Computer Apps Example Exm

8/10/2019 Computer Apps Example Exm

1/5

UoB number: ..

Computer User Name: ..

Computer Applications of Numerical Methods, ENG4037M

*** Example Assessment ***

READ ME FIRST: Save your files in your exams directory

W:\ENG4037M\Assessment1\username

ANSWER ALL THREE QUESTIONS

DO NOT OPEN THE FILE AFTER THE ASSESSMENT AS THIS WILL VOID ITS

CONTENTS

Write your answers, as requested, on this sheet. Leave your solution files numbered by

question number and section in your exam directory. Examples are: q1a.m(for a matlab

solution to question 1 part a.) q1b.m(for a matlab solution to question 1 part b.) q3a.xlsx

(for a spreadsheet solution to question 3, part a).

This Assessment is OPEN BOOK, however all forms of communication are expressly

forbidden

Marks are awarded for:

accuracy of program or spreadsheet,

annotation of program or spreadsheet,

explicit calculation and output of required answers by the program or spreadsheet,

clearly indicated answers in a spreadsheet (Highlight answers in RED)

accuracy and clarity of answers given in this booklet.


2/5

This page will not be with an exam. The following gives a gauge of how marks are

awarded

Answers on script as requested 20%

Program/spreadsheet accuracy 30%

Calculation method (where relevant). Automatic methods better than graphical or trial and

error 20%

(e.g finding time/distance/highest/lowest/fastest etc by algorithmic means

rather than finding point on a plot, or trial and error methods

Annotations 20%

(comments in matlab program, labelled and highlighted matrices & vectors in Excel)

Clearly visible answers 10%

(highlight solution vales in RED in Excel, output answers to screen in Matlab)

Hints:save your work periodically this helps in case something goes wrong (eg a program

lock up

If a minor disaster happens with file naming, you will get all marks provided the relevant work

is there somewhere in your directory.

Note:In Excel the error which can lock-up a spreadsheet

You cannot change part of an array can be escaped by pressingEsc

Then, if appropriate, delete the faulty array/vector and redo it


3/5

Question 1

a. A steel ball of 10 kg mass is fired from a cannon at 800m/s at an angle of 30 degrees to

the horizontal. Air resistance is equal to23

104 V

Newtons, where V is velocity. Write

and submit an annotated time stepping simulation in Matlab, called q1a.m, to plot its flight in

(x,y) coordinates. Take acceleration due to gravity to be 9.81 m/s2 .

How far will the ball travel before hitting the ground, and how long will it take? Give the

answers to 3 significant figures accuracy and show through time step reduction that the

answers are accurate to 3 significant figures. [60%]

Fill in the following answers:

Distance travelled = metres ; Time of flight = seconds

Evidence for 3 significant figure accuracy:

b. A target is 800m horizontally from the cannons mouth, and is 200m vertically higher.

Copy your previous program to q1b.mand add to it to calculate the closest approach of the

steel ball from the target. Find the two distinct angles that the cannon must be fired at to hit

the target (a separation of ball and target of 1 metre or less can be regarded as a hit).

[40%]


4/5

Question 2

a. Table Q2 contains experimentally determined spark advance angles for an engine at

certain load values and engine speeds.

Table Q2

Assuming that the spark advance angle varies quadratically with RPM and quadratically withload, write down the polynomial terms that will be required to fit this data. [10%]

Polynomial terms required:

(you may substitute x=RPM and y=Load , if wished)

b. Create either an annotated Matlab program q2b.m or an annotated Excel spreadsheet

q2b.xlsx to determine the best coefficients to the required polynomial using the least squares

approach. [50%]

c. modify your program or spreadsheet to calculate the 2R value for your fit (and save it as

q2c.m or q2c.xlsx as appropriate). [20%]

d. Calculate the interpolated spark advance angles at a) 3700RPM and Load = 3.5 and b)

3000RPM and Load = 3. Compare your value for case b) with the value from the table and

comment upon it. [20%]

a) interpolated value at 3700RPM, Load=3.5 = degrees (3 sig figs)

b) interpolated value at 3000RPM, Load=3 = degrees (3 sig figs)

Comment on answer for b) :


5/5

Question 3

a. Figure Q3 shows 4 nodes numbered 1 to 4, and 3 rods E1 - E3. The rods are each of

5mm diameter and are made of a material with Youngs modulus of 70GPa.

Figure Q3

The positions of the nodes (in metres) are:

node 1 = (0.0, 0.1, 0.0)

node 2 = (0.1, 0.05, 0.1)

node 3 = (0.0, -0.1, 0.0)

node 4 = (0.4, 0.0, 0.0)

Nodes 1, 3, and 4 are firmly attached to a solid surface so that they cant move, and a force

with components (0, 10000, 0) (Newtons) is applied to node 2. Create an annotated

spreadsheet q3a.xlsxto calculate the displacement components of node 2 using finite

element strut elements, and to also calculate the reaction force components at nodes 1, 3,

and 4. [65%]

Displacement

components ofnode 2 (4 sig.figs)

Reaction forces atnode 1



b) Add to q3a.xlsx calculation of strain and stresses in rods E1 and E2 (there is no need to

start a new spreadsheet). [35%]

Computer Apps Example Exm

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