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SBZ 321 Supplementary Exam
Measurement techniques (University of Pretoria)
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SBZ 321 Supplementary Exam – 26 July 2021
The University of Pretoria commits itself to produce academic work of integrity. I affirm that I am aware of
and have read the Rules and Policies of the University, more specifically the Disciplinary Procedure and the
Tests and Examinations Rules, which prohibit any unethical, dishonest or improper conduct during tests,
assignments, examinations and/or any other forms of assessment. I am aware that no student or any other
person may assist or attempt to assist another student, or obtain help, or attempt to obtain help from
another student or any other person during tests, assessments, assignments, examinations and/or any other
forms of assessment.
Instructions
1. In this test you have to work with your own set of unique numbers for every question provided in
an accompanying PDF document. Make sure that you work with the correct set of numbers.
Answers based on the use of the wrong numbers will not be considered.
2. This is a written examination that will be marked manually. Keep a neat record of your work.
Number your answers identical to the questions. Email a PDF of your script to sw.jacobsz@up.ac.za
before 19h15 on 26 July 2021. USE YOUR STUDENT NO FOR THE FILE NAME.
3. LATE SUBMISSIONS WILL NOT BE CONSIDERED.
4. Take g = 9.81 m/s2.
5. If you have a problem during the test, send an email to me at sw.jacobsz@up.ac.za as soon as
possible, explaining the nature of the problem. Ensure your devices are fully charged before the
test.
6. Be sure that you understand the difference between decimal places and significant figures and
answer the questions to the required number of decimal places or significant figures as instructed,
e.g. the number 0.001 23 is given to 5 decimal places but contains 3 significant figures.
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Question 1
Tacheometry
(12)
You want to chop down a Christmas tree but need to be sure that it will fit in your house and
decided to put your newly acquired survey skills to the test. You asked a friend to hold a survey staff
against the tree trunk and set up a theodolite some distance away. The instrument height above the
ground is 1.45m. The view through the telescope is shown. The resolution of the survey staff is 1cm
and the stadia constant is 100. Use the values for angles ñ and ò provided and answer the following
questions. (Answer the questions in metres to two decimal places.)
1.1
Determine the horizontal distance from the theodolite to the tree.
1.2
Determine the difference in ground elevation between the theodolite location and the tree.
(4)
1.3
Determine the height of the tree.
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(3)
(5)
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Question 2
Coordinate systems
(5)
2.1 Assume that the shape of the earth can be approximated by a sphere with a circumference of
40 000km, determine the circumference of the earth along the 40° S parallel (40°S latitude).
(Answer in km to the nearest km.)
(3)
2.2
Determine the x‐coordinate at 40°S latitude. (Answer to the nearest metre.)
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(2)
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Question 3
Calibration exercise
(8)
You need to calibrate a water pressure sensor and placed it in a container in which you can
accurately control the pressure. You applied the following pressures: 100kPa, 200kPa and 300kPa
and measure the voltages (V100, V200 and V300) respectively (in mV, provided with your unique
numbers). Answer to 3 significant figures.
3.1
Determine the sensor’s calibration coefficient in kPa per Volt.
(4)
3.2 You need to install the pressure sensor in a borehole and took it out of the cell and soldered a
long extension cable onto it which means that the calibration zero offset would have changed. You
therefore need to measure the voltage when the sensor was exposed to the air. You measured a
value of 4mV at zero pressure. What is the depth of installation below the water table if the voltage
changes to 221mV after installation? Assume hydrostatic conditions. Answer in metres to two
decimal places.
(4)
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Question 4
(16)
The figure shows a strain gauged cantilever beam used to weigh big fish. The beam is a 25mm thick
flat plate of rectangular cross section measuring b mm wide (use your unique value for b). The
allowable stress in the cantilever beam is 190 MPa. The Youngs modulus is 210 GPa. The strain
gauge factor is 2. Poisson’s ratio is 0.3. The length of the cantilever section is 2m. Dimensions to
the centres of the strain gauges from the supporting edge are indicated. The strain gauges are
oriented as shown and are wired into a Wheatstone bridge as shown.
You may assume that strain can simply be calculated from ÿ
4.1
What is the maximum mass of a fish the scale can weigh? Answer in kg to the nearest kg. (3)
4.2 Determine the strain in strain gauge a at the full‐scale load. Answer in microstrain to the
nearest microstrain. Use a positive sign for tension and a negative sign for compression.
(3)
4.3 Determine the strain in strain gauge b at the full‐scale load. Answer in microstrain to the
nearest microstrain. Use a positive sign for tension and a negative sign for compression.
(3)
4.4 Determine the sensitivity of the scale in units of mV/V at the full‐scale load. Answer to three
decimal places.
(3)
4.5 What voltage will you measure when you weigh a fish of 100kg? Assuming an excitation
voltage of 3V. Answer in mV to 3 decimal places.
(4)
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Question 5
(10)
5.1 Planck’s constant is used in the definition of (length, mass, time, temperature, electric
current).
(1)
5.2
(1)
Which element is used in the definition of the SI unit for time?
5.3 What distance will light travel during 30.66 vibrations of an atom of the element referred to in
question 5.2?
(1)
5.4
What is meant by a precise instrument?
(1)
5.5
Is a precise instrument necessarily accurate? Give a reason for your answer.
(2)
5.5
Explain how you will express the linearity of an instrument?
(2)
5.6 Observational error is an example of (gross error, systematic error, conformance error,
environmental error)
(1)
5.7 A dumb professor one day wanted to know average age of students in his third year class. He
randomly chose 3 students out of the class of 154, but by coincidence he chose older than average
students and concluded the average third year student in his class to be an ancient 28 years old!
The professor was guilty of (an environmental error, random error, a gross error, a sampling error, a
stupid error, no error ‐ just being an idiot).
(1)
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