Cambridge chapter_1 - Measurement IGCSE.ppt

In the IGCSE Measurement chapter, students delve into the fundamental concepts of measuring physical quantities with precision and accuracy. This chapter introduces key measurements including length, mass, and volume, emphasizing the importance of using appropriate units and tools such as rulers, balances, and graduated cylinders. It explores the differences between precision—how consistently measurements can be repeated—and accuracy—how close measurements are to the true value. The chapter also covers common sources of error and uncertainty in measurements, techniques for converting between units, and the significance of significant figures in reporting data. Practical applications are highlighted to demonstrate how measurement principles are integral to scientific experiments, everyday life, and various professional fields.

1. Chapter 1. Measurement
1.What is Physics?
      
2. Measuring Things
      
3. The International System of Units
      
4. Length
     
5. Time
      
6. Mass
      
7. Changing Units
8.Calculations with Uncertain Quantities

2. What is Physics?
 
Physics is the study of the
basic components of the
universe and their
interactions. Theories of
physics have to be verified
by the experimental
measurements.

3. Measurement
•A scientific measurement requires:
(1) the definition of the physical quantity
(2) the units.
•The value of a physical quantity is actually the
product of a number and a unit .
•The precision of the measurement result is
determined by procedures used to measure
them.

4. Basic Measurements in the Study of Motion
•Length: 
 Our “How far?” question involves
being able to measure the distance between
two points.
•Time: 
 To answer the question, “How long
did it take?”
•Mass:
  
Mass is a measure of “amount of
stuff.”

5. The Système International (SI) of units
•The SI, or metric system of units is the
internationally accepted system of units for
measurement in all of the sciences, including
physics.
•The SI consists of base units and derived
units:
(1) The set of base units comprises an
irreducible set of units for measuring all
physical variables
(2) The derived units can be expressed in
terms of the base units

6. The SI Base Units

7. •Time: One second is the duration of
9.192631770 × 10
9
periods of the
radiation corresponding to the
transition between the two hyperfine
levels of the ground state of the
cesium-133 atom.

8. •Length: One meter is the distance
traveled by light in a vacuum in a time
interval of 1/299 792 458 of a second

9. Mass: One kilogram is the
mass of this thing
(a platinum-iridium cylinder
of height=diameter=39
mm)
Atomic mass units (u)

10. Scientific Notation
All Physics quantities should be written as
scientific notation, which employs powers
of 10.
The Order of magnitude of a number is the
power of ten when the number is
expressed in scientific notation

11. Example
•Determine the order of magnitude of the
following numbers:
(a) A=2.3×10
4
, (b) B=7.8×10
5
.

12. Changing Units
In chain-link conversion, we multiply the original
measurement by one or more conversion factors. A
conversion factor is defined as a ratio of units that is
equal to 1.

For example, because 1 mile and 1.61 kilometers are
identical distances, we have:

13. EXERCISE 1
•(a) Explain why it is correct to write
1 min/60 s = 1, but it is not correct to write
1/60 = 1.
•(b) Use the relevant conversion factors
and the method of chain-link conversions
to calculate how many seconds there are
in a day .

14. EXERCISE 2
•The cran is a British volume unit for freshly
caught herrings: 1 cran=170.474 liters (L) of
fish, about 750 herrings. Suppose that, to be
cleared through customs in Saudi Arabia, a
shipment of 1255 crans must be declared in
terms of cubic covidos, where the covido is an
Arabic unit of length: 1 covido=48.26 cm . What
is the required declaration?

15. Density
The density ρ of a material is the mass per
unit volume:

16. Calculations with Uncertain Quantities
Significant Figures: 
Read the number from left to right,
and count the first nonzero digit and all the digits
(zero or not) to the right of it as significant.
•Significant figures and decimal places are different
•The most right digit gives the absolute precision, which tells you explicitly the
smallest scale division of the measurement.
•Relative Precision 
is the ratio of absolute precision over the physics quantity.

17. EXERCISE
  3

•Determine the number of significant
figures, absolute precision, relative
precision in each of the following numbers:
(a) 27 meters, (b) 27 cows, (c) 0.003 429
87 second, (d) –1.970 500 × 10
–11
coulombs, (e) 5280 ft/mi.

18. EXERCISE 4
Suppose you measure a time to the
nearest 1/100 of a second and get a value
of 1.78 s.
(a) What is the absolute precision of your
measurement?
(b) What is the relative precision of your
measurement?

19. A Simple Rule for Reporting Significant Figures in a
Calculated Result
•Multiplying and Dividing: 
 When multiplying or dividing
numbers, the relative precision of the result cannot exceed
that of the least precise number used
•Addition and Subtraction:
 
 
When adding or subtracting, you
line up the decimal points before you add or subtract. This
means that it's the absolute precision of the least precise
number that limits the precision of the sum or the difference.
•Data that are known exactly should not be included when
deciding which of the original data has the fewest significant
figures.
•Only the final result at the end of your calculation should be
rounded using the simple rule. Intermediate results should
never be rounded.

20. EXERCISE 5
Perform the following calculations and express
the answers to the correct number of significant
figures.
(a) Multiply 3.4 by 7.954.
(b) Add 99.3 and 98.7.
(c) Subtract 98.7 from 99.3.
(d) Evaluate the cos(3°).
(e) If five railroad track segments have an average
length of 2.134 meters, what is the total length of
these five rails when they lie end to end?