Chapter 1
Physics and Measurement
1-1 Standards of Length, Mass, and Time
There are many physical quantities, for example , time, mass, force, pressure, …
The International System of Units (SI) was established in 1971.
The SI system of units has seven base quantities.
The meter was redefined as the distance traveled by light in vacuum
during a time of 1/299 792 458 second.
One second is defined as the time taken by 9 192 631 770 oscillations of
the light emitted by the cesium atom.
The SI standard of mass is a platinum-iridium cylinder kept at the International Bureau
of Weights and Measures near Paris and assigned a mass of 1 kilogram.
The units of all other quantities can be derived from the units of these three quantities.
Basic Quantities (and Units):
Length (meter, m)
Mass (kilogram, kg)
Time (second, s)
Derived Quantities (and Units):
Force (Newton, N = kg . (m/s2))
Energy (Joule, J = N . m)
Power (Watt, W = (J/s))
1.2 Matter and Model Building
Density
The density (ρ) of any substance is defined
as its mass (m) per unit volume (V)
𝑚
ρ=
𝑣
Quick Quiz 1.1 (Page 6)
In a machine shop, two cams are produced, one of
aluminum and one of iron. Both cams have the
same mass. Which cam is larger?
a-The aluminum cam
b-iron cam
c-Both cams have the same size
Density of aluminum is lower than the density of iron
(The answer is a)
ρ(aluminum) = 2.7 x 10-3 kg/m3 ,ρ (iron) = 7.85 x 10-3
kg/ m3
Densities of Some Common Substances (table 14-1 in page 419)
Mass (atom, nucleus, proton, neutron, electrons) is measured by:
atomic mass unit (u) , [ 1 u = 1.6605387 X 10-27 kg]
Problem 2 (Page 15)
The standard kilogram (m = 1 kg) is a platinum – iridium cylinder (39.0 mm) in
height (h) and (39 mm) in diameter .What is the density of the material?
Solution
h = 39 mm = 39 x 10-3 m
r = (39/2) = (19.5 mm) = 19.5 x 10-3 m
The Volume of the Cylinder is V = (π r2) (h)
V = (π r2) (h) = (3.14) (19.5 x 10-3)2 (39 x 10-3) = 4.66 x 10-5 m3
The density of the cylinder is ρ= (m / V) = 1/ (4.66 x 10-5) = 2.15 x 104 kg/m3
1-3 Dimensional Analysis
The dimension of a quantity is its property that we measure.
For distances, we measure length.
For periods, we measure time.
Dimension of distance = length
Dimension of period = time
All quantities in phys 3101 can be expressed in terms of three dimensions:
Length (L)
Time(T)
Mass (M)
The brackets [ ] is used to denote the dimension of a quantity.
[acceleration] stands for the dimension of acceleration
Length L
[distance] = Length = L
,
[speed] =
=
Time
T
,
[pure number] = 1 , [angle] = 1 , [argument of a trigonometric function] = 1
Quantities with dimension 1 are called dimensionless quantities
L/T L
[a] = velocity
= = 𝟐
Time
T 𝐓
Quantities can be added or subtracted only if they have the same dimensions.
L𝑛
( 2n) T m
T
= L𝑛 T m−2𝑛
L1 T 0 = L𝑛 T m−2𝑛
Quick Quiz 1.2(Page 8)True or False: Dimensional analysis can give you the numerical
value of constants of proportionality that may appear in an algebraic expression. (False)
Example
Is the expression 𝑣 = 𝑎 𝑡 2
dimensionally correct
1-4 Conversion of Units
(Appendix A gives conversion factors)
1 mile= 1609 m ,1 mile= 1.609 km
An aspirin tablet contains 325 mg of
acetylsalicylic acid.
Express this mass in grams
Solution : m = 325 mg = 325 x 10-3 g
= 0.325
Example 1.3(page10)
On an interstate highway in a rural
region of Wyoming, a car is traveling
at a speed of 38.0 m/s. Is the driver
exceeding the speed limit of 75.0
mi/h?
Quick Quiz 1.3:
The distance between two cities 100 mile. What is the number of
kilometers between the two cities is:
(a) Smaller than 100
(b)Larger than 100
(c) Equal to 100
1-4 Conversion of Units
(Appendix A gives conversion factors)
An aspirin tablet contains 325 mg of
acetylsalicylic acid.
Express this mass in grams
Solution : m = 325 mg = 325 x 10-3 g
= 0.325
Example:
Convert 15.0 in. to centimeters.
Quick Quiz 1.3:
The distance between two cities 100 mile. What is the number of kilometers between the two cities ?
(a) Smaller than 100
(b)Larger than 100
(c) Equal to 100
Example 1.3(page10)
On an interstate highway in a rural region of Wyoming, a car is traveling at a speed of 38.0 m/s. Is the driver
exceeding the speed limit of 75.0 mi/h?
1-5 Estimates and Order-of-Magnitude Calculations
(It is useful if you want to get a quick rough answer)
In some case we do not need the exact number but rather an estimate, which may be expressed in scientific
notation. The estimate may be made even more approximate by expressing it as an order of magnitude, which is a
power of ten determined as follows:
1. Express the number in scientific notation, with the multiplier of the power of ten between 1 and 10 and a unit.
2. If the multiplier is less than 3.162 (the square root of 10), the order of magnitude of the number is the power of
10 in the scientific notation.
If the multiplier is greater than 3.162, the order of magnitude is one larger than the power of 10 in the scientific
notation.
A = 7 600 = 7.6 x 103 The order of magnitude of A is 4
B = 2 700 = 2.7 x 103 The order of magnitude of B is 3
A = 7 600 ≈ 1 000 = 104 The nearest order of magnitude of A is 4
B = 3 600 ≈ 1 000 = 104 The nearest order of magnitude of B is 4
Example 1.4
Estimate the number of breaths taken during an average human lifetime.
solution
We start by guessing that the typical human lifetime is about 70 years.
the average number of breaths that a person takes in 1 min. we choose 10 breaths per minute as our estimate.
Therefore, a person takes on the order of 109 breaths in a lifetime.