Chapter 1: Summary
the Système International d’Unités, also known as the metric
system of measurement. Examples of metric units are meters, kilograms, and
In these systems,
units that measure the same property, for example units for mass, are related
to each other by powers of ten. Unit prefixes
tell you how many powers of ten. For example, a kilogram is 1000 grams and a
kilometer is 1000 meters, while a milligram is one one-thousandth of a gram,
and a millimeter is one-thousandth of a meter.
Numbers may be
expressed in scientific
notation. Any number can be written as a number between 1 and 10,
multiplied by a power of ten. For example, 875.6 = 8.756×102.
is an agreed-on basis for establishing measurement units, like defining the
kilogram as the mass of a certain platinum-iridium cylinder that is kept at the
International Bureau of Weights and Measures, near Paris. A physical constant
is an empirically measured value that does not change, such as the speed of
In the metric
system, the basic unit of length
is the meter; time
is measured in seconds; and mass
is measured in kilograms.
problem will require you to do unit
conversion. Work in fractions so that you can cancel like units, and make
sure that the units are of the same type (all are units of length, for
When you need to
do arithmetic using scientific notation, remember to deal with the leading
values and the exponents separately. For multiplication,
multiply the leading values and add the exponents. For division,
divide the leading values and subtract the exponents. When adding
or subtracting, first make sure the exponents are the same and then perform
the operation on the leading values. In all cases, if the leading value of the
result is not between one and 10, adjust the result. For example, 0.12×10−2
theorem states that the square of the hypotenuse of a triangle is equal to
the sum of the squares of the two legs.
c2 = a2 + b2
functions, such as sine, cosine and tangent, relate the angles of a right
triangle to the lengths of its sides.
(rad) measure angles. The radian measure of an angle located at the center of a
circle equals the arc length it cuts off on the circle, divided by the radius
of the circle.
Dimensional analysis is a useful tool for analyzing physical
situations and checking whether calculations make sense. In dimensional
analysis, dimensions are treated algebraically. We use the symbols L, T, and M
to represent the dimensions of length, time, and mass. The volume of a cube,
for instance, has dimensions L×L×L or L3.
giga (G) = 109
mega (M) = 106
kilo (k) = 103
centi (c) = 10–2
milli (m) = 10–3
micro (μ) = 10–6
nano (n) = 10–9
c2 = a2 + b2
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
Angle = arc length / radius = s/ r
360° = 2π
1. The following variables are commonly seen
in equations. The name of the quantity represented by each variable, and its
dimension(s), are also shown.
x distance (L); t time (T); m mass
(M); a acceleration (L/T2); v speed (L/T);
F force (ML/T2)
Using the information above, check the boxes of the
equations that are dimensionally correct. Select all that apply.
F = ma; v2 = 2ax; v = at2; F/v = m/t
The dimensions for force are the product of mass and length divided by time
squared. Newton's second law states that force equals the product of mass and
acceleration. What are the dimensions of acceleration?
T2 T2/L L/T2 L/T
3. Multiply 3.65×1023 by 4.12×10154
by 1.11×10−11 and express the answer in scientific notation
4. A drug company has just manufactured 50.0
kg of acetylsalicylic acid for use in aspirin tablets. If a single tablet
contains 500 mg of the drug, how many tablets can the company make out of this
5. Newton's second law states that the net
force equals the product of mass and acceleration. A boat's mass of is 9.6×105
kg and it experiences a net force of 1.5×104 kg·m/s2.
State its acceleration.
YOU DO (#1, due 8.31.15)
Sara has lived 18.0 years. How many seconds has she
lived? Express the answer in scientific notation. Use 365.24 days per year for
The world's tallest man was Robert Pershing Wadlow,
who was 8 feet, 11.1 inches tall. There
are 2.54 centimeters in an inch and 12 inches in a foot. How tall was Robert in meters?