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.
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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
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
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