Essential Physics

Section 1 review

The observable world is described by mass, length, and time. Mass describes the quantity of matter and is measured in grams and kilograms. Length describes space, including concepts such as size or position. Units of length include centimeters, meters, and kilometers in the SI system. The concept of length extends in three dimensions to the concepts of surface area and volume. To fully understand the universe we need to look at different length scales. The macroscopic scale encompasses quantities and sizes that we can experience directly, ranging from about the size of a bacteria upward to the size of planets and larger. In physics, the microscopic scale refers to quantities and sizes comparable to individual atoms and smaller. Many macroscopic phenomena, such as temperature, can only be understood on the microscopic level. Time describes the progression of events that we observe to flow from the past, through the present, and into the future, and never in reverse. Units for measuring time include seconds, minutes, and hours. Read the text aloud

Read the text aloud

measurement, matter, mass, inertia, length, surface area, volume, density, scale, macroscopic, microscopic, temperature, scientific notation, exponent

ρ = \frac{m}{V}

\begin{matrix} Cube & Sphere & Cylinder & Cone \\ S = 2 a b + 2 b c + 2 a c & S = 4 π r^{2} & S = 2 π r h + 2 π r^{2} & S = π r^{2} + π r \sqrt{r^{2} + h^{2}} \\ V = a b c & V = \frac{4}{3} π r^{3} & V = π r^{2} h & V = \frac{1}{3} π r^{2} h \end{matrix}

Review problems and questions

Which of the following is closest to 1 kg in mass?
(a) dime; (b) average size banana; (c) one liter of water; (d) average person

Which of the following is closest to one meter in length?
(a) penny; (b) width of a door; (c) height of a room; (d) size of the Earth

What is the radius of a sphere that has a volume of one cubic meter?

Answer: The sphere has a radius of 0.62 m.

Asked: Radius r of sphere
Given: Sphere has volume v = 1 m³
Relationships: V = ⁴⁄₃πr³
Solve:

V = \frac{4}{3} π r^{3}

Rearrange equation to solve for r:

\begin{array}{l} r^{3} = \frac{3 V}{4 π} \\ r = \sqrt[3]{\frac{3 V}{4 π}} = \sqrt[3]{\frac{3 (1 m^{3})}{4 π}} = 0.62 m \end{array}

A room measures 3 m wide, 4 m long, and 2.5 m high.
1. What is the surface area of the room in square meters?
2. If a certain paint covers 25 square meters per gallon, how many gallons will it take to paint the walls and ceiling, but not the floor?

Answer:

59 m²
1.88 gallons of paint

Solution:

The room has two side walls each of area 3 m × 2.5 m = 7.5 m², two walls each of area 4 m × 2.5 m = 10 m², and two walls (actually the floor and the ceiling) each of area 3 m × 4 m = 12 m². Adding up these six sides to the room totals 2×(7.5 m² + 10 m² + 12 m²) = 59 m².
All the sides except for the floor have an area of 2×(7.5 m² + 10 m²) + 12 m² = 47 m². It will therefore take a volume of paint of $V = 47 m^{2} \times \frac{1 gallon of paint}{25 m^{2}} = 1.88 gallons of paint$

Describe three objects that belong to the microscopic scale and three objects that belong to the macroscopic scale.

A basic concept in science is that things which happen, called effects, have causes and that the cause must precede the effect. Nothing happens before it is caused. Discuss how this might theoretically affect the possibility of time travel.


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