chapter 1 Flashcards
model
an analogy or representation designed to help us make sense of an unfamiliar phenomenon or experience (ex. the wave model of light)
theory
an explanation for patterns in nature that is supported by scientific evidence and has been
uncertainty
assumed to be one or two units in the last digit specified (ex. 5.6 cm has an uncertainty of 0.1 cm)
percent uncertainty
uncertainty devided by the measured value times 100 (0.1/5.6) x 100 = 1.8%
precision
repeatability of the measurement using a given instrument
accuracy
refers to how close the measurement is to the true value
estimated uncertainty?
takes both accuracy and precision into account
significant figures
number of reliably known digits (0.20 has two reliably known digits)
scientific notation
a way to determine the number of sig figs (0.00210 x= 2.10 x 10^-3 and has 3 sig figs)
when multiplying and dividing numbers:
result should have as many digits as the number with the fewest number of sig figs (2.1 x 3.85 = 8.1)
when adding or subtracting:
result is only as precise as the last precise number used (3.6 - 0.57 = 3.0 not 3.03)
what is the sum of 1123 m and 10.3 m written with the correct number of sig figs?
1133 meters
units
term for the measurement of any quantity (5 kg is 5 portions of a kilogram)
How many base units of SI system?
7 base units (table 1.5)
derived units
units derived from the 7 base units (newtons, joules, volts)
speed SI unit?
meter/second
speed = length/time
1 meter is how many feet?
1 meter = 3.2808 feet
using conversion factors, determine how many seconds there are in 5.24 days
4.53 x 10^5 seconds
Example problem: a typical atom has a diameter of about 1.0 x 10^-10 meters.
a.) What is this in inches?
b.) Approximately how many atoms are along a 1.0 cm line, assuming they touch?
a.) 3.94 x 10^-9 inches
b.) 1.0 x 10^8 atoms
Example problem: it is estimated the relative approach speed is 42 m/s.
a.) how many miles per hour does that equal?
b.) could they grab him safely at that speed?
a.) 1m = 3.281 ft 1 mile = 5280 feet. 3600 s = hr
= 94 mph
b.) no
What precision should you expect for a quantity that you determine by estimation in which the variables used are rounded to the nearest power of ten?
just the order of magnitude will be correct, the leading number of the digit will not be the same
order of magnitude estimate
a rough estimate can be made by rounding off all numbers to one significant figure
- generally work because the estimations of the individual terms
how many piano tuners in chicago?
1.) they are approximately 9,000,000 people in Chicago
2.) on average, there are two people per household in Chicago
3.) let’s guess that roughly one household in twenty has a piano that is tuned regularly
4.) they are tuned on average about once per year
5.) (9,000,000 people)/ (2 people per household) * (1 piano/household) * (1 piano tuning per year) = 225,000 piano tuning per year
6.) Piano tuning takes about 2 hours including travel time
7.)The number of tuning that one piano tuner performs is (50 weeks/year)(5 days/week)(8 hours/day)/(2 hours to tune a piano) = 1000 piano tuning a year per piano tuner
8.) (225,000 piano tunings)/(1000 piano tuning per year) = 225 piano tuners
equation
a statement of equality, two things are equal
ex. F= ma
variable
a symbol which can take on various numerical values
ex. Hookes law, F= kx and x is a variable
constant
a symbol which has a fixed numerical value, it does not change
ex.) Hookes law, F=kx and k is a constant (spring constant)
function
a set of paired numbers where each value of an input variable gives one value for the output variable
ex.) x(t) = x0 + v0t
proportionality
two variables are proportional if there is always a constant ratio between them
ex.) F= kx, the ratio F/x always equals k, is k is the proportionality constant
dimensional analysis
only quantities with the same dimensions may be added, subtracted, or equated to each other
if units are different, apply conversion factor
Which of the following is NOT a base unit of the SI system?
volt
The metric prefix for one-thousandth is ______
milli
The metric prefix for one thousand is ______
kilo
What is the sum of 2.67 + 1.976 + 2.1 to the correct precision?
6.7
What is the product of 12.56 x 2.12 to the correct number of significant figures?
26.6
Which of the following numbers is the smallest?
1) 15 x 10-3
2) 0.15 x 10^0
3) 0.00015 x 10^3
4) 0.00000015 x 10^6
15 x 10-3
What is the quantity 13.5 gigameters expressed in decimal notation with standard units?
13,500,000,000 m
giga = 10^9
Which of the following areas is the largest?
1) 2,500,000 mm2
2) 100,000 cm2
3) 7.5 m2
4) 0.75 m2
100,000 cm2
The mass of Mars, 6.40 x 1023 kg, is about one-tenth that of the Earth, and its radius, 3395 km, is about half that of Earth. What is the average density of Mars in kg/m3?
Mass = 6.4 X 10^23 kg
Volume = 4/3 pi (r^3) where r = 3.395 X 10^6 m
V = 1.639 X 10^20 m^3
So, by merely performing the equation D = M/V you can get the answer easily
An average human heart beats at a rate of 70 beats per minute. If someone’s heart beats at that average rate over a 70-year lifetime, how many times will it beat?
3 x 10^9
The last page of a book is numbered 764. The book is 3.00 cm thick, not counting its covers. What is the average thickness in centimeters of a single sheet of paper in the book?
764 pages, means 764/2 sheets of paper. 3 cm/382 sheets =
8 x 10^-3 cm
Which of the following lists contains only SI base units?
candela, kelvin, meter, second
Express the number 0.02 volts using one of the prefixes in Table 1-4.
2 centivolts
Express the following sum with the correct number of significant figures: 1.00 kg + 1531 g + 2.54 x 10^4 mg.
2.56 kg
