late the maximum (dimensional) and relative (%) terms. 7.8 A mechanical speed control system works on the basis of centrifugal force, which is related to angular velocity through the formula. F = mrw² where F is the force, m is the mass of the rotating weights, r is the radius of rotation, and w que is the angular velocity of the system. The following values are measured to determine 500 0.1% N. Find the rotational w:r = 20 ± 0.02 mm, m = 100 ± 0.5 g, and F speed in rpm and its uncertainty. All measured values have a confidence level of 95%. 7.9 A mechanical speed control system works on the basis of centrifugal force, which is related to angular velocity through the formula
late the maximum (dimensional) and relative (%) terms. 7.8 A mechanical speed control system works on the basis of centrifugal force, which is related to angular velocity through the formula. F = mrw² where F is the force, m is the mass of the rotating weights, r is the radius of rotation, and w que is the angular velocity of the system. The following values are measured to determine 500 0.1% N. Find the rotational w:r = 20 ± 0.02 mm, m = 100 ± 0.5 g, and F speed in rpm and its uncertainty. All measured values have a confidence level of 95%. 7.9 A mechanical speed control system works on the basis of centrifugal force, which is related to angular velocity through the formula
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
7.8
![2
Chapter 7 Experimental Uncertainty Analysis
considered to be linear, so that
7.7 A simple spring is used to measure force. The spring
F = kx, where F is the force in newtons. k is the spring constant in newtons per centime-
late the maximum possible error and the uncertainty of the measured force in absolute
ter, and x is the displacement in cm. If x = 20.0 ± 1.25 cm and k = 800 + 16 N/cm, calcu-
(dimensional) and relative (%) terms.
7.8 A mechanical speed control system works on the basis of centrifugal force, which is
related to angular velocity through the formula
mini ad
contribs) F= mrw² to sufey adt brit
where F is the force, m is the mass of the rotating weights, r is the radius of rotation, and
prodre is the angular velocity of the system. The following values are measured to determine
law:r = 20 ± 0.02 mm, m = 100 ± 0.5 g, and F = 500 ± 0.1% N. Find the rotational
speed in rpm and its uncertainty. All measured values have a confidence level of 95%.
7.9 A mechanical speed control system works on the basis of centrifugal force, which is
related to angular velocity through the formula
(AZSSTAT
F = mrw²
using on to soulav ofT
where F is the force, m is the mass of the rotating weights, r is the radius of rotation, and w
is the angular velocity of the system. The following values are measured to determine
w:r = 25 ± 0.02 mm. m = 120 ± 0.5 g. and F = 600 ± 0.2% N. Find the rotational
speed in rpm and its uncertainty. All measured values have a confidence level of 95%.
7.10 Young's modulus of elasticity, E, relates the strain, 8L/L, in a solid to the applied stress,
F/A, through the relationship F/A = E(SL/L). To determine E, a tensile machine is used,
and F, L, 8L, and A are measured. The uncertainties in each of these quantities are 0.5%,
1%, 5%, and 1.5%, respectively, with 95% confidence. Calculate the uncertainty in E in
percentage form. Which of these measurements has the greatest effect on the uncertainty
of E? How can we reduce that uncertainty by 50%?
prio boost nood oved
7.11 The variation of resistance with temperature is expressed by the relationship
R = Ro[1 + a(T-To)], where Ro is the resistance at the reference temperature To and a
for the resistor material has been determined to be 0.0048 ± 0.1% / °C. In the range 0 to
100°C, in which we are calibrating this resistor, temperature measurements have shown a
standard deviation of 0.1°C. The systematic uncertainty of the temperature-measurement
device is known to be 0.1°C. Calculate the percent uncertainty of R at a temperature of
25°C with a 95% confidence level. At 0°C, the resistance is 100.00 ohms.
-12 One of the parameters that is used to evaluate the performance of an engine is its brake-
specific fuel consumption (bsfc), defined as
mfuel
52TNT
bsfc =
where, for a given engine, the parameters on the i
sured and found
podw](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e11f595-a40a-4bf3-b7d2-0a0cab1f1556%2F1ac1bcb7-6416-4db2-9eef-664c1d8eaf58%2Fmjs4o1v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2
Chapter 7 Experimental Uncertainty Analysis
considered to be linear, so that
7.7 A simple spring is used to measure force. The spring
F = kx, where F is the force in newtons. k is the spring constant in newtons per centime-
late the maximum possible error and the uncertainty of the measured force in absolute
ter, and x is the displacement in cm. If x = 20.0 ± 1.25 cm and k = 800 + 16 N/cm, calcu-
(dimensional) and relative (%) terms.
7.8 A mechanical speed control system works on the basis of centrifugal force, which is
related to angular velocity through the formula
mini ad
contribs) F= mrw² to sufey adt brit
where F is the force, m is the mass of the rotating weights, r is the radius of rotation, and
prodre is the angular velocity of the system. The following values are measured to determine
law:r = 20 ± 0.02 mm, m = 100 ± 0.5 g, and F = 500 ± 0.1% N. Find the rotational
speed in rpm and its uncertainty. All measured values have a confidence level of 95%.
7.9 A mechanical speed control system works on the basis of centrifugal force, which is
related to angular velocity through the formula
(AZSSTAT
F = mrw²
using on to soulav ofT
where F is the force, m is the mass of the rotating weights, r is the radius of rotation, and w
is the angular velocity of the system. The following values are measured to determine
w:r = 25 ± 0.02 mm. m = 120 ± 0.5 g. and F = 600 ± 0.2% N. Find the rotational
speed in rpm and its uncertainty. All measured values have a confidence level of 95%.
7.10 Young's modulus of elasticity, E, relates the strain, 8L/L, in a solid to the applied stress,
F/A, through the relationship F/A = E(SL/L). To determine E, a tensile machine is used,
and F, L, 8L, and A are measured. The uncertainties in each of these quantities are 0.5%,
1%, 5%, and 1.5%, respectively, with 95% confidence. Calculate the uncertainty in E in
percentage form. Which of these measurements has the greatest effect on the uncertainty
of E? How can we reduce that uncertainty by 50%?
prio boost nood oved
7.11 The variation of resistance with temperature is expressed by the relationship
R = Ro[1 + a(T-To)], where Ro is the resistance at the reference temperature To and a
for the resistor material has been determined to be 0.0048 ± 0.1% / °C. In the range 0 to
100°C, in which we are calibrating this resistor, temperature measurements have shown a
standard deviation of 0.1°C. The systematic uncertainty of the temperature-measurement
device is known to be 0.1°C. Calculate the percent uncertainty of R at a temperature of
25°C with a 95% confidence level. At 0°C, the resistance is 100.00 ohms.
-12 One of the parameters that is used to evaluate the performance of an engine is its brake-
specific fuel consumption (bsfc), defined as
mfuel
52TNT
bsfc =
where, for a given engine, the parameters on the i
sured and found
podw
Expert Solution
Step 1
Given the variables and their corresponding uncertainty.
Required: Rotational speed and its uncertainty.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY