7/25/2019 PRGA_CWAssignment2013

1/1

Programming and Simulation (PRGA2001, PGSM210B)

Coursework Assignment (40%)Due: November 22, 2013

MATLAB:

A rockets mass decreases as it burns fuel. The equation of motion for a rocket in vertical flight

can be obtained from Newtons law,

( )

0

2

0

1

dmv F mg

dt

where

rtm m

b

Rg g

R x

=

=

=

+

In the above equations,

t= time

x= the rockets altitude above the earths surface (x= 0 when t= 0)

v= upward vertical velocity (v= 0 whent = 0)

R= radius of the earth

Note that mand gare NOT constants. F is the rockets thrust, its mass is a function of time, andgravitational acceleration decreases with altitude. The rockets initial mass is m0, the burn time is

b, and r is the fraction of the total mass accounted for by the fuel.

Constants:

F = 48,000 N

m0= 2200 kg

r = 0.8

g0= 9.81 m/s2

b = 60 s

R= 6.4 x 106m

Write a Matlab program to solve the above differential equation and answer the questions below.

HINT: you may need to reformulate the problem.

1)

Determine:

a. The maximum velocity attained by the rocket (8 pts)

b. The maximum altitude reached by the rocket (8 pts)c.

The time taken for the rocket to fall back to earth (9 pts)

2)

Estimate the value of Frequired for the rocket to escape i.e. not return to earth. (5 pts)

Instructions:

Save your work in two (2) m-files and include your student ID in the file names, e.g. if your

student ID is 50000, then title your files rocket50000.mandfrocket50000.m. Write your programin such a way that when executed, it is error free and it returns only the answers to the questions

above. File names should not include spaces or any special characters only numbers, letters and

underscores. Files names also should begin with a letter. Email both m-files as attachments to

randy.roopchand@utt.edu.tt by November 22, 2013.

SIMULINK:

Van der Pols equation is used to describe many oscillating systems.

( )2

2

21 0

d y dyy y

dt dt + =

Model the above equation in Simulink. For = 1, plot y vs. t for 0 t 20 sec, using initialconditions: when t = 0, y = 2, dy/dt = 0. (10 pts)

Save your work as a Simulink model and include your student ID in the title e.g. CW50000.mdl.

Please note that if you are using a newer version of Matlab, then save/export the model as releaseR2008a. Email the file as an attachment to randy.roopchand@utt.edu.tt by November 22, 2013.