Assignment_MEC1012_surname_S to Z Student number: Name: Submission details:
Attach the NESS form as the front page
Attach the cover form (see blackboard)
Attach the template with all your matlab code and final answers
Attach the feedback form as the final page
Please staple all these documents and submit them to School office at
Stephenson Building by 15 Feb 2019 (Friday @4pm).
Please ensure that you have chosen to work on the appropriate Assignment type according to your surname.
In order to obtain full credit, you should submit printed copies of m-files (or commands in the text file) and the final answers (add appropriate units). For the gravity acceleration, take 𝑔𝑔 = 9.81𝑚𝑚/𝑠𝑠2
A. Roots,zerosandfunctions [5marks]
1) The position y(meter) of a particle in a magnetic field changes with time t (second)
according to :
Find when the particle will return to its original position (i.e. y=0). Please provide the matlab
projectile above the wall.
𝑦𝑦(𝑡𝑡) = 0.3𝑡𝑡5 + 0.45𝑡𝑡4 + 0.8𝑡𝑡3 + 0.5𝑡𝑡2 − 0.2𝑡𝑡
command and the final answers. [ 1 mark]
2) A projectile is fired towards a wall of height H from a distance D with speed v and
h
𝑚𝑚𝑚𝑚𝑚𝑚 2𝑔𝑔 2𝑣𝑣2
22
= 𝑣𝑣 − 𝑔𝑔𝐷𝐷 − 𝐻𝐻
angle Ɵ to the horizontal. The angle Ɵ is chosen to maximize the height, hmax, of the
v
θ
h𝑚𝑚𝑚𝑚𝑚𝑚
H D
Write a function of hmax using the @ method which takes one input, v. Use Matlab’s fzero command to find the critical speed v* for hmax =0, when D=1m and H=1m [2 marks]
Function definition: The critical speed v*=
Assignment_MEC1012_surname_S to Z Student number: Name:
When hmax =0, 𝑣𝑣 = �𝐻𝐻𝑔𝑔 + 𝑔𝑔√𝐻𝐻2 + 𝐷𝐷2 Write a function of 𝑣𝑣 using @ method which takes two input variables D and H, and calculate the critical speed v* , when D=1m and H=1m.
[ 2 marks] Function definition:
The critical speed v*=
B. Loops [5 marks].
1) Useforlooptocalculate 1 +�2+�2+�2+�2+�2+√2+8 4!
2) Use for loop to calculate [3 marks]
[2marks]
C. Solve simultaneous equations [4.5 marks]
𝐹𝐹𝑚𝑚 22
1600 1
� 𝑓𝑓! 𝑓𝑓=0
𝑚𝑚1 𝐹𝐹
α
𝐹𝐹⬚ 𝑚𝑚3
1
In the pulley system above, the friction coefficients between mass 𝑚𝑚1 and 𝑚𝑚2 , 𝑚𝑚1 and the slope are given by 𝜇𝜇1, 𝜇𝜇2, respectively. The mass of the string and pulley as well as the friction between them are negligible.
Based on mechanical analysis, it gives,
𝐹𝐹1 − 𝐹𝐹2 = 𝑚𝑚1𝑔𝑔 cos 𝛼𝛼
Assignment_MEC1012_surname_S to Z Student number: Name:
−𝜇𝜇1𝐹𝐹1−𝜇𝜇2𝐹𝐹2+𝐹𝐹 −𝑚𝑚1𝑎𝑎1=𝑚𝑚1𝑔𝑔sin𝛼𝛼 𝐹𝐹2 =𝑚𝑚2𝑔𝑔cos𝛼𝛼 𝜇𝜇2𝐹𝐹2−𝑚𝑚2𝑎𝑎2 = 𝑚𝑚2𝑔𝑔 sin 𝛼𝛼
−𝐹𝐹 −𝑚𝑚3𝑎𝑎1 = −𝑚𝑚3𝑔𝑔
The forces 𝐹𝐹1, 𝐹𝐹2, 𝐹𝐹 (as shown in the figure above) refer to the orthogonal force acting on 𝑚𝑚1, 𝑚𝑚2, and the tension in the string, respectively. Where 𝑎𝑎1 𝑎𝑎𝑎𝑎𝑎𝑎 𝑎𝑎2 are the accelerations of 𝑚𝑚1, 𝑚𝑚2, respectively. Please note that the acceleration of 𝑚𝑚3 is the same to that for 𝑚𝑚1.
Where the values of the measured parameters (𝜇𝜇1, 𝜇𝜇2, 𝑚𝑚1, 𝑚𝑚2, 𝑚𝑚3, 𝛼𝛼 ) are provided in Table 1 (all the units are SI units). Use matlab to find all the five unknown parameters (𝐹𝐹1, 𝐹𝐹2, 𝐹𝐹 , 𝑎𝑎1, 𝑎𝑎2 ) by solving the simultaneous equations above. Please use matrix. Otherwise, there is some deduction of the mark.
D. Measure gravity acceleration [5.5 marks]
A student did some experiments to measure the gravity acceleration. As shown below, a small vehicle starting from rest, slides down the slope due to the gravity. He recorded the time (t) and distance (d) the vehicle travelled (see the table below). The friction is assumed negligible.
d/cm
0
10
20
34
45
68
80
95
103
t/s
0
1.02
1.52
2.03
2.55
3.10
3.38
3.66
3.80
The height (h) and the length (l) of the slope are 1.77 cm and 127.1cm, respectively.
(1) Plot the distance d against the time squared (𝑡𝑡2 ), with t2 as x-axis and d as y- axis. Then use polyfit command to fit a straight line to the plotted data
[1.5 mark]
(2) Use fplot to plot the fitted curve on the same figure as the data. Where the experimental data is red circle and fitted curve is solid blue line. Label the plots, add title and legends. Hints: please use the fitting parameters you obtained from (1) to define the function prior to using fplot. [2.5 marks]
(3) Find the value of gravity acceleration. Hints: the relation between distance (d), acceleration (𝑎𝑎) and time (t) for a linear motion starting from rest is 𝑎𝑎 = 1 𝑎𝑎𝑡𝑡2
[1.5 marks]
2
l
h