ENGINEERING MECHANICS: STATICS
14th Edition
ISBN: 9780135681879
Author: HIBBELER
Publisher: PEARSON
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Textbook Question
Chapter 9.1, Problem 34P
Determine the location of its center of mass. Also find the reactions at the pin and roller support.
Prob. 9-34
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You are working as an engineer in a bearing systems design company. The flow of
lubricant inside a hydrodynamic bearing (p = 0.001 kg m-1 s-1) can be approximated
as a parallel, steady, two-dimensional, incompressible flow between two parallel plates.
The top plate, representing the moving part of the bearing, travels at a constant speed,
U, while the bottom plate remains stationary (Figure Q1). The plates are separated by
a distance of 2h = 1 cm and are W = 20 cm wide. Their length is L = 10 cm. By
applying the above approximations to the Navier-Stokes equations and assuming that
end effects can be neglected, the horizontal velocity profile can be shown to be
y = +h
I
2h = 1 cm
x1
y = -h
u(y)
1 dP
2μ dx
-y² + Ay + B
moving plate
stationary plate
U
2
I2
L = 10 cm
Figure Q1: Flow in a hydrodynamic bearing. The plates extend a width, W = 20 cm,
into the page.
Question 1
You are working as an engineer in a bearing systems design company. The flow of
lubricant inside a hydrodynamic bearing (µ = 0.001 kg m¯¹ s¯¹) can be approximated
as a parallel, steady, two-dimensional, incompressible flow between two parallel plates.
The top plate, representing the moving part of the bearing, travels at a constant speed,
U, while the bottom plate remains stationary (Figure Q1). The plates are separated by
a distance of 2h = 1 cm and are W = 20 cm wide. Their length is L = 10 cm. By
applying the above approximations to the Navier-Stokes equations and assuming that
end effects can be neglected, the horizontal velocity profile can be shown to be
1 dP
u(y)
=
2μ dx
-y² + Ay + B
y= +h
Ꮖ
2h=1 cm
1
x1
y = −h
moving plate
stationary plate
2
X2
L = 10 cm
Figure Q1: Flow in a hydrodynamic bearing. The plates extend a width, W = 20 cm,
into the page.
(a) By considering the appropriate boundary conditions, show that the constants take
the following forms:
U
U
1 dP
A =…
Question 2
You are an engineer working in the propulsion team for a supersonic civil transport
aircraft driven by a turbojet engine, where you have oversight of the design for the
engine intake and the exhaust nozzle, indicated in Figure Q2a. The turbojet engine can
operate when provided with air flow in the Mach number range, 0.60 to 0.80. You are
asked to analyse a condition where the aircraft is flying at 472 m/s at an altitude of
14,000 m. For all parts of the question, you can assume that the flow path of air through
the engine has a circular cross section.
(a)
← intake
normal
shock
472 m/s
A B
(b)
50 m/s
H
472 m/s
B
engine
altitude: 14,000 m
exhaust nozzle
E
F
exit to
atmosphere
diameter: DE = 0.30 m
E
F
diameter: DF = 0.66 m
Figure Q2: Propulsion system for a supersonic aircraft.
a) When the aircraft is at an altitude of 14,000 m, use the International Standard
Atmosphere in the Module Data Book to state the local air pressure and tempera-
ture. Thus show that the aircraft speed…
Chapter 9 Solutions
ENGINEERING MECHANICS: STATICS
Ch. 9.1 - In each case, use the element shown and specify...Ch. 9.1 - Determine the centroid (x,y) of the shaded area....Ch. 9.1 - Determine the centroid (x,y) of the shaded area....Ch. 9.1 - Determine the centroid of the shaded area. Prob....Ch. 9.1 - Locate the center of mass x of the straight rod if...Ch. 9.1 - Locate the centroid of the homogeneous solid...Ch. 9.1 - Locate the centroid z of the homogeneous solid...Ch. 9.1 - Locate the center of mass of the homogeneous rod...Ch. 9.1 - Determine the location (x,y) of the centroid of...Ch. 9.1 - If the rod has a weight per unit length of 100...
Ch. 9.1 - Locate the center of gravity of the homogeneous...Ch. 9.1 - Determine the distance to the center of gravity...Ch. 9.1 - Locate the centroid of the area.Ch. 9.1 - Locate the centroid x of the parabolic area. Prob....Ch. 9.1 - Locate the centroid of the shaded area. Prob. 9-8Ch. 9.1 - Locate the centroid x of the shaded area. Probs....Ch. 9.1 - Locate the centroid of the shaded area. Probs....Ch. 9.1 - Locate the centroid x of the area. Probs. 9-11/12Ch. 9.1 - Locate the centroid of the area. Probs. 9-11/12Ch. 9.1 - Locate the centroid x of the area. Probs. 9-13/14Ch. 9.1 - Locate the centroid of the area. Probs. 9-13/14Ch. 9.1 - Solve the problem by evaluating the integrals...Ch. 9.1 - Solve the problem by evaluating the integrals...Ch. 9.1 - Locate the centroid of the area. Prob. 9-17Ch. 9.1 - Locate the centroid x of the area. Probs. 9-18/19Ch. 9.1 - Locate the centroid of the area. Probs. 9-18/19Ch. 9.1 - Locate the centroid of the shaded area.Ch. 9.1 - Locate the centroid x of the shaded area. Probs....Ch. 9.1 - Locate the centroid of the shaded area. Probs....Ch. 9.1 - Locate the centroid x of the shaded area. Probs....Ch. 9.1 - Locate the centroid of the shaded area. Probs....Ch. 9.1 - Determine the location of its center of gravity....Ch. 9.1 - Locate the centroid x of the shaded area. Probs....Ch. 9.1 - Locate the centroid of the shaded area. Probs....Ch. 9.1 - Locate the centroid x of the shaded area. Probs....Ch. 9.1 - Locate the centroid of the shaded area. Probs....Ch. 9.1 - Locate the centroid x of the shaded area. Probs....Ch. 9.1 - Locate the centroid of the shaded area. Probs....Ch. 9.1 - Locate the centroid x of the area. Probs. 9-32/33Ch. 9.1 - Locate the centroid of the area. Probs. 9-32/33Ch. 9.1 - Determine the location of its center of mass. Also...Ch. 9.1 - Locate the centroid x of the shaded area. Probs....Ch. 9.1 - Locate the centroid of the shaded area. Probs....Ch. 9.1 - Locate the centroid x of the circular sector.Ch. 9.1 - Determine the location r of the centroid C for the...Ch. 9.1 - The material is homogeneous. Prob. 9-39Ch. 9.1 - Locate the centroid of the paraboloid. Probs....Ch. 9.1 - Locate the centroid z of the frustum of the...Ch. 9.1 - Determine the centroid of the solid. Prob. 9-42Ch. 9.1 - Locate the centroid of the quarter-cone. Prob....Ch. 9.1 - Determine its mass and the distance z to the...Ch. 9.1 - Locate the centroid z of the volume. Prob. 9-45Ch. 9.1 - Locate the centroid of the ellipsoid of...Ch. 9.1 - Locate the center of gravity z of the solid. Prob....Ch. 9.1 - Locate the centroid of the ellipsoid of...Ch. 9.1 - Locate the centroid z of the spherical segment....Ch. 9.1 - Suggestion: Use a triangular plate element...Ch. 9.2 - Locate the centroid (x,y,z) of the wire bent in...Ch. 9.2 - Locate the centroid of the beams cross-sectional...Ch. 9.2 - Locate the centroid of the beams cross-sectional...Ch. 9.2 - Locate the centroid (x,y) of the cross-sectional...Ch. 9.2 - Locate the center of mass (x,y,z) of the...Ch. 9.2 - Determine the center of mass (x,y,z) of the...Ch. 9.2 - If the mass of the gusset plates at the joints and...Ch. 9.2 - Determine the location (x,y,z) of the centroid of...Ch. 9.2 - Determine the location (x,y) of the centroid of...Ch. 9.2 - Neglect the thickness of the material and slight...Ch. 9.2 - Neglect the thickness of the material and slight...Ch. 9.2 - Each plate has a constant width in the z direction...Ch. 9.2 - Neglect the thickness of each segment. The mass...Ch. 9.2 - Neglect the size of the corner welds at A and B...Ch. 9.2 - Prob. 59PCh. 9.2 - Locate the centroid for the beams cross-sectional...Ch. 9.2 - Determine the location of the centroid C of the...Ch. 9.2 - Locate the centroid (x,y) of the shaded area....Ch. 9.2 - Neglect the size of the corner welds at A and B...Ch. 9.2 - Locate the centroid (x,y) of the shaded area....Ch. 9.2 - Determine the location (x,y) of the centroid C of...Ch. 9.2 - The beam is symmetric with respect to the y axis....Ch. 9.2 - Assume all corners are square and neglect the size...Ch. 9.2 - Prob. 68PCh. 9.2 - If it is folded over as shown, determine the...Ch. 9.2 - Locate the center of mass z of the forked level...Ch. 9.2 - Prob. 71PCh. 9.2 - Prob. 72PCh. 9.2 - Prob. 73PCh. 9.2 - The location of the center of gravity of each...Ch. 9.2 - Locate the center of mass (x,y,z) of the...Ch. 9.2 - Determine the location (x,y,z) of its centroid....Ch. 9.2 - It the cord is cut, the part will rotate about the...Ch. 9.2 - Prob. 78PCh. 9.2 - Prob. 79PCh. 9.2 - Prob. 80PCh. 9.2 - The assembly is made from a steel hemisphere. st =...Ch. 9.2 - The assembly is made from a steel hemisphere, st =...Ch. 9.2 - Prob. 83PCh. 9.2 - Determine the distance h to which a...Ch. 9.2 - Determine the distance z to the centroid of the...Ch. 9.2 - The cylinder and the cone are made from materials...Ch. 9.2 - Major floor loadings in a shop are caused by the...Ch. 9.2 - Determine the distance x to its center of gravity...Ch. 9.2 - Determine the mass and location (x,y,z) of its...Ch. 9.3 - Determine the surface area and volume of the solid...Ch. 9.3 - Prob. 14FPCh. 9.3 - Determine the surface area and volume of the solid...Ch. 9.3 - Determine the surface area and volume of the solid...Ch. 9.3 - Prob. 90PCh. 9.3 - Prob. 91PCh. 9.3 - Determine the volume of the storage tank. Probs....Ch. 9.3 - Prob. 93PCh. 9.3 - Determine the total weight of the wall if the...Ch. 9.3 - Determine its volume.Ch. 9.3 - Prob. 96PCh. 9.3 - Determine the volume of concrete needed to...Ch. 9.3 - Do not include the area of the ends in the...Ch. 9.3 - Prob. 99PCh. 9.3 - Prob. 100PCh. 9.3 - Prob. 101PCh. 9.3 - Each gallon of paint can cover 250 ft2. Probs....Ch. 9.3 - Determine the surface area and the volume of the...Ch. 9.3 - Prob. 104PCh. 9.3 - Determine how many joules (J) are radiated within...Ch. 9.3 - Prob. 106PCh. 9.3 - Prob. 107PCh. 9.3 - Prob. 108PCh. 9.3 - Prob. 109PCh. 9.3 - Prob. 110PCh. 9.3 - Prob. 111PCh. 9.3 - Prob. 112PCh. 9.3 - Prob. 113PCh. 9.3 - Prob. 114PCh. 9.5 - Water has a density of = 1 Mg/m3. Prob. F9-17Ch. 9.5 - The specific weight of water is = 62.4 lb/ft3.Ch. 9.5 - Water has a density of = 1 Mg/m3. Prob. F9-19Ch. 9.5 - Water has a density of = 1 Mg/m3. Prob. F9-20Ch. 9.5 - The specific weight of water is = 62.4 lb/ft3....Ch. 9.5 - Determine the magnitude of the resultant force and...Ch. 9.5 - Determine the magnitude of the resultant force and...Ch. 9.5 - The load over the plate varies linearly along the...Ch. 9.5 - The load is defined by the expression p = p0 sin...Ch. 9.5 - If this pressure loading acts uniformly along the...Ch. 9.5 - For the condition of high tide shown, determine...Ch. 9.5 - Determine the resultant force the water exerts on...Ch. 9.5 - If the density of concrete is c = 2.5 Mg/m3, and...Ch. 9.5 - Determine this factor if the concrete has a...Ch. 9.5 - Determine the magnitude of the resultant...Ch. 9.5 - If it is filled to the top, determine the...Ch. 9.5 - Prob. 126PCh. 9.5 - Determine the reactions at these supports due to...Ch. 9.5 - The tank is filled with a liquid that has a...Ch. 9.5 - The gate has a width of 1.5 m. w = 1.0 Mg/m3....Ch. 9.5 - Prob. 130PCh. 9.5 - Locate the centroid x of the area.Ch. 9.5 - Locate the centroid of the area.Ch. 9.5 - Prob. 3RPCh. 9.5 - Locate the centroid of the rod. Prob. R9-4Ch. 9.5 - Prob. 5RPCh. 9.5 - Prob. 6RPCh. 9.5 - Determine the volume of material required to make...Ch. 9.5 - Prob. 8RPCh. 9.5 - Determine the horizontal and vertical components...Ch. 9.5 - Determine the magnitude of the resultant...
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