1.3-1.4 scalar n vector
TRANSCRIPT
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Chapter 1
1.3 Scalar and Vector Quantities
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Understanding Scalar and Vector
Quantities
1. A scalar quantity is a quantity which
has only magnitude or size.
Mass = 58 kg
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Understanding Scalar and Vector
Quantities
2. A vector quantity has both
magnitude/size and direction.
Velocity = 900 km/h
down south.
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Understanding Scalar and Vector
Quantities
3 When we say that the temperature of a room is 28C,
or a bottle contains 500 cm3of milk, we are dealing with
scalar quantities. On the other hand, a force of120 Nacting downwards is a vector quantity.
120N
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Understanding Scalar and Vector
Quantities
4. Time, temperature, mass, volume, distance,density and power are examples ofscalar
quantities. These quantities can be added usingsimple mathematical rules.
40W45 cm3
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Understanding Scalar and Vector
Quantities
5. Force, velocity, displacement, acceleration andmomentum are vector quantities.
Force
Displacement,
AC
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Understanding Scalar and Vector
Quantities
5. Force, velocity, displacement, acceleration andmomentum are vector quantities. To find a
resultant vector, all vector quantities are eitheradded or subtracted taking into account themagnitude and direction of the individual vector.
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Chapter 1
1.4 Measurements
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Understanding Measurements Nature of Measurement
1 Measurementsare trials to determine the true value
of a particular physical quantity.
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Understanding Measurements 2 The difference between the true valueof a
quantity and the value obtained in measurement
is the error.Actual mass = 60 kg
Weighing machine = 59 kg
Error = 60 - 59 = 1kg
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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
1.52 cm
1.518 cm
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Errors in Measurement
1. There are two main types of errors.
(a) Systematic errors
(b) Random errors
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Errors in Measurement
Systematic Errors
1 Systematic errors are cumulative errors
that can be compensated for, if the errorsare known.
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Errors in Measurement
Systematic Errors
2 Systematic errors in measurement result from
(a) an incorrect position of the zero point, or known aszero error, and
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Errors in Measurement
Systematic Errors
2 Systematic errors in measurement result from
(a) an incorrect position of the zero point, or known aszero error, and
(b) an incorrect calibrationof the measuring instrument.
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Errors in Measurement
3 Systematic errors always occur(with
the same value) when we continue to use
the instrument in the same way.
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Errors in Measurement
4 A zero errorarises when the measuring
instrument does not start from exactly zero.
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Errors in Measurement
5 Zero errors are consistently presentinevery reading of a measurement so that the
results obtained may be precise but lack inaccuracy.
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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.
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Errors in Measurement
Random Errors
1 Random errors occurs due to mistakes made when
making measurement either through incorrect positioningof the eye or the instrument. It will produce a different
errorevery time you repeat the experiment. They may
vary from observation to observation.
You measure the mass of a ring three times using thesame balance and get slightly different values: 17.46 g,
17.42 g, 17.44 g
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Errors in Measurement
Random Errors
2. Random errors can be minimised by repeating the
measurements several times and taking the average ormean value of the readings.
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
Average/mean = g44.173
44.1742.1746.17
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Errors in Measurement
Random Errors
3. A parallax erroris an error caused by incorrect
positioning of the eye when reading a measurement.
Error = + 0.2ml
Error = - 0.1ml
Error = + 0.1ml
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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 thatis closer to the true value; butrepeating measurements
does nothing at all for the first observer.
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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 positionC.
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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
reading is obtained by making
sure that that the eye is exactly
in front of the pointer, so thatthe reflection of the pointer in
the mirror is behind it (refer
Figure 1.3).
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Errors in Measurement
5 (b)
EyeEye
Consistenc Acc rac and
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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
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Consistency, Accuracy and
Sensitivity
Consistency/Precision
2 A set of readings from identical instruments will havea small relative deviation or no deviation from the meanvalue.
High consistency => Small deviation from the mean value
Big deviation: 54kg, 56kg, 57kg
Small deviation: 54kg, 54kg, 55kgPrecise
Consistency Accuracy and
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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 = 3.263.24 = 0.02 cm
Consistency Accuracy and
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Consistency, Accuracy and
Sensitivity
Consistency/Precision
4 Relative deviation is defined by the
formula below.
Relative deviation = x 100%valueAverage
deviationAverage
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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.
Average diameter =
= 3.11 cm
3.14 3.15 3.12 3.09 3.05
5
Consistency Accuracy and
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Consistency, Accuracy and
Sensitivity
Example 1:Diameter/cm Deviation/cm
3.14 (3.143.11) cm = 0.03 cm
3.15 (3.153.11) cm = 0.04 cm
3.12 (3.123.11) 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
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Consistency, Accuracy and
Sensitivity
Example 1:
Mean deviation = = 0.03 cm
Relative deviation = x 100%
= x 100%
= 0.96%
0.03 0.04 0.01 0.02 0.06
5
0.03
3.11
valueAveragedeviationAverage
Consistency Accuracy and
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Consistency, Accuracy and
Sensitivity
Consistency/Precision
5 The consistency of a measuring instrument can beimproved by:
(a) eliminating parallax errors during measurement.
Consistency Accuracy and
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Consistency, Accuracy and
Sensitivity
Consistency/Precision
5 The consistency of a measuring instrument can beimproved by:
(b) exercising greater care and effort when taking
readings.
Consistency Accuracy and
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Consistency, Accuracy and
Sensitivity
Consistency/Precision
5 The consistency of a measuring instrument can beimproved by:
(c) using an instrument which is not defective.
Consistency Accuracy and
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Consistency, Accuracy and
Sensitivity
Accuracy
1 Accuracy is the degree to which a
measurement represents the actual value.
Gravity = 9.81 ms-2
Experimental valueA = 9.76 ms-2
B = 9.62 ms-2 9.819.769.62
Consistency Accuracy and
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Consistency, Accuracy and
Sensitivity
Accuracy
2 An accurate instrument is able to give
readings close to or almost equal to the actualvalue of a quantity.
9.819.769.62
Closer
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Consistency, Accuracy and
Sensitivity
Accuracy
3 An instrument with 100% accuracy does not
exist.
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Consistency, Accuracy and
Sensitivity
Accuracy
4 The error is the difference between the
measured valueand the actual or true value
9.81A.9.769.62
Error A = 0.05
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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 tothe actual value.
Relative error = x 100%valueactual
valueerror
9.81A.9.76B.9.62
Error A = 0.05
Error B = 0.19
R. Error A = %100x81.9
05.0
R. Error B = %100x81.9
19.0
=0.5%
=1.9%
Consistency Accuracy and
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Consistency, Accuracy and
Sensitivity
6 A measured value with a very small error has a highaccuracy. If the relative error is of a small value, the levelof accuracy is high and vice versa.
Relative error Accuracy R. Error A = %100x
81.9
05.0
R. Error B = %100x81.919.0
=0.5%
=1.9%
Accuracy
high
Consistency Accuracy and
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Consistency, Accuracy and
Sensitivity
Accuracy
7 How to improve the accuracy of a measurement?
(a) Repeated readings are taken and the average value iscalculated.
Consistency Accuracy and
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Consistency, Accuracy and
Sensitivity
Accuracy
7 How to improve the accuracy of ameasurement?
(b) Avoid parallax errors,
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Consistency, Accuracy and
Sensitivity
Accuracy
7 How to improve the accuracy of ameasurement?
(c) Avoid zero errors.
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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.
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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
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Consistency, Accuracy and
Sensitivity
Sensitivity
2 A measuring instrument that has a scale withsmaller divisionsis more sensitive.
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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 of0.1 cm and 0.5 cm respectively,as shown in Figure 1.5. Which of the rulers is more
sensitive?
Consistency Accuracy and
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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
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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 narrowcapillary and a thin-walled bulb has a higher sensitivity.
Consistency Accuracy and
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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 toillustrate the meaning of consistency and accuracy.
Consistency, Accuracy and
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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 measuredquantity.
Consistency, Accuracy and
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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.