# Chapter 1: Introduction to Physics by 1ezLyH5

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```									Chapter 1

1.3 Scalar and Vector Quantities
Understanding Scalar and Vector
Quantities

   1. A scalar quantity is a quantity which
has only magnitude or size.

Mass = 58 kg
Understanding Scalar and Vector
Quantities

   2. A vector quantity has both
magnitude/size and direction.

Velocity = 900 km/h
down south.
Understanding Scalar and Vector
Quantities

   3 When we say that the temperature of a room is 28°C,
or a bottle contains 500 cm3 of milk, we are dealing with
scalar quantities. On the other hand, a force of 120 N
acting downwards is a vector quantity.

120N
Understanding Scalar and Vector
Quantities

   4. Time, temperature, mass, volume, distance,
density and power are examples of scalar
quantities. These quantities can be added using
simple mathematical rules.

40W
45 cm3
Understanding Scalar and Vector
Quantities

   5. Force, velocity, displacement, acceleration and
momentum are vector quantities.

Force

Displacement,
AC
Understanding Scalar and Vector
Quantities

   5. Force, velocity, displacement, acceleration and
momentum are vector quantities. To find a
resultant vector, all vector quantities are either
added or subtracted taking into account the
magnitude and direction of the individual vector.
Chapter 1

1.4 Measurements
Understanding Measurements
   Nature of Measurement
   1 Measurements are trials to determine the true value
of a particular physical quantity.
Understanding Measurements
   2 The difference between the true value of a
quantity and the value obtained in measurement
is the error.
Actual mass = 60 kg
Weighing machine = 59 kg

Error = 60 - 59 = 1kg
Understanding Measurements
   Nature of Measurement
   3 No measurement can be absolutely accurate;
there will be some sort of error in a measurement.

Thickness of book

1.5 cm
1.518 cm

1.52 cm
Errors in Measurement

   1. There are two main types of errors.
   (a)     Systematic errors
   (b)     Random errors
Errors in Measurement

   Systematic Errors
   1 Systematic errors are cumulative errors
that can be compensated for, if the errors
are known.
Errors in Measurement

   Systematic Errors
   2 Systematic errors in measurement result from
   (a) an incorrect position of the zero point, or known as
zero error, and
Errors in Measurement

   Systematic Errors
   2 Systematic errors in measurement result from
   (a) an incorrect position of the zero point, or known as
zero error, and
   (b) an incorrect calibration of the measuring instrument.
Errors in Measurement

   3 Systematic errors always occur (with
the same value) when we continue to use
the instrument in the same way.
Errors in Measurement

   4 A zero error arises when the measuring
instrument does not start from exactly zero.
Errors in Measurement

   5 Zero errors are consistently present in
every reading of a measurement so that the
results obtained may be precise but lack in
accuracy.
Errors in Measurement

   6. Systematic errors cannot be eliminated by repeating
the measurements and averaging out the results. It only
can be eliminated or corrected if the measuring
instruments are calibrated or adjusted frequently.
Errors in Measurement

   Random Errors
   1 Random errors occurs due to mistakes made when
making measurement either through incorrect positioning
of the eye or the instrument. It will produce a different
error every time you repeat the experiment. They may
vary from observation to observation.
You measure the mass of a ring three times using the
same balance and get slightly different values: 17.46 g,
17.42 g, 17.44 g
Errors in Measurement

   Random Errors
   2. Random errors can be minimised by repeating the
measurements several times and taking the average or
You measure the mass of a ring three times using the
same balance and get slightly different values: 17.46 g,
17.42 g, 17.44 g
17.46  17.42  17.44
Average/mean =                        17.44 g
3
Errors in Measurement
   Random Errors
   3. A parallax error is an error caused by incorrect
positioning of the eye when reading a measurement.

Error = + 0.2ml
Error = + 0.1ml
Error = - 0.1ml
Errors in Measurement

   Random Errors
   4. If he repeats his reading several times, and takes the
average of the results, he will end up with an answer that
is closer to the true value; but repeating measurements
does nothing at all for the first observer.
Errors in Measurement

   Random Errors
   5 (a) To avoid parallax errors, the position of the eye
must be in line with the reading to be taken, as in position
C.
Errors in Measurement

   5 (b) To overcome parallax
errors in instruments with a
scale and pointer, e.g. an
ammeter, often have a mirror
behind the pointer. The correct
sure that that the eye is exactly
in front of the pointer, so that
the reflection of the pointer in
the mirror is behind it (refer
Figure 1.3).
Errors in Measurement

   5 (b)

Eye
Eye
Consistency, Accuracy and
Sensitivity
   Consistency/Precision
   1 The consistency of a measuring instrument is its
ability to register the same reading when a measurement
is repeated.
Consistency, Accuracy and
Sensitivity

   Consistency/Precision
   2 A set of readings from identical instruments will have
a small relative deviation or no deviation from the mean
value.

   High consistency => Small deviation from the mean value

Big deviation: 54kg, 56kg, 57kg
Small deviation: 54kg, 54kg, 55kgPrecise
Consistency, Accuracy and
Sensitivity

   Consistency/Precision
   3 A deviation is the difference between a measured
value and its mean value or the average value.

Average reading of diameter = 3.24 cm
One of the reading = 3.26 cm
Deviation = 3.26 – 3.24 = 0.02 cm
Consistency, Accuracy and
Sensitivity

   Consistency/Precision
   4 Relative deviation is defined by the
formula below.
   Relative deviation =   Average deviation x   100%
Average value
Consistency, Accuracy and
Sensitivity

   Consistency/Precision
   Example 1
   The diameter of an object was measured 5 times using vernier caliper.
The results are 3.14 cm, 3.15 cm, 3.12 cm, 3.09 cm and 3.05 cm.
Calculate the relative deviation.
                      3.14  3.15  3.12  3.09  3.05
   Average diameter =                 5
   = 3.11 cm
Consistency, Accuracy and
Sensitivity
Example 1:
Diameter/cm             Deviation/cm

3.14       (3.14 – 3.11) cm = 0.03 cm

3.15       (3.15 – 3.11) cm = 0.04 cm

3.12       (3.12 – 3.11) cm = 0.01 cm

3.09       (3.09 – 3.11) cm = |– 0.02 cm| =
0.02 cm
3.05       (3.05 – 3.11) cm = |– 0.06 cm| =
0.06 cm
Consistency, Accuracy and
Sensitivity

   Example 1:
      Mean deviation = 0.03  0.04  0.01  0.02  0.06   = 0.03 cm
5

Average deviation
       Relative deviation =                     x 100%
Average value

0.03
                          =               x 100%
3.11

                          = 0.96%
Consistency, Accuracy and
Sensitivity

   Consistency/Precision
 5 The consistency of a measuring instrument can be
improved by:
   (a) eliminating parallax errors during measurement.
Consistency, Accuracy and
Sensitivity

   Consistency/Precision
 5 The consistency of a measuring instrument can be
improved by:
   (b) exercising greater care and effort when taking
Consistency, Accuracy and
Sensitivity

   Consistency/Precision
 5 The consistency of a measuring instrument can be
improved by:
   (c) using an instrument which is not defective.
Consistency, Accuracy and
Sensitivity

   Accuracy
   1 Accuracy is the degree to which a
measurement represents the actual value.
Gravity = 9.81 ms-2
Experimental value
A = 9.76 ms-2
B = 9.62 ms-2                    9.62   9.76 9.81
Consistency, Accuracy and
Sensitivity

   Accuracy
   2 An accurate instrument is able to give
readings close to or almost equal to the actual
value of a quantity.

9.62     9.76 9.81
Closer
Consistency, Accuracy and
Sensitivity

   Accuracy
   3 An instrument with 100% accuracy does not
exist.
Consistency, Accuracy and
Sensitivity

   Accuracy
   4 The error is the difference between the
measured value and the actual or true value

9.62    A.9.76 9.81

Error A = 0.05
Consistency, Accuracy and
Sensitivity

   Accuracy
   5 The level of accuracy is related to the relative
error which is defined as the ratio of the error to
the actual value.
error value
 Relative error =                x 100%
actual value

B.9.62 A.9.76 9.81                   0.05
R. Error A =        x100%   =0.5%
9.81
Error A = 0.05                  0.19
R. Error B =        x100% =1.9%
Error B = 0.19                  9.81
Consistency, Accuracy and
Sensitivity

   6 A measured value with a very small error has a high
accuracy. If the relative error is of a small value, the level
of accuracy is high and vice versa.
   Relative error  Accuracy 
0.05                  Accuracy
R. Error A =        x100%   =0.5%    high
9.81
0.19
R. Error B =        x100% =1.9%
9.81
Consistency, Accuracy and
Sensitivity
   Accuracy
   7 How to improve the accuracy of a measurement?
   (a) Repeated readings are taken and the average value is
calculated.
Consistency, Accuracy and
Sensitivity
   Accuracy
   7 How to improve the accuracy of a
measurement?
   (b) Avoid parallax errors,
Consistency, Accuracy and
Sensitivity
   Accuracy
   7 How to improve the accuracy of a
measurement?
   (c) Avoid zero errors.
Consistency, Accuracy and
Sensitivity
   Accuracy
   7 How to improve the accuracy of a measurement?
   (d) Use measuring instruments with a higher accuracy.
For example, a vernier caliper is more accurate than a
ruler.
Consistency, Accuracy and
Sensitivity
   Sensitivity
   1 The sensitivity of a measuring instrument is its ability
to detect quickly a small change in the value of a
measurement.
Consistency, Accuracy and
Sensitivity
   Sensitivity
   2 A measuring instrument that has a scale with
smaller divisions is more sensitive.
Consistency, Accuracy and
Sensitivity
   Sensitivity
   3 As an example, the length of a piece of wire is
measured with rulers A and B which have scales
graduated in intervals of 0.1 cm and 0.5 cm respectively,
as shown in Figure 1.5. Which of the rulers is more
sensitive?
Consistency, Accuracy and
Sensitivity
   Sensitivity

   3 Results:
   Ruler A: Length = 4.8 cm
   Ruler B: Length = 4.5 cm
   Ruler A is more sensitive as it can measure to an accuracy
of 0.1 cm compared to 0.5 cm for ruler B
Consistency, Accuracy and
Sensitivity
   4 In addition to the size of the divisions on the scale of
the instrument, the design of the instrument has an effect
on the sensitivity of the instrument. For example, a
thermometer has a higher sensitivity if it can detect small
temperature variations. A thermometer with a narrow
capillary and a thin-walled bulb has a higher sensitivity.
Consistency, Accuracy and
Sensitivity
   Comparisons between Consistency, Accuracy,
and Sensitivity
   1 The drawings in Figure 1.5, which show the
distribution of gunshots fired at a target board, serve to
illustrate the meaning of consistency and accuracy.
Consistency, Accuracy and
Sensitivity
   2 A consistent measuring instrument is not necessarily
accurate. For example, a measurement with a metre rule is
consistent but not accurate due to end errors. In this
respect, this type of instrument gives readings which,
however, do not represent the true value of the measured
quantity.
Consistency, Accuracy and
Sensitivity
   3 A sensitive measuring instrument too, may not
be accurate or consistent. This is due to external
variations which cause variations in the readings.

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