### Description

**Chapter 1: Summary**

Scientists use
the *Système International d’Unités*, also known as the metric
system of measurement. Examples of metric units are meters, kilograms, and
seconds.

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 = 8.756×10^{2}.

A standard 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 light.

In the metric system, the basic unit of length is the meter; time is measured in seconds; and mass is measured in kilograms.

Sometimes a 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 instance).

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}
becomes 1.2×10^{−3}.

The Pythagorean theorem states that the square of the hypotenuse of a triangle is equal to the sum of the squares of the two legs.

*c*^{2} = *a*^{2} + *b*^{2}

Trigonometric functions, such as sine, cosine and tangent, relate the angles of a right triangle to the lengths of its sides.

Radians (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 L^{3}.

**Equations:**

**Prefixes**

giga (G) = 10^{9}

mega (M) = 10^{6}

kilo (k) = 10^{3}

centi (c) = 10^{–2}

milli (m) = 10^{–3}

micro (*μ*) = 10^{–6}

nano (n) = 10^{–9}

**Pythagorean Theorem**

*c*^{2} = *a*^{2} + *b*^{2}

**Trigonometric functions**

sin *θ* = opposite / hypotenuse

cos *θ* = adjacent / hypotenuse

tan *θ* = opposite / adjacent

**Radian measure**

Angle = arc length / radius = *s*/ *r*

360° = 2*π*
rad

**WE DO**

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/T^{2}); *v* speed (L/T);

*F* force (ML/T^{2})

Using the information above, check the boxes of the
equations that are dimensionally correct. Select all that apply.

*F* = *ma; **v ^{2} =* 2

*ax;*

*v*=

*at*

^{2; }*F*/

*v*=

*m*/

*t*

2.
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?

T^{2 }T^{2}/L L/T^{2 }L/T

3. Multiply 3.65×10^{23} by 4.12×10^{154}
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 batch?

5. Newton's second law states that the net
force equals the product of mass and acceleration. A boat's mass of is 9.6×10^{5}
kg and it experiences a net force of 1.5×10^{4} kg**·**m/s^{2}.
State its acceleration.

**YOU DO (#1, due 8.31.15)**

**1.
**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
your calculations.

**2.
**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?