23F ENME 461 Assign.5
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University of Calgary *
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Jan 9, 2024
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Foundations of Mechatronics (ENME 461)
Instructor:
Mr. Benjamin Durante
Email:
benjamin.durante@ucalgary.ca
Assignment No. 5
Due: November 30
th
by 11:59 pm, 2023
Problem #1.
Missions to Mars have been sent by multiple countires. Of all missions
between 1999-2023, 64% were from the USA, 12% from the ESA, 12%
from China, 6% from UAE, and 6% from India. The success rate
associated with each country is 82% (USA), 0% (ESA), 50% (China), 100%
(UAE), and 100% (India), respectively. What is the probability that a
randomly chosen mission within the 1999-2023 timeframe would have
succeed?
Problem #2.
Robotic surgery is being applied to an already risky procedure with the
following outcomes becoming apparent:
Procedure Type
Success
Failure
Normal Surgery (62%)
50%
50%
Robotic Surgery (38%)
54%
46%
If a randomly selected case was successful, what is the probability that the
surgery was performed using robotic surgery?
Problem #3.
The amount of a chemical compound (y) the dissolves in 100 grams of
water at various temperatures (x) was recorded as follows:
x (°C)
y (grams)
Measurement #1
Measurement #2
Measurement #3
0
8
6
8
15
12
10
14
30
25
21
24
45
31
33
28
60
44
39
42
75
48
51
44
a)
Find the equation of the linear regression line. (Feel free to use
Excel if desired, however post screenshots and identify all
intermediary summation totals).
b)
Estimate the amount of chemical that will dissolve in 100 grams of
water at 50°C.
Problem #4.
The density of air must be known to within ±0.5%. If the air temperature
at 25°C can be determined to within ±1°C (95%), what uncertainty can
be tolerated in the pressure measurement if air behaves as an ideal gas?
Problem #5.
A digital thermometer was used to measure the average temperature of a
circulating water bath that is being used in an experiment. The experiment
lasted a total of 30 min. Temperature measurements were collected every
minute resulting in a total of 31 data points. The data, and the associated
equipment used, are presented in the following two tables.
a)
Determine the uncertainty due to random err
or.
b)
Determine the uncertainty due to systematic error.
c)
Determine the expanded uncertainty.
Equipment
Systematic Standard
Uncertainty, °C
Digital thermometer
0.05
Environmental influences
0.005
Effects of conduction/radiation
0.0005
Uniformity of water bath temperature
(spatial uncertainty)
0.05
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