Chapter 1. Measurement

CHAPTER 1. MEASUREMENT1.WHAT IS PHYSICS?      2. MEASURING THINGS      3. THE INTERNATIONAL SYSTEM OF UNITS      4. LENGTH      5. TIME       6. MASS       7. CHANGING UNITS8.CALCULATIONS WITH UNCERTAIN QUANTITIES

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.

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.

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.”

THE SYSTÈME INTERNATIONAL (SI) OF UNITSThe 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

THE SI BASE UNITS

Time: One second is the duration of 9.192631770 × 109 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.

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

Mass: One kilogram is the mass of this thing

(a platinum-iridium cylinder of height=diameter=39 mm)

Atomic mass units (u)

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

EXAMPLE

Determine the order of magnitude of the following numbers:

(a) A=2.3×104, (b) B=7.8×105.

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:

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 .

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?

DENSITY

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

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.

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.

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?

A SIMPLE RULE FOR REPORTING SIGNIFICANT FIGURES IN A CALCULATED RESULTMultiplying 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.

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?