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Chapter 2: The Language of Science
Multiple Choice Questions
1. The purpose of mathematical equations in science is to
a. prove how difficult science can be.
b. help nonscientists understand the physical world.
c. provide a common language for all scientists.
d. serve as a qualitative description of nature.
e. all of the above.
Ans: c
2. Which of the following, according to your text, is an attribute of a “useful”
language?
a. communicates without ambiguity
b. contains no more than a thousand words
c. includes specialized vocabularies for complex systems
d. a and c
e. all of the above
Ans: d
3. How do scientists describe the physical world?
a. tables
b. graphs
c. words
d. equations
e. all of the above
Ans: e
4. Which of the following is a scalar?
a. three blocks west
b. 30 59’45” North Latitude
c. 30 miles per hour to the East
d. 98.6 F
e. none of the above are scalars
Ans: d
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5. A vector
a. is a mathematical quantity.
b. has a magnitude.
c. has a direction.
d. all of the above
e. none of the above.
Ans: d
6. Which of the following is a vector quantity?
a. velocity of a runner in the 100-meter dash
b. one week
c. a troy ounce
d. insulation efficiency ratings
e. lipstick colors
Ans: a
7. Vectors can be added
a. by just adding the scalar quantities together.
b. by the head and tail method of graphically connecting the head of one
vector to the tail of a second, and then drawing the sum as a new arrow
that extends from the origin of the first arrow to the tip of the second
vector.
c. by summing all the x components of the vectors and then summing all the
y components.
d. b and c
e. a and c
Ans: d
8. A jet plane flies due north for 3 hours at 600 miles per hour. It flies into a wind of
50 miles an hour due south for the first 2 hours. No significant wind is
encountered in the third hour. Where is the jet located after 3 hours?
a. 1200 miles north of its original position
b. 1500 miles north of its original position
c. 1700 miles north of its original position
d. 1800 miles north of its original position
e. 2100 miles north of its original position
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Ans: c
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9. A jet flies at 500 mph for 2 and a half hours due east. A brisk wind from the north
of 60 miles per hour blows during the entire time. Where is the plane located after
2 and a half hours of flight?
a. 1400 miles east
b. 1400 miles east and 150 miles south
c. 1250 miles east and 150 miles south
d. 1250 miles east and 120 miles south
e. 1100 miles east and 120 miles south
Ans: c
10. A plane flies within a jet stream that is moving at 100mph. The plane is moving at
500 mph relative to this jet stream. Both the plane and the jet stream travel due
east for 4 hours. How far does the plane travel in this time?
a. 1600 miles east
b. 1800 miles west
c. 2000 miles east
d. 2200 miles east
e. 2400 miles east
Ans: c
11. A swimmer traveling at 2 meters per second swims across a river 50 meters wide.
The current is flowing downstream at 3 meters per second. How far down the
stream will the swimmer end up when she reaches the other side?
a. 25 meters
b. 50 meters
c. 62.5 meters
d. 75 meters
e. 98 5 meters
Ans: d
12. Which of these does NOT show a direct relationship?
a. price of gas per gallon
b. age and height
c. acceleration and force
d. A = kB
e. all of the above
Ans: b
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13. In nature, if one variable decreases as another variable increases, the relationship
between the variables is
a. vectors.
b. inverse.
c. direct.
d. scalared.
e. none of the above
Ans: b
A solid object is dropped from rest from a great height. The following data is
collected:
Distance
Time (s)
Fallen (m)
0
0
1
5.2
2
20.1
3
44.8
4
79.3
5
122
14. Which of the below curves best depicts the data?
Time
Distanc
e
c.
Distanc
e
b.
Distanc
e
a.
Time
Time
Ans: a
15. The formula that best describes the data (where k is a constant and n is any
number) is
a. A  k  B
k
b. A 
B
c. A  k  B n
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d. A 
k
Bn
Ans: c
16. You may notice that none of the above formulae perfectly describes the data set.
What does this mean?
a. None of the formulae above is of any use
b. Small differences between a formula and a set of data are of no
importance
c. The (best) formula is an approximation of the motion
Ans: c
17. Power law equations describe situations in nature in which
a.
b.
c.
d.
e.
one variable is stronger than another variable.
three variables all change inversely.
variables cancel each other out.
one variable changes more quickly than another.
two variables have a direct relationship.
Ans: d
18. Which is an example of an inverse square relationship?
a. I = k/D2
b. I = kD2
c. distance and time
d. light intensity and light wave units
e. age and height
Ans: a
19. What are the two systems of units in the United States?
a. English system and System Etats Unis
b. metric system and Systeme Internationale
c. SI system and International System
d. International System and English system
e. all of the above
Ans: d
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20. Which phrase describes a liter?
a. the volume enclosed by a cube 10 centimeters on a side
b. the volume enclosed by 1000 cubes with sides each one centimeter long
c. 0.264 gallons
d. a commonly used metric unit in the United States
e. all of the above
Ans: e
21. The metric system is a product of
a. the French Revolution.
b. the Magna Carta.
c. a Babylonian mina.
d. King John of England.
e. French trade fairs.
Ans: a
22. Which of the following defines the kilogram?
a. wave crests of light
b. mass of an alloy kept in a vault in Paris
c. length of a rod of iridium and platinum.
d. radiation from a krypton atom
e. distance divided by time
Ans: b
23. Which of the following defines a meter?
a. 3.281 feet
b. distance between two marks on a particular bar of metal
c. the length of 1,650,763.73 wave lengths of the radiation from a krypton
atom
d. how far light travels in (1/299,792, 485) of a second
e. all of the above
Ans: e
In the 18th century, some astronomers suggested that the spacings
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between the planets is not random, but rather follows a pattern or series of numbers
named Bode’s Law. Take the series of numbers 0, 3, 6, 12, 24…, add 4 to each number,
and
divide each result by 10. Then compare the answers to the average distances of the
planets from the Sun as measured in Astronomical Units (AU), one AU being the average
distance of the Earth from the Sun:
Planet
Mercury
Venus
Earth
Mars
?
Jupiter
Saturn
Uranus
Neptune
Pluto
Bode’s Law (AU)
0.4
0.7
1.0
1.6
2.8
5.2
10.0
19.6
38.8
77.2
Distance
From Sun (AU)
0.39
0.72
1.00
1.52
?
5.20
9.53
?
?
?
24. The planet Uranus was discovered in 1786, soon after Bode’s Law was published.
Its distance from the Sun was established to be 19.2 AU. How do you think other
astronomers reacted?
a. Bode’s Law is a fundamental law of nature
b. Bode’s Law has nothing to do with the spacings of the orbits of the planets
c. Astronomers should continue look for other planets to see if they too obey
Bode’s Law
Ans: c
25. After the discovery of Uranus, astronomers began looking for a planet in
the gap between Mars and Jupiter. Ceres was discovered in 1801 with a distance
of 2.77 AU from the Sun. How would you have reacted as an astronomer of that
time?
a. Bode’s Law has once again been confirmed
b. Bode’s Law has nothing to do with the spacings of the orbits of the planets
c. Astronomers should continue to look for other planets to see if they too
obey Bode’s Law
Ans: c
26. Several other objects (Juno, Vesta, Pallas etc.) were found within a few
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years of the discovery of Ceres and all had orbital distances near 2.8 AU.
Futhermore, the objects were all much smaller than other planets, or even our own
Moon. How might you have reacted as an astronomer of that time?
a. Bode’s Law still applies to the orbits of planets
b. Bode’s Law still applies, but now we need to rethink our conceptions of
what planets are
c. Bode’s Law cannot apply, since there are no planets at 2.8 AU from the
Sun
d. Bode’s Law never applied in the first place
Ans: b
27. In the 1840’s, some astronomers noted slight discrepancies in the orbit
of Uranus. One suggestion was that the gravity of an unknown planet beyond the
orbit of Uranus was affecting the motion of Uranus. What was the predicted
average distance of the “new” planet from the Sun?
a. 2.8 AU
b. 19.6 AU
c. 38.8 AU
d. 77.2 AU
Ans: c
28. When Neptune was discovered in 1846, its average distance from the Sun was
found to be 30.1 AU. How might you have reacted as an astronomer of that time?
a. Bode’s Law was confirmed once again
b. Neptune’s orbit is not so far off from Bode’s Law to say that the law is
invalid
c. Bode’s Law was disproved and has no value as a scientific model
d. Bode’s Law never applied in the first place
Ans: b
29. Pluto was discovered in 1930 and has an average distance of 39.5 AU
from the Sun. Furthermore, its orbit is highly eccentric, occasionally bringing it
closer to the Sun than Neptune. What do you believe modern astronomers think of
Bode’s Law?
a. While Bode’s Law is incorrect, it does point out that planets tend to have
large spaces between their orbits
b. Bode’s Law has been completely invalidated by the observations and has
nothing of value to offer us
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c. Bode’s Law never had any theoretical or observational basis and has
nothing of value to offer us
Ans: a
30. The number 7.93 x 10-3 can also be written as
a. 3.00793.
b. 0.000793.
c. $7.93.
d. 7.93 millimeters.
e. 0.00793
Ans: e
31. The number 5,398,000,000 can also be written as
a. 5.398 x 10-7
b. 53.98 x 107
c. 5.398 x 108
d. 53. 98 x 108
e. five billion three-hundred and ninety-eight thousand
Ans: d
32. 106 x 104 equals
a. 2400
b. 2400000000
c. 100
d. 10,000,000,000
e. 100,000,000,000
Ans: d
33. Which is the unit of mass in the metric system?
a. pound
b. erg
c. kilogram
d. liter
e. carat
Ans: c
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34. 104 x 10-3 pounds is equal to how many kilograms? (1 kg = 2.2 lbs)
a. 2.46
b. 3.65
c. 4.54
d. 5.16
e. 5.43
Ans: c
35. What units would you use to measure precious metals?
a. knot
b. troy ounce
c. carat
d. caliber
e. any one of the above
Ans: b
36. What is the relationship between a cubic centimeter and a gram?
a. They are equal.
b. The cubic centimeter is larger than the gram.
c. The gram weighs more than the cubic centimeter.
d. They are inversely proportional.
e. None of the above.
Ans: e
37. What is the approximate distance between Montreal and Quebec, if the distance is
250 kilometers? (1 mile = 1.6 km)
a. 500 miles
b. 1.55 x 103 miles
c. 200 miles
d. 150 miles
e. 100 miles
Ans: d
38. (4 x 106) divided by (2 x 104) =
a. 80
b. 800
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c. 2 x1010
d. 200
e. 2 x 10-2
Ans: d
39. In the list below, which is the largest amount of money?
a. six giga dollars
b. 4.3 x 1012 dollars
c. $500 per day for 12 years
d. (7.2 x 107) + (8.9 x 106) dollars
e. 5,000 mega dollars
Ans: b
Review the graphs below to answer the following questions about stars:
Radius vs. Mass of Nearby Stars
2.5
Radius (Solar Radii)
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
Mass (Solar Masses)
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Distance vs. Mass for Nearby Stars
8
Distance from Earth (parsecs)
7
6
5
4
3
2
1
0
0
0.5
1
1.5
2
2.5
3
Mass (Solar Masses)
40. Based on the graph of star radii vs. star masses, what can you
conclude about the relationship between these two quantities?
a. It shows a direct relationship
b. It shows an inverse relationship
c. It shows a power law relationship
d. It shows an inverse square relationship
e. It shows no relationship at all
Ans: a
41. Is this result surprising or not, and why?
a. Surprising; there is no reason why any object should be larger across
because it weighs more
b. Surprising; stars are such complex objects that such a simple relationship
should not be expected
c. Not surprising; most objects in nature are larger if they weigh more
d. Not surprising; stars are easy to describe and model
Ans: c
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42. Based on the graph of star distances (i.e. distances of the stars from
the Earth) vs. star masses, what can you conclude about the relationship between
these two quantities?
a. It shows a direct relationship
b. It shows an inverse relationship
c. It shows a power law relationship
d. It shows an inverse square relationship
e. It shows no relationship at all
Ans: e
43. Is this result surprising or not, and why?
a. Surprising; the weight of an object usually depends on its distance from us
b. Surprising; there is always some kind of relationship between two
variables
c. Not surprising; there is no reason why an object’s weight should depend
on its distance from us
c
d. Not surprising; the data is not very good and we can’t derive relationships
if this is the case
Ans: c
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Luminosity vs. Temperature
25
Luminosity (solar luminosities)
20
15
10
5
0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Temperature (kelvins)
Log (L) vs. Log (T)
2
1
0
3.4
3.5
3.6
3.7
3.8
3.9
Log (L)
-1
-2
-3
-4
-5
-6
Log (T)
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44. Based on the graph of star luminosities (i.e. brightnesses) vs. star
temperatures, what can you conclude about the relationship between these two
quantities?
a. It shows a direct relationship
b. It shows an inverse relationship
c. It shows a power law relationship
c
d. It shows an inverse square relationship
e. It shows no relationship at all
Ans: c
45. What is your opinion on the usefulness of the luminosity vs. temperature graph?
a. The range of numbers makes it difficult to fully comprehend the
relationship
b. The relationship is very easy to read from the graph
c. It is obvious that there is no relationship between the variables
Ans: a
Astronomers often use base 10 logarithms. A base 10 logarithm states
how many times one needs to multiply the number 10 by itself in order to produce a
specified value. For example, 100 equals 10 times 10, so the base ten log of 100 is 2.
Obviously, not all numbers are multiples of 10, but logarithms can be extended to all real
numbers.
46. In your opinion, which graph is easier to understand?
a. The luminosity vs. temperature graph is easier to understand
b. The log (L) vs. log (T) graph is easier to understand
c. It makes no difference; each graph is equally understandable
Ans: b
47. A straight line on a log-log graph implies a power law relationship. What does the
log (L) vs. log (T) graph suggest?
a. There is no relationship at all between luminosity and temperature
b. Luminosity and temperature are indeed related by a power law
c. Luminosity and temperature are related, but by some other type of
relationship
Ans: b
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The following questions refer to a hypothetical trip from Atlanta to Columbia, SC,
and then to Charleston, WV. The distance from Atlanta to Columbia is about 300
kilometers along an east-west road (highway 20), and the distance from Columbia
to Charleston is about 400 km along a north-south road (Hwy 77).
Charleston
Atlanta
Columbia
48. To find the total driving distance from Atlanta to Columbia to Charleston requires
the use of _____; to find the net (direct) distance from Atlanta to Charleston
requires the use of _____.
a. Scalars; vectors
b. Scalars; scalars
c. Vectors; scalars
d. Vectors; vectors
Ans: a
49. What is the net distance from Atlanta to Charleston?
a. 300 km
b. 400 km
c. 500 km
d. 700 km
Ans: c
50. Which of the following could be used to estimate the net distance from Atlanta to
Charleston?
a. Sketch a scale drawing (as above) and measure the distance directly
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b. Use the Pythagorean Theorem to calculate the distance
c. Fly in an airplane directly between the two cities
d. All of the above
Ans: d
51. Suppose you take a different route instead (perhaps from Atlanta to Nashville to
Frankfort, KY, and then to Charleston). What happens to the distances involved?
a. The driving distance increases but the net distance is unaffected
b. The net distance increases but the driving distance is unaffected
c. Changing routes does not affect either type of distance
Ans: a
52. Since different people use different systems (units) of measurement,
why define an international standard at all?
a. It keeps scientists busy and out of trouble
b. No reason; each discipline has its own units and ignores the international
standard anyway
c. Nobody could ultimately compare measurements in any meaningful way
without a common standard
d. It helps bring different peoples together
Ans: c
53. Which of the following is an argument for changing United States measurements
entirely to the metric system?
a. It will promote international trade
b. It will produce immediate savings for government and business
c. It promotes strife amongst different nations
d. It will make measurements less understandable to non-scientists
Ans: a
54. Which of the following is an argument for keeping the United States on the
English system?
a. This is the way we have always measured quantities
b. The metric system is counterintuitive
c. The cost of conversion to the metric system will be prohibitive
d. It works on a base-ten number system
Ans: c
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55. Why might scientists decide to use other units besides the SI units?
a. The quantities they measure can’t be expressed in SI units
b. Scientists are stubborn and don’t wish to change
c. Scientists are unable to make conversions between different units
d. Some quantities are easier to understand in other (non-SI) units
Ans: d
56. What is a reason for using prefixes and/or powers of ten notation for expressing
numbers?
a. Some numbers are easier to understand by expressing them this way
b. Scientists are fond of using Latin and Greek words
c. We have ten fingers (or ten toes), which makes it easier to count
d. Scientists prefer to use obscure jargon
Ans: a
True or False
1. To be scientifically literate, a person must understand the specialized jargon that
scientists use.
Ans: False
2. The mass of stars is measured in scalars.
Ans: True
3. A vector has both a magnitude and a direction.
Ans: True
4. A runner’s time on a 100-meter race will be longer than that same runner’s time
on 100-yard race, when all other variables are kept constant.
Ans: True
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5. The intensity of light at the Earth’s surface is inversely proportional to the
distance from the Sun.
Ans: True
6. Vectors are used to describe objects in motion.
Ans: True
7. The metric and the English systems have different units for time, distance and
mass.
Ans: False
8. Scientists work exclusively in the metric system
Ans: False
9. A kilogram is to a dekagram as a megameter is to a hectometer.
Ans: True
10. A deciliter is to dekaliter as a nanosecond is to a centisecond.
Ans: False
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