VECTOR MECH. FOR EGR: STATS & DYNAM (LL
12th Edition
ISBN: 9781260663778
Author: BEER
Publisher: MCG
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Textbook Question
Chapter 5.1, Problem 5.31P
The homogeneous wire ABCD is bent as shown and is attached to a hinge at C. Determine the length L for which portion AB of the wire is horizontal.
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(I) [40 Points] Using centered finite difference approximations as done in class, solve the equation for O:
d20
dx²
+ 0.010+ Q=0
subject to the boundary conditions shown in the stencil below. Do this for two values of Q: (a) Q = 0.3,
and (b) Q= √(0.5 + 2x)e-sinx (cos(5x)+x-0.5√1.006-x| + e −43*|1+.001+x* | * sin (1.5 − x) +
(cosx+0.001 + ex-1250+ sin (1-0.9x)|) * x - 4.68x4. For Case (a) (that is, Q = 0.3), use the stencil in Fig.
1. For Case (b), calculate with both the stencils in Fig. 1 and Fig 2. For all the three cases, show a table as
well as a plot of O versus x. Discuss your results. Use MATLAB and hand in the MATLAB codes.
1
0=0
x=0
2
3
4
0=1
x=1
Fig 1
1 2 3 4 5 6 7 8 9 10
11
0=0
x=0
0=1
x=1
Fig 2
Fig 2
(II) [60 Points] Using centered finite difference approximation as done in class, solve the equation:
020 020
+
მx2 მy2
+0.0150+Q=0
subject to the boundary conditions shown in the stencils below. Do this for two values of Q: (a) Q = 0.3,
and (b) Q = 10.5x² + 1.26 * 1.5 x 0.002 0.008. For Case (a) (that is, Q = 0.3) use Fig 3. For Case (b),
use both Fig. 3 and Fig 4. For all the three cases, show a table as well as the contour plots of versus
(x, y), and the (x, y) heat flux values at all the nodes on the boundaries x = 1 and y = 1. Discuss your
results. Use MATLAB and hand in the MATLAB codes. (Note that the domain is (x, y)e[0,1] x [0,1].)
0=0
0=0
4
8
12
16
10
Ꮎ0
15
25
9
14
19
24
3
11
15
0=0
8-0
0=0
3
8
13
18
23
2
6
сл
5
0=0
10
14
6
12
17
22
1
6
11
16
21
13
e=0
Fig 3
Fig 4
Textbook: Numerical Methods for Engineers, Steven C. Chapra and Raymond P. Canale, McGraw-Hill, Eighth
Edition (2021).
Ship construction question. Sketch and describe the forward arrangements of a ship. Include componets of the structure and a explanation of each part/ term.
Ive attached a general fore end arrangement. Simplfy construction and give a brief describion of the terms.
Chapter 5 Solutions
VECTOR MECH. FOR EGR: STATS & DYNAM (LL
Ch. 5.1 - 5.1 through 5.9 Locate the centroid of the plane...Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - Locate the centroid of the plane area shown.
Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - PROBLEM 5.16 Determine the y coordinate of the...Ch. 5.1 - Show that as r1 approaches r2, the location of the...Ch. 5.1 - Prob. 5.18PCh. 5.1 - Prob. 5.19PCh. 5.1 - A built-up beam is constructed by nailing seven...Ch. 5.1 - The horizontal x axis is drawn through the...Ch. 5.1 - The horizontal x-axis is drawn through the...Ch. 5.1 - PROBLEM 5.23 The first moment of the shaded area...Ch. 5.1 - A thin, homogeneous wire is bent to form the...Ch. 5.1 - A thin, homogeneous wire is bent to form the...Ch. 5.1 - Prob. 5.26PCh. 5.1 - A thin, homogeneous wire is bent to form the...Ch. 5.1 - Prob. 5.28PCh. 5.1 - The frame for a sign is fabricated from thin, flat...Ch. 5.1 - The homogeneous wire ABCD is bent as shown and is...Ch. 5.1 - The homogeneous wire ABCD is bent as shown and is...Ch. 5.1 - Prob. 5.32PCh. 5.1 - Knowing that the distance h has been selected to...Ch. 5.2 - Determine by direct integration the centroid of...Ch. 5.2 - 5.34 through 5.36 Determine by direct integration...Ch. 5.2 - 5.34 through 5.36 Determine by direct integration...Ch. 5.2 - 5.37 through 5.39 Determine by direct integration...Ch. 5.2 - 5.37 through 5.39 Determine by direct integration...Ch. 5.2 - Prob. 5.39PCh. 5.2 - 5.40 and 5.41 Determine by direct integration the...Ch. 5.2 - 5.40 and 5.41 Determine by direct integration the...Ch. 5.2 - 5.42 Determine by direct integration the centroid...Ch. 5.2 - 5.43 and 5.44 Determine by direct integration the...Ch. 5.2 - 5.43 and 5.44 Determine by direct integration the...Ch. 5.2 - 5.45 and 5.46 A homogeneous wire is bent into the...Ch. 5.2 - 5.45 and 5.46 A homogeneous wire is bent into the...Ch. 5.2 - A homogeneous wire is bent into the shape shown....Ch. 5.2 - 5.48 and 5.49 Determine by direct integration the...Ch. 5.2 - Prob. 5.49PCh. 5.2 - Prob. 5.50PCh. 5.2 - Determine the centroid of the area shown when a =...Ch. 5.2 - Determine the volume and the surface area of the...Ch. 5.2 - Determine the volume and the surface area of the...Ch. 5.2 - Determine the volume and the surface area of the...Ch. 5.2 - Determine the volume and the surface area of the...Ch. 5.2 - Determine the volume of the solid generated by...Ch. 5.2 - Prob. 5.57PCh. 5.2 - Prob. 5.58PCh. 5.2 - Prob. 5.59PCh. 5.2 - Determine the capacity, in liters, of the punch...Ch. 5.2 - Determine the volume and total surface area of the...Ch. 5.2 - Prob. 5.62PCh. 5.2 - Determine the total surface area of the solid...Ch. 5.2 - Determine the volume of the brass collar obtained...Ch. 5.2 - The shade for a wall-mounted light is formed from...Ch. 5.3 - 5.66 and 5.67 For the beam and loading shown,...Ch. 5.3 - 5.66 and 5.67 For the beam and loading shown,...Ch. 5.3 - 5.68 through 5.73 Determine the reactions at the...Ch. 5.3 - 5.68 through Determine the reactions at the beam...Ch. 5.3 - 5.68 through 5.73 Determine the reactions at the...Ch. 5.3 - 5.68 through Determine the reactions at the beam...Ch. 5.3 - 5.68 through 5.73 Determine the reactions at the...Ch. 5.3 - 5.68 through 5.73 Determine the reactions at the...Ch. 5.3 - Determine (a) the distance a so that the vertical...Ch. 5.3 - Prob. 5.75PCh. 5.3 - Determine the reactions at the beam supports for...Ch. 5.3 - Determine (a) the distributed load w0 at the end D...Ch. 5.3 - The beam AB supports two concentrated loads and...Ch. 5.3 - For the beam and loading of Prob. 5.78, determine...Ch. 5.3 - The cross section of a concrete dam is as shown....Ch. 5.3 - Prob. 5.81PCh. 5.3 - The dam for a lake is designed to withstand the...Ch. 5.3 - Prob. 5.83PCh. 5.3 - The friction force between a 6 6-ft square sluice...Ch. 5.3 - A freshwater marsh is drained to the ocean through...Ch. 5.3 - Prob. 5.86PCh. 5.3 - The 3 4-m side of an open tank is hinged at its...Ch. 5.3 - Prob. 5.88PCh. 5.3 - A 0.5 0.8-m gate AB is located at the bottom of a...Ch. 5.3 - Prob. 5.90PCh. 5.3 - Prob. 5.91PCh. 5.3 - Prob. 5.92PCh. 5.3 - Prob. 5.93PCh. 5.3 - Prob. 5.94PCh. 5.3 - The square gate AB is held in the position shown...Ch. 5.4 - Consider the composite body shown. Determine (a)...Ch. 5.4 - A cone and a cylinder of the same radius a and...Ch. 5.4 - Determine the location of the center of gravity of...Ch. 5.4 - Prob. 5.99PCh. 5.4 - For the stop bracket shown, locate the x...Ch. 5.4 - Fig. P5.100 and P5.101 5.101 For the stop bracket...Ch. 5.4 - For the machine element shown, locate the x...Ch. 5.4 - Fig. P5.102 and P5.103 5.103 For the machine...Ch. 5.4 - For the machine element shown, locate the y...Ch. 5.4 - For the machine element shown, locate the x...Ch. 5.4 - 5.106 and 5.107 Locate the center of gravity of...Ch. 5.4 - 5.106 and 5.107 Locate the center of gravity of...Ch. 5.4 - A corner reflector for tracking by radar has two...Ch. 5.4 - A wastebasket, designed to fit in the corner of a...Ch. 5.4 - Prob. 5.110PCh. 5.4 - Prob. 5.111PCh. 5.4 - Prob. 5.112PCh. 5.4 - Locate the center of gravity of the sheet-metal...Ch. 5.4 - A thin steel wire with a uniform cross section is...Ch. 5.4 - The frame of a greenhouse is constructed from...Ch. 5.4 - Locate the center of gravity of the figure shown,...Ch. 5.4 - PROBLEM 5.117 Locate the center of gravity of the...Ch. 5.4 - A scratch awl has a plastic handle and a steel...Ch. 5.4 - Prob. 5.119PCh. 5.4 - PROBLEM 5.120 A brass collar, of length 2.5 in.,...Ch. 5.4 - Prob. 5.121PCh. 5.4 - Prob. 5.122PCh. 5.4 - Prob. 5.123PCh. 5.4 - Prob. 5.124PCh. 5.4 - PROBLEM 5.125 Locate the centroid of the volume...Ch. 5.4 - PROBLEM 5.126 Locate the centroid of the volume...Ch. 5.4 - Prob. 5.127PCh. 5.4 - Prob. 5.128PCh. 5.4 - PROBLEM 5.129 Locate the centroid of the volume...Ch. 5.4 - Prob. 5.130PCh. 5.4 - Prob. 5.131PCh. 5.4 - PROBLEM 5.132 The sides and the base of a punch...Ch. 5.4 - Locate the centroid of the section shown, which...Ch. 5.4 - Prob. 5.134PCh. 5.4 - Prob. 5.135PCh. 5.4 - Alter grading a lot, a builder places four stakes...Ch. 5 - 5.137 and 5.138 Locate the centroid of the plane...Ch. 5 - 5.137 and 5.138 Locate the centroid of the plane...Ch. 5 - Prob. 5.139RPCh. 5 - Prob. 5.140RPCh. 5 - Prob. 5.141RPCh. 5 - Prob. 5.142RPCh. 5 - Determine the reactions at the supports for the...Ch. 5 - A beam is subjected to a linearly distributed...Ch. 5 - Prob. 5.145RPCh. 5 - Prob. 5.146RPCh. 5 - An 8-in.-diameter cylindrical duct and a 4 8-in....Ch. 5 - Three brass plates are brazed to a steel pipe to...
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