Nota Physics Vol 1 l Six Cap 1 ( Physical Quantities and Units)

PHYSICAL QUANTITIES AND UNITS

BASE QUANTITIES & SI UNITS

• Base quantities and units•SI Units• Derived quantities & Units

DIMENSIONS

• Dimensions of base quantities•Dimensional analysis

ERRORS

• Error or uncertainties•Systematic and random errors• Significant figures

• Scalar and vector quantities•Vector algebra•Vector components

SCALAR & VECTORS

PHYSICAL QUANTITIES AND UNITS

1. Physical Quantity is a quantity that can be measured.2. It can be expressed in numerical magnitude together with a unit.

Mass of a book = 340.25 g

Physical quantityNumerical magnitude

Unit

3. Physical Quantities can be classified as Base Quantities or Derive Quantities

1. Base Quantities - are stand alone quantities that cannot be derived from other quantities.

2. Derived Quantities- are quantities that can be derived from other quantities. They can be expressed as products or quotients of base quantities

Base Quantities

Unit- Standard size for a physical quantity

Derive units are the units that are created from combination of two or more base units .

Next

Next

CHECKING EQUATION BY COMPARING UNITS

DIMENSIONS OF PHYSICAL QUANTITIES

DIMENSIONS- A physical quantities which are not give any idea about the magnitude

Example 1 : The basic quantity of displacement is length – [ L ]

Example 2 : The basic quantity of period – [ T ]

Answer:

22

1

2

1

vEEv

Then, dimension of E, 21223

213213

2

TMLTLML

LTMLmsm

kgv

V

m

kmh – 1

DIMENTIONAL ANALYSIS

Activity 1

Activity 2

The Young’s modulus of a solid of density ρ can be determined by propagating a wave of wavelength λ in the solid. Using dimensional analysis, derive a formula for Young’s modulus. Dimension of Young’s modulus is Y = ML – 1T – 2

zyxvkY Solution: Let say Young’s modulus, , where k, x, y and z are non-dimensionalConstants.

Then,

][

])][()][([][

][][

3

31211

zyzyx

zyx

zyx

MTL

MLLTLTLM

vkY

Equating indices of M :

T :

L :

1z2y

0,13 xzyx

Hence, ρkvY 2

ERRORS IN MEASUREMENT,RANDOM AND SYSTEMATIC ERRORS

SIMPLE RULER

ERROR READING UP TO ± 0.05 cm

MEASUREMENT BY A SIMPLE RULE

VERNIER SCALE

ERROR READING UP TO ± 0.01 cm

0.021.40

1.40+ 0.02= ( 1.42 ± 0.01 ) cm

Vernier scale 0.1 ÷ 10 = 0.01

Answer: 3

Compare

Compare

MICROMETER SCREW

ERROR READING UP TO ± 0.001 cm

VECTOR

RUN THE CD

RUN THE CD

VECTOR ADDITION

EXAMPLE

ANSWER

ACTIVITY

ANSWER

ACTIVITY

ANSWER

RESOLVING VECTORS

Look on cd for detail explanation

EXAMPLE

ANSWER

ACTIVITY

ANSWER

RESULTANT VECTORS

ACTIVITY

ANSWER

ACTIVITY

ANSWER

EXAMPLE

θ = 640

Sin 64 0 = 0.8987

ANSWER

ACTIVITY

ANSWER

ACTIVITY

ANSWER

UNCERTAINTIES ( ERRORS) IN MEASUREMENTS

All measured values have errors.The accuracy of a measured value depends on the sensitivity of the instruments.

The possible sources of errors are:

1.The instruments2.The physical conditions of the surroundings3.Physical limitation of the observer.

RULER

Example: The length of a wire measured by using a ruler = 34.2 cm. It is correct to record the measurement = 34.20 cm. This is because the ruler is not reliable enough to measure to the nearest 0.05 cm.

It is not appropriate to record the value as = 34 cm. Because the ruler has the degree of accuracy until 0.1 cm.

VERNIAR CALIPERS

This instrument has more accurate than a ruler. This is because it can measure with accuracy of0.01 cm. But a ruler has degree of accuracy up to 0.1 cm.

MICROMETER SCREW GAUGE

This instrument has more accurate compare verniar calipers. This is because the degree of accuracyof this instrument can reach to 0.001 cm.

TYPE OF ERRORS

SYSTEMATIC ERRORS

• Magnitude of the error is constant.• Error is always positive

( measurement is always greater than actual value) or negative ( measurement is always smaller than actual value)

• Example- Micrometer screw gauge.• Value of these errors can’t be

reduced or eliminated by taking several readings use the same method or instrument or the same observer.

RANDOM ERRORS

• Magnitude of the error is not constant.

• The error can be positive or negative. Mean, measurement may be greater or smaller than the actual value.

• Example- 1. Read wrongly the scale of an instrument ( simple ruler / miniscus of water or mercury level in a tube. 2. Wrong count the number of oscillations of a simple pendulum.

• To eliminate the error, taking more reading for the measurement.

METHOD OF ERROR ANALYSIS

Precision: Meaning – the degree of a measuring instrument used to record consistent readings for each measurement by the same way. It refers to the repeatability of a measurement. It does not require us to know the correct or true value.

Accuracy:Refers to how to close a measured value is to the actual value or its refers tothe degree of agreement between the experimental result and its true value.

High Precision : A measurement with relatively small random error.

High Accuracy : A measurement with small random error and small Systematic error

SIGNIFICANT FIGURES: CHARACTERISTICS

1.The number of digits known with certainty for a measured value is called the number ofsignificant figures.

2. A greater number of significant figures of a measured value shows a greater accuracycompared with another value of fewer numbers of significant figures.

3.Whenever you make a measurement, the number of meaningful digits that you write downimplies the error in the measurement.

Example: 1. If the length of an object is 0.528m, you imply uncertainty is about 0.001m.

2. If the reading is 0.5 m, the uncertainty is 0.1 m.

3. If the reading is 0.52819667 m, the uncertainty is 0.00000001 m.

4. The quantity of 0.528 m is said to have 3 significant figures. The same measurement in centimetres would be 52.8 cm is still be 3 significant figures.

5. The accepted convection is that only one digit uncertainty is to be reported in a measurement, then for error of 0.01 m, the result must be written as ( 0.53 ± 0.01 ) m, not ( 0.53 ± 0.001 )m

6. The position of 0 digit to be accounted as a significant figures .

a. If 0 has a non-zero digit anywhere on its left, then the 0 is significant. Otherwise, it is not.

Examples: 6.00 has 3 significant figures.

0.0006 has 1 significant figure.

b. If 0 in between non-zero digits, then the 0 is significant.

Example : 20.0005 has 6 significant figures.

7. The number of significant figures for 400 is not well define. If we write 4 x 10 2 , one significant figure. If we write 4.00 x 10 2 , It be 3 significant figures.

8. The number of significant figures that should be retained after multiplication or division of a number of quantities should follow the significant number of the least accurately known quantity.

Example: The lengths of an rectangular are 35.44 cm and 23.5 cm. The area of the object is calculated as:

35.44 cm x 23. 5 cm = 832. 84 cm 2 = 833 cm 2 . ( Follow the fewer number of

significant figures of 23.5 cm. )

9. For addiction and subtraction of two ore more values, the calculated answer should follow the least number of decimal places of the primary data.

Example: 28.366 cm + 1.5 cm = 29.866 cm.

The final value be written as = 29.9 cm ( follow the fewer number of decimal ( places of 1.5 cm )

UNCERTAINTIES IN MEASUREMENT

1. Uncertainty of a measured value is an interval around that value such that any repetition of the measurement will produce a new result that lies within this interval.

2. Let say the length measured by a ruler normally be recorded as ( 34.2 ± 0.1 ) cm. This means that the uncertainty of the length measured by the ruler is ± 0. 1 cm. Then any repetition of this measurement falls between 34.1 cm and 34. 3 cm.

3. Similarly a length measured by a vernier calipers normally recorded as 4.20 ± 0.01 cm. A recorded value of 4.20 ± 0.01 cm gives us the confidence that the measured value lies between 4.19 cm and 4.21 cm.