
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.

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


$$\begin{array}{cccc}\text{Cube}& \text{Sphere}& \text{Cylinder}& \text{Cone}\\ S=2ab+2bc+2ac\text{}& \text{}S=4\pi {r}^{2}\text{}& \text{}S=2\pi rh+2\pi {r}^{2}\text{}& S=\pi {r}^{2}+\pi r\sqrt{{r}^{2}+{h}^{2}}\text{}\\ V=abc& V=\frac{4}{3}\pi {r}^{3}\text{}& V=\pi {r}^{2}h\text{}& V=\frac{1}{3}\pi {r}^{2}h\end{array}$$


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

(c) A volume of one liter of water has a mass of one kilogram.


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

(b) A typical exit door (36 in) is a bit less than one meter (39.4 in) wide.


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 m^{3} Relationships: V = ^{4}⁄_{3}πr^{3} Solve: $$V=\frac{4}{3}\pi {r}^{3}$$Rearrange equation to solve for r:$$\begin{array}{l}{r}^{3}=\frac{3V}{4\pi}\\ r=\sqrt[3]{\frac{3V}{4\pi}}=\sqrt[3]{\frac{3\left(1\text{\hspace{0.17em}}{\text{m}}^{3}\right)}{4\pi}}=0.62\text{\hspace{0.17em}}\text{m}\end{array}$$


A room measures 3 m wide, 4 m long, and 2.5 m high.
 What is the surface area of the room in square meters?
 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 m^{2}
 1.88 gallons of paint
Solution: The room has two side walls each of area 3 m × 2.5 m = 7.5 m^{2}, two walls each of area 4 m × 2.5 m = 10 m^{2}, and two walls (actually the floor and the ceiling) each of area 3 m × 4 m = 12 m^{2}. Adding up these six sides to the room totals 2×(7.5 m^{2} + 10 m^{2} + 12 m^{2}) = 59 m^{2}.
 All the sides except for the floor have an area of 2×(7.5 m^{2} + 10 m^{2}) + 12 m^{2} = 47 m^{2}. It will therefore take a volume of paint of $$V=47{\text{m}}^{2}\times \frac{1\text{gallonofpaint}}{25{\text{m}}^{2}}=1.88\text{gallonsofpaint}$$


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

Microscopic scale: chromosomes; molecules; electrons. Macroscopic scale: planets; universe; zoo animals.


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.

In physics, many of the processes are reversible; i.e., they can proceed forward or in reverse using the same physics. Motion is a good example of a process that can go forward or backward. Time, however, is not reversible. Consider the process of a glass falling to the floor and breaking into a hundred pieces. Reversing time would mean the broken pieces could spontaneously reassemble themselves back into a whole glass. This does not happen! Backward time travel suffers similar problem. If backward time travel were possible then it would be possible to create a scenario in which the glass shatters into a hundred pieces by hitting the floor before it falls. Time travel is fun to watch in science fiction movies but, in the real universe, time travel only works in the forward direction!

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