Theory and Design for Mechanical Measurements
6th Edition
ISBN: 9781118881279
Author: Richard S. Figliola, Donald E. Beasley
Publisher: WILEY
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Chapter 4, Problem 4.7P
A student conducts a lab exercise to calculate the acceleration of gravity, g, and gets a value of 9.5 m/s2 with a standard deviation of 0.1. He knows that the answer at his altitude and earth coordinates should be 9.8 m/s2. What is the probability of getting this result due to random chance (random error) alone? Neglecting outright blunders (he is a careful experimenter), give a possible cause for the result.
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Cardiologists use the short-range scaling exponent α1, which measures the randomness of heart rate patterns, as a tool to assess risk of heart attack. The article “Applying Fractal Analysis to Short Sets of Heart Rate Variability Data” compared values of α1 computed from long series of measurements (approximately 40,000 heartbeats) with those estimated from the first 300 beats to determine how well the long-term measurement (y) could be predicted the short-term one (x). Following are the data (obtained by digitizing a graph).
Short
Long
0.54
0.55
1.02
0.79
1.4
0.81
0.88
0.9
1.68
1.05
1.16
1.05
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1.05
0.93
1.07
1.26
1.1
1.18
1.19
0.81
1.19
0.81
1.2
1.28
1.23
1.18
1.23
0.71
1.24
Note: This problem has a reduced data set for ease of performing the calculations required. This differs from the data set given for this problem in the text.
Compute the least-squares line for predicting the long-term measurement from the short-term measurement.…
Designing safe boilers depends on knowing how steam behaves under certain changes in
temperature and pressure. Steam tables, such as the one below, are published giving values
of the function V = f(T, P) where V is the volume (in cubic feet) of one pound of steam at
a temperature of T (in degrees Fahrenheit) and pressure P (in pounds per square inch).
T//P
480
500
520
540
20 22
24
26
27.85 25.31 23.19 21.39
28.46 25.86 23.69 21.86
29.06 26.41 24.20 22.33
29.66 26.95 24.70 22.79
a) Find the tangent plane to V = f(T, P) for T near 520°F and P near 24 lb/in². [Hint:
Use the tables to approximate your partial derivatives and recall the equation of our tangent
plane is: V = VT(T − To) + Vp(P - Po) + f(T, P) ]
b) Use the tangent plane to estimate the volume of a pound of steam at a temperature of
525°F and P near 24.3 lb/in².
Fluid runs through a drainage pipe with a 10-cm radius and a length of 30m (3000cm). The velocity of the fluid gradually decreases from the center of the pipe toward the edges as a result of friction with the walls of the pipe. For the data shown, v(x) is the velocity of the fluid (in. cm/sec) and x represents the distance (in. cm) from the center of the pipe toward the edge.
x
0
1
2
3
4
5
6
7
8
9
v(x)
195.2
194.7
193.7
192.3
190.6
188.4
185.8
182.8
179.5
175.7
Use regression to find a quadratic function to model the data. Use all of the given data points and round each coefficient to 4 decimal places.
Chapter 4 Solutions
Theory and Design for Mechanical Measurements
Ch. 4 - Prob. 4.1PCh. 4 - Prob. 4.2PCh. 4 - At a fixed operating setting, the pressure in a...Ch. 4 - Consider the toss of four coins. There are 24...Ch. 4 - As a game, slide a matchbook across a table,...Ch. 4 - Prob. 4.6PCh. 4 - A student conducts a lab exercise to calculate the...Ch. 4 - From a large database, the Highway Patrol...Ch. 4 - Prob. 4.9PCh. 4 - Prob. 4.10P
Ch. 4 - Prob. 4.11PCh. 4 - Prob. 4.12PCh. 4 - Prob. 4.13PCh. 4 - Prob. 4.14PCh. 4 - Prob. 4.15PCh. 4 - From 19 measurements of a pressure controller, the...Ch. 4 - From 19 measurements of a pressure controller, the...Ch. 4 - When the parameters of a population are known, the...Ch. 4 - A professor grades students on a normal curve. For...Ch. 4 - Prob. 4.20PCh. 4 - 4.21 An automotive manufacturer removes the...Ch. 4 - Prob. 4.22PCh. 4 - Prob. 4.23PCh. 4 - A sampling of 409 motor shafts from a very large...Ch. 4 - During the course of a motor test, the motor rpm...Ch. 4 - A baich of rivets is tested for shear strength. A...Ch. 4 - Three independent sets of data are collected front...Ch. 4 - Prob. 4.28PCh. 4 - 4.29 An engineer measures the diameter of 20 tubes...Ch. 4 - Prob. 4.30PCh. 4 - For Problems 4.30 through 4.36. itwould be helpful...Ch. 4 - For Problems 4.30 through 4.36. itwould be helpful...Ch. 4 - For Problems 4.30 through 4.36. itwould be helpful...Ch. 4 - Prob. 4.34PCh. 4 - Prob. 4.35PCh. 4 - Prob. 4.36PCh. 4 - A manufacturer of general aircraft dry vacuum...Ch. 4 - Strength tests made on a batch of cold-drawn steel...Ch. 4 - 4.39 Determine the one-sided 95 th-percentile of...Ch. 4 - 4.40 The manufacturer of an electrical fuse claims...Ch. 4 - How many independent random measurements of a...Ch. 4 - Based on 51 measurements of a time-dependent...Ch. 4 - 4.43 Estimate the probability with which an...Ch. 4 - Prob. 4.44PCh. 4 - Prob. 4.45PCh. 4 - Prob. 4.46PCh. 4 - Prob. 4.47PCh. 4 - 4.48 A cantilever is loaded at its tip. Tip...Ch. 4 - Prob. 4.49PCh. 4 - Prob. 4.50PCh. 4 - A transducer is used to indicate the pressure of a...Ch. 4 - An engineer takes water samples from 15 lakes in...Ch. 4 - A random sample of 51 aircraft rivets is taken...Ch. 4 - Prob. 4.54PCh. 4 - Estimate the p-value for N = 16. t = 1.798...
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