MAT1820 DIGITAL SKILLS FOR MATERIALS Spring 2020-2021 Exam
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MAT1820
Spring 2020-2021 Exam
DIGITAL SKILLS FOR MATERIALS
1. (a) Convert 1805 Pa to pounds / square inch and give your answer to 3 significant
figures.
[1 mark]
(b) Which value (Pa or lbs/sq inch) is the larger pressure? [1 mark]
2. The magnetic field strength of a magnet can be determined using the formula below:
Write an m-file that
● calculates the field strength of a magnet, printing it to the screen in units of kAm-1
● calculates the error in the field strength, printing it to the screen.
● NOTE: assume that only the radius has an error associated with it.
● does not allow the user to enter negative values for the radius.
Use this code to calculate the field strength for the following data.
p = 200 Am
l = 0.15 m
r = 0.060 ± 0.005 m
Show in your answer both your m-file, the output you obtain for the field strength
and the error associated with the value. [6 marks]
3. The table below shows a range of formulae used to fit some data on voltage and current. While small errors were found to be present in the data, there was no systematic error present.
Explain which of the five fits shown should be used.
|
Fit Number |
Fit |
R2 |
|
1 |
y = 27.3 x |
0.983 |
|
2 |
y = 8.4 x2 – 2x + 4 |
0.947 |
|
3 |
y = 24.1 x + 3.2 |
0.991 |
|
4 |
y = 16 x + 2 x0.5 + 6 |
0.915 |
|
5 |
y = 7.2 x2 |
0.996 |
[2 marks]
4. The table below lists data collected from an experiment looking at the change in the melting point with defect concentration.
● Use MATLAB to plot this data into a correctly labelled graph.
● Perform a fit to this data using the function y = mx2 + n where x is the defect concentration and m and n are constants.
● Add this fitted data to the graph as a line.
● Calculate the R2 value of your fit.
In your answer, please provide MATLAB code to answer this: the R2 value, your fitted parameters and your graph.
|
Defect concentration (%) |
Change in melting point (K) |
|
0.1 |
-4.9 |
|
0.5 |
-4.6 |
|
1.0 |
-4.7 |
|
2.0 |
-6.8 |
|
5.0 |
-28 |
|
7.0 |
-53 |
|
10 |
-110 |
|
11 |
-134 |
[8 marks]
5. The table below lists the conductivities from experiments on copper wire samples.
|
Conductivity (x107 σm-1) |
|
5.96 |
|
8.94 |
|
5.96 |
|
5.96 |
|
7.45 |
|
1.49 |
|
1.19 |
|
1.34 |
|
4.47 |
|
1.19 |
|
1.34 |
(a) Calculate the standard error of the conductivities. [1 mark]
(b) A single experiment records a value of 5.98x107 σm-1 with a systematic error
of ±2.4x105 σm-1 for the conductivity. Explain the difference between this error
and the standard error you calculated in part (a). [2 marks]
(c) Five further conductivities are taken as listed in the table below. After combining this data with the values above a colleague suggests that they are confident that they have enough data to report the properties reliably. Do you agree? Explain your reasoning with evidence.
|
Conductivity (x107 σm-1) |
|
11.0 |
|
1.68 |
|
6.50 |
|
9.32 |
|
8.25 |
[3 marks]
6. The code below is designed to tell a student their ranking in an exam compared to all the scores. The student simply has to enter their exam score. The code will then produce the ranking and the average. If the student enters a score that did not exist it will ask for a new score.
There are three mistakes in the code. Identify what these are, explain why they are a problem and suggest a correction.
CODE
scores = [ 5 10 4 8 9 12 7 2 11 11 ];
ranked = sort(scores);
average = mean(scores);
stop=0;
while (stop~=1)
student = input('Enter your exam score\n');
i=1;
while i <= length(scores)
stop = 0;
if (student==ranked(i))
position = i;
fprintf('Your position was %.0f in the class of %.0f\n', position,
length(scores));
fprintf('The average mark was %.2f\n', average)
stop=1;
end
i = i + 1;
end
fprintf('That was not an exam score\n')
end
[6 marks]
2022-08-04