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MAT1820 2022

Examination

1 (a) Convert a density of 28.0 kgm-3 to pounds/cubic foot.

[1 mark]

(b) Convert 18.32 miles per hour to meters per second.

[1 mark]

(c) Convert 51250 eVs-1 to nW [1 mark]

2. (a) Calculate the momentum, p, and error of a particle with a mass, m, of 3.7 ± 0.4 kg and a velocity, v, of 21.5 ± 0.2 ms-1 given the relationship.

p = m x v

[2 marks]

(b) Calculate the error associated with the kinetic energy, KE, of the particle given the relationship

KE = ½ m x v2

[2 marks]

3. 1) Show the line(s) of code you would use in MATLAB to calculate

a) log 2 (1000) [1 mark]

b) the inverse sine of 0.57 in degrees [1 mark]

c) Generate a vector from -2π to 2π in 150 steps. [1 mark]

d) Assume you have a file named“exam-answers.txt”which has three columns separated by tabs and four rows of headings before the data starts. Write the MATLAB code that explicitly reads this in using the key command importdata.  Put the data into an array called Answers and read out the first column to the variable called temp.

[2 marks]

4. The table below lists values for stress and strain of a steel sample. The elastic region covers strain 0.001-0.014 inclusive. The inelastic region covers 0.02 to 0.145 inclusive.

Strain

Stress (MPa)

0.001

188

0.002

348

0.003

529

0.004

700

0.005

850

0.006

1032

0.007

1205

0.008

1379

0.009

1544

0.01

1701

0.011

1876

0.012

2051

0.014

2296

0.016

2311

0.018

2516

0.02

2957

0.025

3126

0.035

3351

0.045

3557

0.055

3740

0.065

3895

0.075

4020

0.085

4110

0.095

4165

0.105

4180

0.115

4173

0.125

4106

0.135

4013

0.145

3887

(a) Plot a correctly labelled graph of this data with stress on the y-axis and strain on the x-axis. Copy your graph into your answer sheet.

[4 marks]

(b) Fit the data for the elastic region. Give the formula of your fit and the R2  value. Estimate the Young’s modulus of the steel sample. Add a line for the fit to your graph.

[4 marks]

(c) Use a spline fit in the inelastic region to estimate the ultimate tensile of the steel sample and the strain at this point.

[2 marks]

5. The grains in a ceramic sample have been examined via microscopy, producing a large amount of data.

(a) Write a m-file that will:

.    calculate the surface area of each grain in nm2

.    calculate the volume of each grain in nm3

.    calculate the average volume of all the grains in nm3

.    calculate the total volume of all the grains in nm3

You may assume the grains are spherical. Copy your m-file (with comments where needed) into your answer document.

[4 marks]

(b) Add a further feature that calculates the standard error of the volume and area of the grains and prints to the screen the total number of grains (with 0 decimal places), total volume, average volume (with two decimal places) and the standard error (with 3 decimal places).  Copy your m-file (with comments where needed) into your answer document.

[4 marks]

(c) A key functional property of the material depends on identifying grains with a volume between 1 and 2.5 μm3.  Modify your code to count how many grains are this size and what percentage of all the grains are this size. Copy your m-file (with comments where needed) into your answer document.

[3 marks]

6. Students on a course were asked for feedback on a module. They could rate it from 1-5 with the following guide:

1- bad, 2 – poor, 3- ok, 4 – good, 5 – excellent.

The average of the scores is collected as 3.6 ± 0.7.

(a) Your colleague says the score shows the students think the course is good as 3.6 rounds to 4. Do you agree? Explain your answer.

[2 marks]

(b) The students were also asked to give comments with their scores.  The students could write comments (but did not have to) in both the positive and negative boxes. An example of some of the comments are given below:

Negative comments

Worst course ever.

Terrible.

Hate this course.

Positive Comments

I really enjoyed this course and found it very      interesting. The lecturers were really good.         Could this course be better – possibly but I’m not sure how.

It was hard but very rewarding. I learned lots and really benefited from taking it.

Your colleague has added up all the words written in the negative box (52) and all the words written in the positive box (258).   They point out that there are 206 more words in the positive comments than negative comments and say this shows the course is very popular and good. Do you agree with their interpretation. Explain your answer.

[2 marks]