loss through a window that is 1 m by 3 m on a side? The thermal conductivity of glass is 1.4
A glass window of width W = 1 m and height H = 2 m is 5 mm thick and has a thermal conductivity of kg = 1.4 W/m. K if the inner and outer surface temperatures of the glass are 15°C and -20°e,
A freezer compartment consists of a cubical cavity that is 2 m on a side. Assume the bottom to be perfectly insulated. What is the minimum thickness of Styrofoam insulation (k = 0.030 W/m. K) that
An inexpensive food and beverage container is fabricated from 25-mm-thick polystyrene (k = 0.023 W/m. K) and has interior dimensions of 0.8 m x 0.6 m x 0.6 m. Under conditions for which an inner
What is the thickness required of a masonry wall having thermal conductivity 0.75 W/m. K if the heat rate is to be 80% of the heat rate through a composite structural wall having a thermal
The 5-mm-thick bottom of a 200-mm-diameter pan may be made from aluminum (k = 240 W/m. K) or copper (k = 390 W/m. K). When used to boil water, the surface of the bottom exposed to the water is
A square silicon chip (k = 150 W/m. K) is of width w = 5 mm on a side and of thickness t = 1 mm. The chip is mounted in a substrate such that its side and back surfaces are insulated, while the front
A gage for measuring heat flux to a surface or through a laminated material employs five thin-films, chromel/ alumel (type K) thermocouples deposited on the upper and lower surfaces of a wafer with a
You've experienced convection cooling if you've ever extended your hand out the window of a moving vehicle or into a flowing water stream. With the surface of your hand at a temperature of 30°C,
Air at 40°C flows over a long, 25-mm-diameter cylinder with an embedded electrical heater In a series of tests, measurements were made of the power per unit length, P', required to maintain the
An electric resistance heater is embedded in a long cylinder of diameter 30 mm. When water with a temperature of 25°C and velocity of 1 m/s flows crosswise over the cylinder, the power per unit
A cartridge electrical heater is shaped as a cylinder of length L = 200 mm and outer diameter D = 20 mm. Under normal operating conditions the heater dissipates 2 kW while submerged in a water flow
A common procedure for measuring the velocity of an air stream involves insertion of an electrically heated wire (called a hot-wire anemometer) into the air flow, with the axis of the wire oriented
A square isothermal chip is of width w = 5 mm on a side and is mounted in a substrate such that its side and back surfaces are well insulated, while the front surface is exposed to the flow of a
The case of a power transistor, which is of length L = 10 mm and diameter D = 12 mm, is cooled by an air stream of temperature T∞, = 25°C.Under conditions for which the air maintains an average
The use of impinging air jets is proposed as a means of effectively cooling high-power logic chips in a computer. However, before the technique can be implemented, the convection coefficient
The temperature controller for a clothes dryer consists of a bimetallic switch mounted on an electrical heater attached to a wall-mounted insulation pad.The switch is set to open at 70°C, the
The free convection heat transfer coefficient on a thin hot vertical plate .suspended in still air can be determined from observations of the change in plate temperature with time as it cools.
A transmission case measures W = 0.30 m on a side and receives a power input of Pi = 150 hp from the engine.If the transmission efficiency is η = 0.93 and air flow over the case corresponds to T∞
Under conditions for which the same room temperature is maintained by a heating or cooling system, it is not uncommon for a person to feel chilled in the winter but comfortable in the summer. Provide
A spherical interplanetary probe of 0.5-m diameter contains electronics that dissipate 150 W. If the probe surface has an emissivity of 0.8 and the probe does not receive radiation from other
An instrumentation package has a spherical outer surface of diameter D = 100 mm and emissivity B = 0.25. The package is placed in a large space simulation chamber whose walls are maintained at 77 K.
Consider the conditions of Problem 1.22. However, now the plate is in a vacuum with a surrounding temperature of 25°C. What is the emissivity of the plate? What is the rate at which radiation is
An overhead 25-m-Iong, un-insulated industrial steam pipe of 100 mm diameter is routed through a building whose walls and air are at 25°C. Pressurized steam maintains a pipe surface temperature of
If Ts ≈ Tsur in Equation 1.9, the radiation heat transfer coefficient may be approximated as hr,a = 4εσT3 where T ≡ (Ts + Tsur)/2. We wish to assess the validity of this approximation by
Consider the conditions of Problem 1.18. With heat transfer by convection to air, the maximum allowable chip power is found to be 0.35 W. If consideration is also given to net heat transfer by
Chips of width L = 15 mm on a side are mounted to a substrate that is installed in an enclosure whose walls and air are maintained at a temperature of Tsur = Tx = 25Â°C. The chips have an
A vacuum system, as used in sputtering electrically conducting thin films on microcircuits, is comprised of a base plate maintained by an electrical heater at 300 K and a shroud within the enclosure
Consider the transmission case of Problem 1.23, but now allow for radiation exchange with the ground chassis, which may be approximated as large surroundings at Tsur = 30°C. If the emissivity of the
An electrical resistor is connected to a battery, as shown schematically. After a brief transient, the resistor assumes a nearly uniform, steady-state temperature of 95Â°C, while the battery and
An aluminum plate 4 mm thick is mounted in a horizontal position and its bottom surface is well insulated. A special, thin coating is applied to the top surface such that it absorbs 80% of any
The energy consumption associated with a home water heater has two components: (i) the energy that must be supplied to bring the temperature of groundwater to the heater storage temperature, as it is
Three electric resistance heaters of length L = 250 mm and diameter D = 25 mm are submerged in a 10 gallon tank of water, which is initially at 295 K. The water may be assumed to have a density and
A hair dryer may be idealized as a circular duct through which a small fan draws ambient air and within which the air is heated as it flows over a coiled electric resistance wire.
In one stage of an annealing process, 304 stainless steel sheet is taken from 300 K to 1250 K as it passes through an electrically heated oven at a speed of V, = 10 mm/s. The sheet thickness and
Annealing, an important step in semiconductor materials processing, can be accomplished by rapidly heating the silicon wafer to a high temperature for a short period of time. The schematic shows a
In the thermal processing of semiconductor materials, annealing is accomplished by heating a silicon wafer according to a temperature-time recipe and then maintaining a fixed elevated temperature for
A furnace for processing semiconductor materials is formed by a silicon carbide chamber that is zone heated on the top section and cooled on the lower section. With the elevator in the lowest
Radioactive wastes are packed in a long, thin-walled cylindrical container. The wastes generate thermal energy non-uniformly according to the relation q = qv [1 – (r/ro) 2], where q is the
Consider the conducting rod of Example 1.3 under steady-state conditions. As suggested in Comment 3, the temperature of the rod may be controlled by varying the speed of air flow over the rod, which,
A long bus bar (cylindrical rod used for making electrical connections) of diameter D is installed in a large conduit having a surface temperature of 30°C and in which the ambient air temperature is
A small sphere of reference-grade iron with a specific heat of 447 J/kg 0 K and a mass of 0.515 kg is suddenly immersed in a water-ice mixture. Fine thermocouple wires suspend the sphere, and the
A spherical, stainless steel (AISI 302) canister is used to store reacting chemicals that provide for a uniform heat flux q”i to its inner surface. The canister is suddenly submerged in a liquid
Liquid oxygen, which has a boiling point of 90 K and a latent heat of vaporization of 214kJ/kg, is stored in a spherical container whose outer surface is of 500-mm diameter and at a temperature of -
A freezer compartment is covered with a 2-mm-thick layer of frost at the time it malfunctions. If the compartment is in ambient air at 20°C and a coefficient of h = 2 W/m2 ∙ K characterizes heat
A vertical slab of Woods metal is joined to a substrate on one surface and is melted as it is uniformly irradiated by a laser source on the opposite surface. The metal is initially at its fusion
Following the hot vacuum forming of a paper-pulp mixture, the product, an egg carton, is transported on a conveyor for 18 s toward the entrance of a gas-fired oven where it is dried to a desired
Electronic power devices are mounted to a heat sink having an exposed surface area of 0.045 m2 and an emissivity of 0.80. When the devices dissipate a total power of 20 Wand the air and surroundings
A computer consists of an array of five printed circuit boards (PCBs), each dissipating Pb = 20 W of power. Cooling of the electronic components on a board is provided by the forced flow of air,
The roof of a car in a parking lot absorbs a solar radiant flux of 800 W/m2, while the underside is perfectly insulated. The convection coefficient between the roof and the ambient air is 12 W/m2 ∙
Consider the conditions of Problem 1.22, but the surroundings temperature is 25°C and radiation exchange with the surroundings is not negligible. If the convection coefficient is 6.4 W/m2 ∙ K and

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