Numerical Methods For Engineers, 7 Ed
7th Edition
ISBN: 9789352602131
Author: Canale Chapra
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 24, Problem 3P
Repeat Prob. 24.1, but use a two- and a three-point GaussLegendre formula. Interpret your results.
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For the walking-beam mechanism shown in Figure 3, find and plot the x and y coordinates of the
position of the coupler point P for one complete revolution of the crank O2A. Use the coordinate
system shown in Figure 3. Hint: Calculate them first with respect to the ground link 0204 and
then transform them into the global XY coordinate system.
y
-1.75
Ꮎ
Ꮎ
4
= 2.33
0242.22
L4
x
AP = 3.06
L2 = 1.0
W2
31°
B
03 L3 = 2.06
P
1
8
5
.06
6
7
P'
The link lengths, gear ratio (2), phase angle (Ø), and the value of 02 for some geared five bar
linkages are defined in Table 2. The linkage configuration and terminology are shown in Figure
2. For the rows assigned, find all possible solutions for angles 03 and 04 by the vector loop
method. Show your work in details: vector loop, vector equations, solution procedure.
Table 2
Row
Link 1 Link 2
Link 3
Link 4
Link 5
λ
Φ
Ө
a
6
1
7
9
4
2
30°
60°
P
y 4
YA
B
b
R4
R3
YA
A
Gear ratio:
a
02
d
05
r5
R5
R2
Phase angle: = 0₂-202
R1
05
02
r2
Figure 2.
04
X
Problem 4
A .025 lb bullet C is fired at end B of the 15-lb slender bar AB. The
bar is initially at rest, and the initial velocity of the bullet is 1500 ft/s
as shown. Assuming that the bullet becomes embedded in the bar,
find (a) the angular velocity @2 of the bar immediately after impact,
and (b) the percentage loss of kinetic energy as a result of the impact.
(c) After the impact, does the bar swing up 90° and reach the
horizontal? If it does, what is its angular velocity at this point?
Answers: (a). @2=1.6 rad/s; (b). 99.6% loss
=
(c). Ah2 0.212 ft. The bar does not reach horizontal.
y
X
4 ft
15 lb
V₁
1500 ft/s
0.025 lb
C
30°7
B
A
Chapter 24 Solutions
Numerical Methods For Engineers, 7 Ed
Ch. 24 - Perform the same computation as Sec. 24.1, but...Ch. 24 - 24.2 Repeat Prob. 24.1, but use Romberg...Ch. 24 - 24.3 Repeat Prob. 24.1, but use a two- and a...Ch. 24 - 24.4 Integration provides a means to compute how...Ch. 24 - Use numerical integration to compute how much mass...Ch. 24 - 24.6 Fick’s first diffusion law states...Ch. 24 - The following data were collected when a large oil...Ch. 24 - 24.8 You are interested in measuring the fluid...Ch. 24 - Prob. 10PCh. 24 - 24.11 Glaucoma is the second leading cause of...
Ch. 24 - One of your colleagues has designed a new...Ch. 24 - Video an giography is used to measure blood flow...Ch. 24 - 24.14 Perform the same computation as in Sec....Ch. 24 - Perform the same computation as in Sec. 24.2, but...Ch. 24 - 24.16 As in Sec. 24.2, compute F using the...Ch. 24 - Stream cross-sectional areas (A) are required for...Ch. 24 - 24.18 As described in Prob. 24.17, the...Ch. 24 - 24.21 A transportation engineering study requires...Ch. 24 - 24.22 A wind force distributed against the side of...Ch. 24 - 24.23 Water exerts pressure on the upstream ...Ch. 24 - 24.24 To estimate the size of a new dam, you have...Ch. 24 - The data listed in the following table gives...Ch. 24 - The heat flux q is the quantity of heat flowing...Ch. 24 - 24.27 The horizontal surface area of a lake at a...Ch. 24 - 24.28 Perform the same computation as in Sec....Ch. 24 - 24.29 Repeat Prob. 24.28, but use five...Ch. 24 - Repeat Prob. 24.28, but use Romberg integration to...Ch. 24 - Faradays law characterizes the voltage drop across...Ch. 24 - 24.32 Based on Faraday’s law (Prob. 24.31), use...Ch. 24 - Suppose that the current through a resistor is...Ch. 24 - If a capacitor initially holds no charge, the...Ch. 24 - 24.35 Perform the same computation as in Sec....Ch. 24 - 24.36 Repeat Prob. 24.35, but use (a) Simpson’s ...Ch. 24 - 24.37 Compute work as described in Sec. 24.4, but...Ch. 24 - As was done in Sec. 24.4, determine the work...Ch. 24 - 24.39 The work done on an object is equal to the...Ch. 24 - The rate of cooling of a body (Fig. P24.40) can be...Ch. 24 - 24.41 A rod subject to an axial load (Fig....Ch. 24 - If the velocity distribution of a fluid flowing...Ch. 24 - 24.43 Using the following data, calculate the work...Ch. 24 - 24.44 A jet fighter’s position on an aircraft...Ch. 24 - 24.45 Employ the multiple-application Simpson’s...Ch. 24 - The upward velocity of a rocket can be computed by...Ch. 24 - Referring to the data from Problem 20.61, find the...Ch. 24 - Fully developed flow moving through a 40-cm...Ch. 24 - Fully developed flow of a Bingham plasticfluid...Ch. 24 - 24.50 The enthalpy of a real gas is a ...Ch. 24 - Given the data below, find the isothermal work...Ch. 24 - 24.52 The Rosin-Rammler-Bennet (RRB) equation is...Ch. 24 - For fluid flow over a surface, the heat flux to...Ch. 24 - The pressure gradient for laminar flow through a...Ch. 24 - 24.55 Velocity data for air are collected at...
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- The link lengths and the value of 2 and offset for some fourbar crank-slide linkages are defined in Table 1. The linkage configuration and terminology are shown in Figure 1. For the rows assigned, find (a) all possible solutions for angle & and slider position d by vector loop method. (b) the transmission angle corresponding to angle 03. (Hint: Treat the vector R4 as virtual rocker) Show your work in details: vector loop, vector equations, solution procedure. Table 1 Row Link 2 Link 3 Offset Ө a 1.4 4 1 45° b 3 8 2 -30° C 5 20 -5 225° 03 slider axis B X offset Link 2 A R3 Link 3 R4 04 R2 02 R1 d Figure 1. Xarrow_forward4. Two links made of heat treated 6061 aluminum (Sy = 276 MPa, Sys = 160 MPa) are pinned together using a steel dowel pin (Sy = 1398 MPa, Sys = 806 MPa) as shown below. The links are to support a load P with a factor of safety of at least 2.0. Determine if the link will fail first by tearout, direct shear of the pin, bearing stress on the link, or tensile stress at section AA. (Hint: find the load P for each case and choose the case that gives the smallest load.) P 8 mm P 8 mm ¡+A 3 mm →A 10 mm Parrow_forward1. For a feature other than a sphere, circularity is where: A. The axis is a straight line B. The modifier is specified with a size dimension C. All points of the surface intersected by any plane perpendicular to an axis or spine (curved line) are equidistant from that axis or spine D. All points of the surface intersected by any plane passing through a common center are equidistant from that center 2. What type of variation is limited by a circularity toler- ance zone? A. Ovality B. Tapering C. Bending D. Warping 3. How does the Rule #1 boundary affect the application of a circularity tolerance? A. The modifier must be used. B. The feature control frame must be placed next to the size dimension. C. The circularity tolerance value must be less than the limits of size tolerance. D. Circularity cannot be applied where a Rule #1 boundary exists. 4. A circularity tolerance may use a modifier. A. Ø B. F C. M D. ℗ 5. A real-world application for a circularity tolerance is: A. Assembly (i.e.,…arrow_forward
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