Basic Quantities,Prefixes&Dimensions.ppt

The Systeme Intérnational d’Unités ( SI )
Basic Quantities
BM English
Kuantiti Quantity SI Unit Symbol
Panjang length meter m
Jisim Mass kilogram kg
Masa Time second s
Arus elekrik Current Ampere A
Suhu temperature Kelvin K
Jumlah bahan Mole
(amount of
substance)
mole mol
Keamatan
cahaya
Luminous
intensity
candela Cd

Dimensional Analysis
Dimension is the qualitative nature of a physical quality. For
example, when we measure the distance between 2 points,
whether in feets or meters, the dimension that is being measured
is the length. That is: [ length ] = L
Quantity
Dimension Unit
Length L m
Time T s
Mass M kg
Current A A
Temperature θ K

Determine the dimensions for the derived quantities below:
Quantity
Dimension Unit
Area L2 m2
Volume L3 m3
Velocity L/T ms-1
Acceleration L/T2 ms-2
momentum ML/T kgms-1

1. To check if an equation is correct

Any equation must be dimensionally consistent that is the
dimensions on both sides must be the same.
Example :
1. Show that the expression v = u + at is dimensionally
correct, where u & v represents initial and final velocities, a is
acceleration and t is time interval.
Solution:
The aim is to analyze if both sides of the equation are
dimensionally the same.
Start with v = u + at
[v] =L/T, [U] = L/T , [a] = L/T2 and [t] = T
so, the dimensions of [at] = L /T2 x T = L /T
Hence, dimension for both side of eqtn. are the same.
Conclusion : This equation is dimensionally correct !
*What about the expression v = u + at2 and v2= ax

2. To determine units for unknown
quantities

By using dimensional analysis, we can also find the
the units of an unknown quantity.
Example:
Suppose that the displacement of an object is related
to time according to the expression x=Bt2 . What are
the dimensions of B?
Solution:
X = Bt2
B = x / t2
[B] = [x] / [t2] = L / T2
and the units for B is m/s2

Another usage of dimensional analysis is to work out an equation:
Example:
To keep an object moving in a circle at constant speed requires a
force called the centripetal force; which depends on its mass m,
speed v, and the radius of its circular path r. Do a dimensional
analysis of the centripetal force.
Solution :
Centripetal force, F α ma vb rc , where a, b and c are numerical
exponents. We know that force has the units of kg.m/s2, and therefore
its dimensions are [F] = MLT-2 and so
[F] = [ma ][vb ][rc ]
MLT-2 = Ma (L/T)b Lc
= Ma Lb+c T-b
Next, we must equate the exponents
Exponents of M : a = 1
Exponents of T : b = 2
Exponents of L : b+c = 1 so c = -1
The resulting expression is
F α mv2 /r

Precision
Significant Figures
Uncertainty

Often we need to group these into larger or smaller
numbers to make them more manageable. For
example, you don't say that you are going to see
someone who lives 100,000 m away from you, you
say they live 100 km away from you.

Prefixes
for
Powers
of
Ten
Power prefix abbreviation
10-18 atto a
10-15 femto f
10-12 pico p
10-9 Nano n
10-6 micro µ
10-3 milli m
10-2 centi c
10-1 deci d
101 deca da
102 hecto h
103 kilo k
106 mega M
109 giga G
1012 tera T
1015 peta P
1018 exa E

P
I
C
O
E N T I
G
I
G
A
K L
M G
E R
M
I
L
L
I
F
E
M
T
O
N
A
N
O
M C R

Precision
 Uncertainty in measuring can be reduced : use more
sensitive instrument.
 A measured value with lesser uncertainty is said to be
more precise.
 Value with more significant figures have higher degree
of precision.
(e.g. 35cm , 35.4cm, 35.36cm)

Significant Figures
 Each digit carried by any measurement is known as
significant figures.
 It is meaningless to state a measurement value with
more significant figures then necessary if it does not
possess that degree of precision. (e.g. 32.234 mm for a
length measured by a metre rule, the scale only to the
nearest 1mm)

Significant Figures-Zeros
 Zeros to the left of the first digit of a measured value
is not significant. (e.g. 02.34 cm : 3 s.f.)
 Zeros to the right of a (round) value is not signifcant.
(e.g. 800cm : 1s.f.)
 Zeros after decimal point is significant
(e.g. 7.00 kg : 3 s.f.)
 Zeros between two significant digits is significant.
(e.g. 3.06 s : 3 s.f.)

How many Sig. Fig.?
 2.56 cm
 4.05 cm
 0.25 cm
 2.560 cm
 2.00 x 103 N
Answer : 3, 3, 2, 4, 3

Processing Sig.Fig.
 Addition and Subtraction : final calculated value
must have the same number of decimal places as
the measured value which has the least number of
decimal places.
e.g. 2.345 + 1.25 = 3.595 ( 3 dec.places) therefore the
answer should has only 2 decimal places. So round
answer to 2 d.p.
3.595 = 3.60.

Determine…
 P = 1.275 cm + 11.2 cm
 Q = 5.232 cm – 2.35 cm
Answer : P = 12.475 round off to 12.5cm
Q = 2.882 round off to 2.88

Processing Sig. Fig.
 Multiplication and Division : the final calculated value
must have as many significant figures as the measured
value which has the least number of sig. fig.
e.g. 2.345 x 1.25 = 2.93125 ( 6 s.f.)
Answer must have only 3s.f. so round off answer to
2.93125 = 2.93

Determine…
… the area of a rectangle of length 72.95 cm and
breadth 6.57 cm.
Area = 72.95 x 6.57 = 479. 2815 cm2
round off to 479 cm2

Important reminder!
 Sometimes the final answer may be obtained only after
several intermediate calculations. In this case, results
of intermediate calculations should not be rounded
off.
 Round off only the final answer.

Example…
An object has density 4.85x103kgm-3 and volume
3.375x10-4m3. A net force of 11.5N acts on the
object. Determine
(a) The mass of the object
(b) The acceleration.

Answer
(a) Mass = density x volume
= (4.85x103kgm-3)(3.375x10-4m3)
= 1.636875
 1.64 kg
(b) Acceleration = force/mass
= 11.5 / 1.637
= 7.025045816
 7.03 ms-2

The error or uncertainty in a measurement is
an estimate of the amount it can be off the
true value.

Errors
 Systematic error- its magnitude is almost constant.
(limitations of the measuring devices, zero error of
instruments, reaction time of observer, errors due to wrong
assumptions e.g. the value of g)
 Random error- parallax errors, human errors, errors due to
changes of surrounding such as temperature.

Uncertainty in Measurement
 A measured value of a physical quantity is not exact
because it has some uncertainty. (e.g. measure using a
metre rule)
 The farthest digit to the right of a measured value
always has some uncertainty. ( e.g. 35cm : the 5cm is
the uncertain value)

Treatment of Errors
 If a measurement has a value of x & its maximum
uncertainty is Δx, it is written as (x ± Δx).
 The measurement must have the same number of
decimal places as in the maximum uncertainty. ( e.g.
10.0 ± 0.1 cm and NOT 10 ± 0.1 cm)
 Uncertainty must be suitable with measurement (e.g. ±1
mm in 100 cm is negligible compared to in 1 cm)

• Percentage errors is given by;
Uncertainty Errors
 The measurement with its uncertainty is written
as x ± Δx
 E.g The measurement of diameter of a wire is
(1.32 ± Δ0.01) mm
%
100
% 


x
x
error

Consequential Uncertainties
 Addition & Substraction :
 Multiplication & Division :
2
1 R
R
R 




R
R
R
R
R
R ]
[
2
2
1
1 





Example:
Given R1= 41.2 0.1 and R2=
20.1 0.1 , determine the value
of
•R1 + R2 ,
•R1 - R2,
•R1xR2 and
•R1 R2 .

Q1:
 The lengths A and B are (4.2 ± 0.1) cm and (5.5 ± 0.1)
cm. Find the percentage uncertainty of S and D where
(a) S = A + B
(b) D = 3A – 2B
Answer : (a) 2.1% (b) 31%

Q2
 Find the diameter of one ball bearing and its associated
uncertainty. The scale reading at X and Y are estimated
as (1.0 ± 0.2 ) cm and (5.0 ± 0.2 ) cm respectively.

Q3
 The dimensions of a piece of A4 paper are as follows:
 Length x = (297 ± 1) mm
 Width y = ( 209 ± 1) mm
 Calculate :
 The fractional uncertainty of x
 The percentage uncertainty of x
 The area xy with its uncertainty

Q4
 The density of a rectangular block is
 Where mass = ( 240.0 ± 0.1) g, length = (6.00 ± 0.01)
cm, breadth = ( 5.00 ± 0.01) cm and height = (2.00 ±
0.01) cm.
Calculate the density of the block.
Find the uncertainty of the density.
height
breadth
length
mass
density




Q5:
In an experiment, the external diameter d1
and the internal diameter d2 of a metal tube
are found to be (64 2) mm and (47 1) mm
respectively. The percentage error in (d1-d2)
expected from these readings is at most…

Q6:
The velocity of a liquid in a pipe can be
calculated by measuring the force on a small
disc placed in the centre of the pipe with its
plane perpendicular to the flow. The equation
relating the force to the velocity is
Force = constant x (velocity)2
If the velocity is to be found with a maximum
uncertainty of 1%, what is the maximum
permissible percentage uncertainty in
measuring the force?

Q7:
In a simple electrical circuit, the current in a
resistor is measured as (2.50 0.05) mA.
The resistor is marked as having a value of
4.7 2%.
If these values were used to calculate the
power dissipated in the resistor, what would
be the percentage uncertainty in the value
obtained?
*P =I2R

Q8:
After the pressure of the air in a bicycle tyre
has been increased slightly by pumping air
into the tyre, it is found that the number of
moles of air in the tyre has increased by 2%,
the thermodynamic temperature by 1% and
the internal volume of the tyre by 0.2%. By
what percentage has the pressure of the air
in the tyre increased?
* PV=nRT

Basic Quantities,Prefixes&Dimensions.ppt

More Related Content

Similar to Basic Quantities,Prefixes&Dimensions.ppt (20)

Recently uploaded (20)

Basic Quantities,Prefixes&Dimensions.ppt