Transcript Mathematics for engineering technicians Unit 4

Mathematics for engineering
technicians
Unit 4
Handout No. 2
I Ford
Electronic Calculators'
• Part of the pass criteria
for this Math’s unit 2 is to
be able to use a scientific
calculator to solve
calculations.
• This includes being able
to enter & solve
calculations in one single
expression (this is
sometimes referred to as
a chained calculation).
• You therefore need to
know how to enter (and
correct) complex
expressions involving the
use of brackets and
fractions as well as basic
arithmetic operations.
Calculator examples (simple arithmetic)
1.
2+6x3–8÷4
Key in the following:
[2] [+] [6] [x] [3] [-] [8] [÷] [4] [=]
The answer should be 18
Do the following examples:
a)
b)
c)
d)
27 – 9 x 2 + 12 ÷ 3
2 + 4 ÷ 0.5 – 1.5 x 2
15 ÷ (9 – 4) + 1.5 x 2 – 5
2 x 0.4 – 10 ÷ (3.5 – 1.5)
(13)
(7)
(1)
(-4.2)
Calculator examples (indices)
2
.
33 x 45 ÷ 48
Key in the following:
[3] [X▪] [3] [►] [x] [4] [X▪] [5] [►] [÷] [48] [=]
The answer should be 576
Do the following examples:
a)
b)
c)
43 ÷ 44
103 x 102
d)
√9 x √16
6 4 x6 2
65
(0.25)
(100,000)
(6)
(12)
Calculator examples
(Engineering notation)
3
.
1.23 x 103 + 7.7 x 104
Key in the following:
[1] [ . ] [2] [3] [x10x] [3] [+] [7] [ . ] [7] [x10x] [4] [=] [ENG]
The answer should be 78.23 x 103
Do the following examples:
a)
b)
c)
d)
0.6 x 106 + 1.9 x 105
5.1 x 10-3 - 3.6 x 10-2
27 x 105 x 0.15 x 10-3
0.45 x 105 ÷ 17 x 107
(790 x 10-3)
(30.9 x 10-3)
(405)
(26.4705882 x 10-3)
Formulae (use of)
• When we need to understand the
relationship between different quantities,
we often express this in the form of a
formula (equation).
• To save time and effort, we write the
equation using symbols rather than words
Formulae (use of) example
•
The relationship between the distance travelled
in relation to speed and time could be written
as:
‘The distance travelled is the same as speed divided
by time’
•
However, it is easier to write an equation:
S=vxt
•
Engineers frequently need to find the value of
an unknown quantity
Statement of a formula
• The following statement is a formula for R
in terms of ρ, l and a
R
l
a
• The term on the left side is called the
subject of the formula.
• If the value of three of the four symbols
are given then the forth may be calculated.
Formulae examples
1.
A current of 0.5 A flows in a 56  resistor. Given that V = I R, determine the
voltage that appears across the resistor.
Solution
It is a good idea to get into the habit of writing down what you know before
attempting an equation:
We know that:
I = 0.5 A
R = 56 
Formula given is:
V=IR
Therefore:
V = 0.5 x 56
V = 28 V
Evaluating Formulas
1.
The surface area (A) of a hollow cone is given by the fomulae:
A = rl
Find the surface area in cm2 when r = 4.0 cm and l = 9.0 cm.
2.
Give the answer to 3 significant figures.
(Answer=113 cm2)
In an electrical circuit the voltage (V) is given by V = IR.
Find the voltage, when I = 7.240 ampres and R = 12.57 ohms.
3.
Give the answer to 4 significant figures.
(Answer=91.01V)
A formula for calculating velocity (v m/s) is given by v = u + at.
If u = 12.47 m/s, a = 5.46 m/s2 and t = 4.92 s, find v to 2 decimal places.
(Answer=39.33 m/s)
4.
The area (A m2) of a circle is given by A = r2.
Find the area correct to 2 decimal places given r = 4.156 m
(Answer=54.26 m2)
Evaluating Formulas continued
5.
The power (P watts) in an electrical circuit may be expressed by
the formula:
V2
P
R
6.
Evaluate the power correct to 2 decimal places, given that V =
24.62 volts and R = 45.21 ohms.
(Answer=13.41W)
The volume (V cm3) of a right circular cone is given by the
formula:
1
V  r 2 h
3
Given r = 5.637 cm and h = 16.41 cm, find the volume in standard
form to 3 significant figures.
(Answer=5.46x102 cm3)
Evaluating Formulas continued
7.
If force (F newtons) is given by:
F
Gm1 m 2
d2
Where m1 and m2 are masses
d their distance apart
and G a constant
Find the force (F) given:
G = 6.67 x 10-11 Nm2kg-2
m1 = 8.43 kg
m2 = 17.2 kg
d = 24.2 m
Express the answer in standard form to 3 significant figures.
(Answer=1.65x10-11 N)
Evaluating Formulas continued
8.
The time (t seconds) of a swing of a simple pendulum is given by the formulas:
l
t  2  
g
9.
Find the time, correct to 3 decimal places, given l = 13.0 m and g = 9.91 ms-2
(Answer=7.233 s)
A formula for resistance variation with temperature is:
R = R0 ( 1 + t)
Given that :
R0 = 15.42 ohms
 = 0.002 70
t = 78.4C
Evaluate R, correct to 2 decimal places
(Answer=18.68)
Evaluating Formulas continued
10. The area of a rectangle is given by:
A = bh.
Find h when:
A = 43.5 cm2
b = 4.63 cm
(Answer=9.98 cm)