ECOR 1101 Mechanics I
Sections D and E
Jack van den Berg
Lecture 04 Vector Dot Product + Review of Chapter
2
(Chapter 2: Section 2.9)
January 17, 2017
Dot Product (Scalar Product)
In statics it is often important to find:
the angle between two forces;
ECOR 2606 Lab Test #2 v19
The present value of a stream of annual payments that begin at zero for the first year and then
increase at G dollars a year thereafter (i.e. the first payment is zero, the second payment is G
dollars, the third payment is 2G dol
ECOR 2606 Lab Test #2 v18
The drag coefficient of a sphere is given by the following formula:
CD
24
VD
6
0.4
VD
1
where CD = drag coefficient (dimensionless)
= viscosity of fluid (N-s)/m2)
= density of fluid (kg/m3)
V = velocity (m/s)
D = diameter of
ECOR 2606 Lab Test #2 v11
The upward velocity v of a rocket is given by:
m0
gt
v u ln
m0 qt
where v = upward velocity of rocket (m/s)
u = relative velocity at which fuel is expelled (m/s)
q = fuel consumption rate (kg/s)
m0 = initial mass of rocket
ECOR 2606 Lab Test #2 v3
The cross sectional area of a nozzle at some point can be calculated using the following formula
A * 2 1 2
A
M
1
M 1
2
1 / 2 1
where A is the cross sectional area at the point of interest
M is the Mach number of the flow at
ECOR 2606 Lab Test #2 v7
The friction factor (f ) for turbulent flow in a pipe can be calculated using the Colebrook
equation:
e / D 2.51
1
2 log 10
3.7 Re f
f
where f = is the friction factor (dimensionless)
e = surface roughness (in m)
D = pipe diam
ECOR 2606 Lab Test #2 v16
The frequency response for a 1st order Bessel Band Pass Filter is given by:
1
H
2
( f fc 2 )
1
Bf
where H is filter frequency response in Volts/Volts
fc is the center frequency of the filter (in Hz)
f is the input frequency (in H
ECOR 2606 Lab Test #2 v19
The present value of a stream of annual payments that begin at zero for the first year and then
increase at G dollars a year thereafter (i.e. the first payment is zero, the second payment is G
dollars, the third payment is 2G dol
ECOR 2606 Lab Test #2 v17
The frequency response for a 2nd order Bessel High Pass Filter is given by:
H
3G
( fo / f ) 3( fo / f ) 3
2
where H is filter frequency response in Volts/Volts
fo is the cut-off frequency of the filter (in Hz)
f is the input freq
ECOR 2606 Lab Test #2 v4
A circular turtle pond having diameter D contains a semi-spherical island having radius R.
The volume of water in the pond is given by
V
wD 2
2 R 3 ( R w) 2 (2 R w)
4
3
where V is the volume of water (in m3)
w is the height of w
Problem (text 13-29): The table below gives the population of a small but
growing suburb over a twenty year period.
Year
Population
0
5
10
15
20
100
200
450
950
2000
The growth is assumed to be exponential:
population = *exp(t), where t is a time in years
Golden Section Search
Very similar to a bisection search (the key difference is that we are looking for a
minimum instead of a zero)
A bracketing method (to get started we need a pair of x values that bracket the
solution).
At each iteration the interval
General linear least-squares regression:
Linear Regression:
Fit a curve of the form y = ax+b to data points
Use polyfit (x, y, 1)
Polynomial Regression:
Fit a curve of the form y = anxn+an-1xn-1+ a1x + a0 to data points
Use polyfit (x, y, n), where n is t
Problem: The velocity of a falling skydiver is given by the equation below.
v(t ) =
gcd
gm
t
tanh
m
cd
Assuming that m = 68.1 kg and cd = 0.25 kg/m, how far will the skydiver fall between
t = 4 seconds and t = 7 seconds?
Ideal solution:
7
7
4
4
s
ECOR 2606
Lecture 12
Overflow
Underflow
Standard Quadratic formula
Rationalized Quadratic formula
Cancellation error (appears when subtracting two quantities close to each other, -b-r)
Lecture 13
Gaussian elimination
Pivot row
Lecture 14
Determinant (clos
function [ separation ] = calcSep( m1,r1,m2,r2,t )
% CALCSEP calculates and returns the seperation between the two skydivers
% Inputs:
% m1 - mass of the first skydiver (in kg)
% r1 - drag coefficient of the first skydiver (in kg/m)
% m2 - mass of the sec
% Simrat Lyall
% 101040431
% Plot of the door function using inputed values.
f = @(t) door(5,3,t);
% Plotting using fplot
figure(1);
fplot (f, [0 45]);
title('Distance between two Doors vs. Time Since Opening');
xlabel('Time Elapsed (s)');
ylabel('Distanc
function [ F ] = force( q, Q, a, x )
% FORCE calculates the force exerted on the charge by the ring
% Inputs:
% q - a charge that is located x distance from the centre of the ring (in
Coulombs)
% Q - an electrical charge which is uniformly distributed aro
function [ distance ] = door( A, B, t )
% DOOR - This function calculates and returns the distance between the two ends
of
% the two parts of the door (metres).
% Inputs:
% A - The width of the left door (metres).
% B - The width of the right door (metres
% Simrat Lyall 101040431
F = @(q,Q,a,x) force(2e-5,2e-5,0.9,x);
% plotting graph using fplot
figure(1);
fplot(F,[-0.2,1.4]);
title('Force vs distance(x)')
xlabel('distance(x) of charge located from the centre of the ring (in m)')
ylabel('force(F) exerted
% Simrat Lyall
% 101040431
f = @(t) calcSep(60,0.3,50,0.2,t); % anonymous function for t
% Plot Function
figure(1)
fplot(f,[0 30]);
xlabel('Time (s)');
ylabel('Seperation');
title('Seperation vs Time');
grid on;
% Table
fprintf('Time
Sepaaration\n');
for
DZs - ECOR 4995 REVIEW
Notes:
1.
These are questions Ive gathered to help myself study, hopefully they may help you to
MC = Multiple Choice | TF = True or False | LIST = List the answers by memory |WHY/WHAT = Short Answer
Highlighted in yellow are the ans
DZs - ECOR 4995 REVIEW
Notes:
1.
These are questions Ive gathered to help myself study, hopefully they may help you to
MC = Multiple Choice | TF = True or False | LIST = List the answers by memory |WHY/WHAT = Short Answer
Highlighted in yellow are the ans
Ecor Review
Engineering graphics has evolved into six major areas:
Technical Illustration,
Descriptive Geometry,
Engineering Computer Graphics,
Nomography,
Graphical Mathematics,
Empirical Equations
Engineers convey information in three main ways:
Writt
Make be sure to read all Questions completely & carefully.
;o
1. Life cycle analysis: (_
(a) Extends a products useful life. J
Encourages reuse and recycling. /
. 7 c Evaluates the total environmental impact of a product from manufacturing through
. appli