Transcript CHAPTER 1 : PHYSICS AND MEASUREMENT 1.1) Standards of Length, Mass and Time • Basic quantities  Length (L), Mass (M), Time (T) • Basic.

CHAPTER 1 : PHYSICS AND MEASUREMENT
1.1) Standards of Length, Mass and Time
•
Basic quantities  Length (L), Mass (M), Time (T)
•
Basic unit  to report the results of a measurement, a standard must be
defined.
•
SI system (metric system)
 a set of standards fro length, mass, time, and
other basic quantities.
 the units of length, mass, and time are the
meter, kilogram, and second.
 temperature (the Kelvin), electric current (the ampere), luminous intensity
(the candela), and the amount of substance (the mole).
•
Prefixes for SI units – Table (1.4) pg. 7.
1.3) Density and Atomic Mass
• Derived quantity – density,  = its mass per unit volume
m

V
•Aluminum has a density of 2.70 g/cm3
•Lead has a density of 11.3 g/cm3.
•A piece of aluminum of volume 10.0 cm3 has a mass of 27.0 g.
•An equivalent volume of lead has a mass of 113 g.
•Table 1.5 – list of densities for varous substances.
•The numbers of protons and neutrons in the nucleus of an atom of an element –
related to the atomic mass of the element
•Atomic mass = the mass of a single atom of the element measured in atomic
mass unit (u).
1 u = 1.660 538 7 x 10-27 kg
•The atomic mass of lead = 207 u.
•The atomic mass of Aluminum = 27.0 u
•The ratio of atomic masses = 207 u / 27.0 u = 7.67 :- does not correspond to
the ratio of densities (11.3x103 kg/m3)/(2.70x103 kg/m3) = 4.19
•This dicrepancy is due to the difference in atomic spacings and atomic
arrangements in the crystal structures of the two elements.
Example 1.1 How many atoms in the cube?
A solid cube of aluminum (density 2.70 g/cm3) has a volume of 0.200 cm3. It is
known that 27.0 g of aluminum contains 6.02 x 1023 atoms. How many
aluminum atoms are contained in the cube?
1.4) Dimensional analysis
•
The symbol to specify length, mass, and time are L, M, T.
•
Brackets [ ]  denote the dimensions of the physical quantity.
•
Example – the symbol we use for speed is , and the dimensions of speed are
written [] = L/T.
- the dimensions of area, A are [A] = L2.
•
The dimensions of area, volume, speed, and acceleration are listed in
Table (1.6) pg. 11.
System
Area
(L2)
Volume
(L3)
Speed
(L/T)
Acceleration
(L/T2)
SI
m2
m3
m/s
m/s2
British
Engineering
ft2
ft3
ft/s
ft/s2
Table (1.6)
Dimensional analysis
• Help minimize the need for rote memorization of equations.
• Can be treated as algebraic quantities – added and subracted, only if they have
the same dimensions
• The terms on both sides of an equation must have the same dimentsions.
• Help determine whether an expression has the correct form.
• The reletionship can be correct only if the dimensions are the same on both
sides of the equation.
• Example – suppose you wish to derive a formula for the distance x traveled by a
car in a time t if the car starts from rest and moves with constant acceleration a.
The expression is (from Chapter 2) :
x  at
1
2
2
L 2
L 2 T L
T
• A more general procedure, is to set
up an expression of the form :
xa t
n m
[a n t m ]  L  LT0
n
• Returning to original expression
x  a n t m , we conclude that
x  at 2 .
Example (1.2) : Analysis of an
Equation
 L m
1
T

L
 2
T 
Show that the expression v = at is
dimensionally correct, where v
represents speed, a acceleration,
and t a time interval.
Ln T m  2 n  L1
Example (1.3) : analysis of a
Power Law
• Same on both sides, balanced under
the conditions :
m – 2n = 0
n=1
m=2
Suppose we are told that the
acceleration a of a particle moving
with uniform speed v in a circle of
radius r is proportional to some
power of r, say rn, and some power
of v, say vm. How can we
determine the values of n and m?
1.5) Conversion of Units
• Conversion factors between the SI units and conventional units of length are as
follows :
1 mi = 1 609 m = 1.609 km
1 ft = 0.3048 m = 30.48 cm
1 m = 39.37 in. = 3.281 ft
1 in. = 0.0254 m = 2.54 cm
• Unit can be treated as algebraic quantities that can cancel each other.
Example (1.4)
The mass of a solid cube is 856 g, and each edge has a length of 5.35 cm.
Determine the density  of the cube in basic SI units.
1.7) Significant Figures
• When certain quantities are measured, the measured values are known only to
within the limits of the experimental uncertainty.
• Factors  the quality of the apparatus
 the skill of the experimenter,
 the number of measurements performed.
• Suppose that we are asked to measure the area of a computer disk label using a
meter stick as a measuring instrument.
• Let us assume that the accuracy to which we can measure with this stick is ± 0.1
cm.
• If the length of the label is measured to be 5.5 cm, we can claim only that its
length lies somewhere between 5.4 cam and 5.6 cm.
• The measured value has two significant figures.
• Label’s width is measured to be 6.4 cm, the actual value lies between 6.3 cm
and 6.5 cm.
• The measured values are (5.5 ± 0.1) cm and (6.4 ± 0.1) cm.
Rule for Multiplying and Dividing
When multiplying several quantities, the number of significant figures in the final
answer is the same as the number of significant figures in the least accurate of
the quantities being multiplied, where “least accurate” means “having the lowest
number of significant figures”.
Zeros
• Zeros may or may not be significant figures
• Used to position the decimal point in such numbers as 0.03 and 0.0075 are not
significant.
0.03  one significant figures
0.0075  2 significant figures
• When the zeros come after other digits :
1500 g (mass of an object) – use scientific notation to indicate the number of
significant figures.
• We would express the mass as :
1.5 103 g
1.50103 g
(2 significant figures)
(3 significant figures)
1.500103 g (4 significant figures)
• Same rule holds when the number is less than 1.
2.3 104
(2 significant figures) or could be written as (0.00023)
2.30104
(3 significant figures) or could be written as (0.000230)
Rule for Addition and Subtraction
When numbers are added or substracted, the number of decimal places in the
result should equal the smallest number of decimal places of any term in the
sum.
Example (1.8) : The Area of a Rectangle
A rectangular plate has a length of (21.3 ± 0.2) cm and a width of (9.80 ± 0.1) cm.
Find the area of the plate and the uncertainty in the calculated area.
Example (1.9) : Installing a Carpet
A carpet is to be installed in a room whose length is measured to be 12.71 m and
whose width is measured to be 3.46 m. Find the area of the room.
SUMMARY (Chapter 1)

3 fundamental physical quantities of mechanic – length, mass, time.

SI system – SI units for length, mass and time are meters(m), kilograms(kg)
and seconds(s), respectively.

Prefixes – indicate various power of ten.

Dimensional analysis – can be treated as algebraic quantities.

Conversion of units.

Significant figures.