Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Chapter 23, Problem 10P
Develop a user-friendly program to apply a Romberg algorithm to estimate the derivative of a given function.
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An AISI 1018 steel ball with 1.100-in diameter is used as a roller between a flat plate
made from 2024 T3 aluminum and a flat table surface made from ASTM No. 30 gray
cast iron. Determine the maximum amount of weight that can be stacked on the
aluminum plate without exceeding a maximum shear stress of 19.00 kpsi in any of the
three pieces. Assume the figure given below, which is based on a typical Poisson's
ratio of 0.3, is applicable to estimate the depth at which the maximum shear stress
occurs for these materials.
1.0
0.8
Ratio of stress to Pmax
0.4
90
0.6
στ
Tmax
0.2
0.5a
a
1.5a
2a
2.5a
За
Distance from contact surface
The maximum amount of weight that can be stacked on the aluminum plate is
lbf.
A carbon steel ball with 27.00-mm diameter is pressed together with an aluminum ball
with a 36.00-mm diameter by a force of 11.00 N. Determine the maximum shear
stress and the depth at which it will occur for the aluminum ball. Assume the figure
given below, which is based on a typical Poisson's ratio of 0.3, is applicable to estimate
the depth at which the maximum shear stress occurs for these materials.
1.0
0.8
Ratio of stress to Pma
9 0.6
στ
24
0.4
Tmax
0.2
0
0.5a
a
1.5a
Z
2a
2.5a
За
Distance from contact surface
The maximum shear stress is determined to be
MPa.
The depth in the aluminum ball at which the maximum shear stress will occur is
determined to be [
mm.
Show all work please
Chapter 23 Solutions
Numerical Methods for Engineers
Ch. 23 - 23.1 Compute forward and backward difference...Ch. 23 - 23.2 Repeat Prob. 23.1, but for evaluated at...Ch. 23 - 23.3 Use centered difference approximations to...Ch. 23 - Use Richardson extrapolation to estimate the first...Ch. 23 - Repeat Prob. 23.4, but for the first derivative of...Ch. 23 - 23.6 Employ Eq. (23.9) to determine the first...Ch. 23 - 23.7 Prove that for equispaced data points, Eq....Ch. 23 - Compute the first-order central difference...Ch. 23 - Prob. 9PCh. 23 - Develop a user-friendly program to apply a Romberg...
Ch. 23 - 23.11 Develop a user-friendly program to obtain...Ch. 23 - 23.12 The following data are provided for the...Ch. 23 - 23.13 Recall that for the falling parachutist...Ch. 23 - The normal distribution is defined as f(x)=12ex2/2...Ch. 23 - 23.15 The following data were generated from the...Ch. 23 - Evaluate f/x,f/y, and f/(xy) for the following...Ch. 23 - 23.17 Evaluate the following integral with...Ch. 23 - 23.18 Use the diff command in MATLAB and compute...Ch. 23 - The objective of this problem is to compare...Ch. 23 - Use a Taylor series expansion to derive a centered...Ch. 23 - Use the following data to find the velocity and...Ch. 23 - 23.22 A plane is being tracked by radar, and data...Ch. 23 - 23.23 Develop an Excel VBA macro program to read...Ch. 23 - Use regression to estimate the acceleration at...Ch. 23 - You have to measure the flow rate of water through...Ch. 23 - The velocity y (m/s) of air fl owing past a flat...Ch. 23 - Chemical reactions often follow the model:...Ch. 23 - 23.28 The velocity profile of a fluid in a...Ch. 23 - 23.29 The amount of mass transported via a pipe...
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