# Chapter 2: the Language of Science

Chapter 2: The Language of Science

## Multiple Choice Questions

- The purpose of mathematical equations in science is to
- prove how difficult science can be.
- help nonscientists understand the physical world.
- provide a common language for all scientists.
- serve as a qualitative description of nature.
- all of the above.

Ans: c

- Which of the following, according to your text, is an attribute of a “useful” language?
- communicates without ambiguity
- contains no more than a thousand words
- includes specialized vocabularies for complex systems
- a and c
- all of the above

Ans: d

- How do scientists describe the physical world?
- tables
- graphs
- words
- equations
- all of the above

Ans: e

- Which of the following is a scalar?
- three blocks west
- 30 59’45” North Latitude
- 30 miles per hour to the East
- 98.6 F
- none of the above are scalars

Ans: d

- A vector
- is a mathematical quantity.
- has a magnitude.
- has a direction.
- all of the above
- none of the above.

Ans: d

- Which of the following is a vector quantity?
- velocity of a runner in the 100-meter dash
- one week
- a troy ounce
- insulation efficiency ratings
- lipstick colors

Ans: a

- Vectors can be added
- by just adding the scalar quantities together.
- 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.
- by summing all the x components of the vectors and then summing all the y components.
- b and c
- a and c

Ans: d

- 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?
- 1200 miles north of its original position
- 1500 miles north of its original position
- 1700 miles north of its original position
- 1800 miles north of its original position
- 2100 miles north of its original position

Ans: c

- 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?
- 1400 miles east
- 1400 miles east and 150 miles south
- 1250 miles east and 150 miles south
- 1250 miles east and 120 miles south
- 1100 miles east and 120 miles south

Ans: c

- 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?
- 1600 miles east
- 1800 miles west
- 2000 miles east
- 2200 miles east
- 2400 miles east

Ans: c

- 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?
- 25 meters
- 50 meters
- 62.5 meters
- 75 meters
- 98 5 meters

Ans: d

- Which of these does NOT show a direct relationship?
- price of gas per gallon
- age and height
- acceleration and force
- A = kB
- all of the above

Ans: b

- In nature, if one variable decreases as another variable increases, the relationship between the variables is
- vectors.
- inverse.
- direct.
- scalared.
- 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

- Which of the below curves best depicts the data?

a.b.c.

Ans: a

15. The formula that best describes the data (where k is a constant and n is any number) is

a.

b.

c.

d.

Ans: c

- You may notice that none of the above formulae perfectly describes the data set. What does this mean?
- None of the formulae above is of any use
- Small differences between a formula and a set of data are of no importance
- The (best) formula is an approximation of the motion

Ans: c

- Power law equations describe situations in nature in which

- 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

- Which is an example of an inverse square relationship?

- I = k/D2
- I = kD2
- distance and time
- light intensity and light wave units
- age and height

Ans: a

- What are the two systems of units in the United States?
- English system and System Etats Unis
- metric system and Systeme Internationale
- SI system and International System
- International System and English system
- all of the above

Ans: d

- Which phrase describes a liter?
- the volume enclosed by a cube 10 centimeters on a side
- the volume enclosed by 1000 cubes with sides each one centimeter long
- 0.264 gallons
- a commonly used metric unit in the United States
- all of the above

Ans: e

- The metric system is a product of
- the French Revolution.
- the Magna Carta.
- a Babylonian mina.
- King John of England.
- French trade fairs.

Ans: a

- Which of the following defines the kilogram?
- wave crests of light
- mass of an alloy kept in a vault in Paris
- length of a rod of iridium and platinum.
- radiation from a krypton atom
- distance divided by time

Ans: b

- Which of the following defines a meter?
- 3.281 feet
- distance between two marks on a particular bar of metal
- the length of 1,650,763.73 wave lengths of the radiation from a krypton atom
- how far light travels in (1/299,792, 485) of a second
- all of the above

Ans: e

In the 18th century, some astronomers suggested that the spacings

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:

Distance

Planet Bode’s Law (AU) From Sun (AU)

Mercury 0.4 0.39

Venus 0.7 0.72

Earth 1.0 1.00

Mars 1.6 1.52

? 2.8 ?

Jupiter 5.2 5.20

Saturn10.0 9.53

Uranus19.6 ?

Neptune38.8 ?

Pluto77.2 ?

- 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?
- Bode’s Law is a fundamental law of nature
- Bode’s Law has nothing to do with the spacings of the orbits of the planets
- Astronomers should continue look for other planets to see if they too obey Bode’s Law

Ans: c

- 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?

- Bode’s Law has once again been confirmed
- Bode’s Law has nothing to do with the spacings of the orbits of the planets
- Astronomers should continue to look for other planets to see if they too obey Bode’s Law

Ans: c

- Several other objects (Juno, Vesta, Pallas etc.) were found within a few

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?

- Bode’s Law still applies to the orbits of planets
- Bode’s Law still applies, but now we need to rethink our conceptions of what planets are
- Bode’s Law cannot apply, since there are no planets at 2.8 AU from the Sun
- Bode’s Law never applied in the first place

Ans: b

- 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?

- 2.8 AU
- 19.6 AU
- 38.8 AU
- 77.2 AU

Ans: c

- 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?

- Bode’s Law was confirmed once again
- Neptune’s orbit is not so far off from Bode’s Law to say that the law is invalid
- Bode’s Law was disproved and has no value as a scientific model
- Bode’s Law never applied in the first place

Ans: b

- 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?

- While Bode’s Law is incorrect, it does point out that planets tend to have large spaces between their orbits
- Bode’s Law has been completely invalidated by the observations and has nothing of value to offer us
- Bode’s Law never had any theoretical or observational basis and has nothing of value to offer us

Ans: a

- The number 7.93 x 10-3 can also be written as
- 3.00793.
- 0.000793.
- $7.93.
- 7.93 millimeters.
- 0.00793

Ans: e

- The number 5,398,000,000 can also be written as
- 5.398 x 10-7
- 53.98 x 107
- 5.398 x 108
- 53. 98 x 108
- five billion three-hundred and ninety-eight thousand

Ans: d

- 106 x 104 equals
- 2400
- 2400000000
- 100
- 10,000,000,000
- 100,000,000,000

Ans: d

- Which is the unit of mass in the metric system?
- pound
- erg
- kilogram
- liter
- carat

Ans: c

- 104 x 10-3 pounds is equal to how many kilograms? (1 kg = 2.2 lbs)
- 2.46
- 3.65
- 4.54
- 5.16
- 5.43

Ans: c

- What units would you use to measure precious metals?
- knot
- troy ounce
- carat
- caliber
- any one of the above

Ans: b

- What is the relationship between a cubic centimeter and a gram?
- They are equal.
- The cubic centimeter is larger than the gram.
- The gram weighs more than the cubic centimeter.
- They are inversely proportional.
- None of the above.

Ans: e

- What is the approximate distance between Montreal and Quebec, if the distance is 250 kilometers? (1 mile = 1.6 km)
- 500 miles
- 1.55 x 103 miles
- 200 miles
- 150 miles
- 100 miles

Ans: d

- (4 x 106) divided by (2 x 104) =
- 80
- 800
- 2 x1010
- 200
- 2 x 10-2

Ans: d

- In the list below, which is the largest amount of money?
- six giga dollars
- 4.3 x 1012 dollars
- $500 per day for 12 years
- (7.2 x 107) + (8.9 x 106) dollars
- 5,000 mega dollars

Ans: b

Review the graphs below to answer the following questions about stars:

- Based on the graph of star radii vs. star masses, what can you

conclude about the relationship between these two quantities?

- It shows a direct relationship
- It shows an inverse relationship
- It shows a power law relationship
- It shows an inverse square relationship
- It shows no relationship at all

Ans: a

- Is this result surprising or not, and why?

- Surprising; there is no reason why any object should be larger across because it weighs more
- Surprising; stars are such complex objects that such a simple relationship should not be expected
- Not surprising; most objects in nature are larger if they weigh more
- Not surprising; stars are easy to describe and model

Ans: c

- 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?

- It shows a direct relationship
- It shows an inverse relationship
- It shows a power law relationship
- It shows an inverse square relationship
- It shows no relationship at all

Ans: e

- Is this result surprising or not, and why?

- Surprising; the weight of an object usually depends on its distance from us
- Surprising; there is always some kind of relationship between two variables
- Not surprising; there is no reason why an object’s weight should depend on its distance from us c
- Not surprising; the data is not very good and we can’t derive relationships if this is the case

Ans: c

- Based on the graph of star luminosities (i.e. brightnesses) vs. star

temperatures, what can you conclude about the relationship between these two quantities?

- It shows a direct relationship
- It shows an inverse relationship
- It shows a power law relationshipc
- It shows an inverse square relationship
- It shows no relationship at all

Ans: c

- What is your opinion on the usefulness of the luminosity vs. temperature graph?

- The range of numbers makes it difficult to fully comprehend the relationship
- The relationship is very easy to read from the graph
- 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.

- In your opinion, which graph is easier to understand?

- The luminosity vs. temperature graph is easier to understand
- The log (L) vs. log (T) graph is easier to understand
- It makes no difference; each graph is equally understandable

Ans: b

- A straight line on a log-log graph implies a power law relationship. What does the log (L) vs. log (T) graph suggest?

- There is no relationship at all between luminosity and temperature
- Luminosity and temperature are indeed related by a power law
- Luminosity and temperature are related, but by some other type of relationship

Ans: b

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

###### AtlantaColumbia

- 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 _____.

- Scalars; vectors
- Scalars; scalars
- Vectors; scalars
- Vectors; vectors

Ans: a

- What is the net distance from Atlanta to Charleston?

- 300 km
- 400 km
- 500 km
- 700 km

Ans: c

- Which of the following could be used to estimate the net distance from Atlanta to Charleston?

- Sketch a scale drawing (as above) and measure the distance directly
- Use the Pythagorean Theorem to calculate the distance
- Fly in an airplane directly between the two cities
- All of the above

Ans: d

- 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?

- The driving distance increases but the net distance is unaffected
- The net distance increases but the driving distance is unaffected
- Changing routes does not affect either type of distance

Ans: a

- Since different people use different systems (units) of measurement,

why define an international standard at all?

- It keeps scientists busy and out of trouble
- No reason; each discipline has its own units and ignores the international standard anyway
- Nobody could ultimately compare measurements in any meaningful way without a common standard
- It helps bring different peoples together

Ans: c

- Which of the following is an argument for changing United States measurements entirely to the metric system?

- It will promote international trade
- It will produce immediate savings for government and business
- It promotes strife amongst different nations
- It will make measurements less understandable to non-scientists

Ans: a

- Which of the following is an argument for keeping the United States on the English system?

- This is the way we have always measured quantities
- The metric system is counterintuitive
- The cost of conversion to the metric system will be prohibitive
- It works on a base-ten number system

Ans: c

- Why might scientists decide to use other units besides the SI units?

- The quantities they measure can’t be expressed in SI units
- Scientists are stubborn and don’t wish to change
- Scientists are unable to make conversions between different units
- Some quantities are easier to understand in other (non-SI) units

Ans: d

- What is a reason for using prefixes and/or powers of ten notation for expressing numbers?

- Some numbers are easier to understand by expressing them this way
- Scientists are fond of using Latin and Greek words
- We have ten fingers (or ten toes), which makes it easier to count
- Scientists prefer to use obscure jargon

Ans: a

True or False

- To be scientifically literate, a person must understand the specialized jargon that scientists use.

Ans: False

- The mass of stars is measured in scalars.

Ans: True

- A vector has both a magnitude and a direction.

Ans: True

- 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

- The intensity of light at the Earth’s surface is inversely proportional to the distance from the Sun.

Ans: True

- Vectors are used to describe objects in motion.

Ans: True

- The metric and the English systems have different units for time, distance and mass.

Ans: False

- Scientists work exclusively in the metric system

Ans: False

- A kilogram is to a dekagram as a megameter is to a hectometer.

Ans: True

- A deciliter is to dekaliter as a nanosecond is to a centisecond.

Ans: False