only the circles questions
2
Home Experiments and Observations
15
E5. A woman’s foot is 9 inches long. If she steps off the length
of a room by placing one foot directly in front of the other,
and finds the room to be 15 foot-lengths long, what is the
length of the room in inches? In feet?
E6. A book is 220 mm in width. What is this width in centime-
ters? In meters?
E7. A crate has a mass of 8.60 kg (kilograms). What is this
mass in grams? In milligrams?
E8. A tank holds 2.18 KL (kiloliters) of water. How many liters
is this? How many milliliters?
E9. A mile is 5280 ft long. The sample exercise in example
box 1.2 shows that 1 foot is approximately 0.305 m. How
many meters are there in a mile? How many kilometers
(km) are there in a mile?
E10. If a mile is 5280 ft long and a yard contains 3 ft, how many
yards are there in a mile?
E11 Area is found by multiplying the length of a surface times
the width. If a floor measures 6.25 m², how many square
centimeters does this represent? How many square cen-
timeters are there in 1 m??
E12. A common speed limit in Vancouver, British Columbia, is
80 km/hr. If you are going 55 MPH, are you speeding?
Show by converting 55 MPH to km/hr using the conversion
factors on the inside front cover.
E13. If gas costs 80¢ a liter, how much does a gallon of gas
cost? Show by converting gallons to liters using the conver-
sion factors on the inside front cover.
synthesis problems
SP1) Astrologers claim that they can predict important events in
your life by the configuration of the planets and the astro-
logical sign under which you were born. Astrological pre-
dictions, called horoscopes, can be found in most daily
newspapers. Find these predictions in a newspaper and ad-
dress the questions:
a. Are the astrological predictions testable?
b. Choosing the prediction for your own sign, how would
you go about testing its accuracy over the next month
or so?
c. Why do newspapers print these readings? What is their
appeal?
SP2) In the United States a common quantity of hard liquor was
historically a fifth, which represents a fifth of a US gallon.
However, since the US wants to market its alcohol globally,
and everyone else uses the metric system, it has retooled its
packaging, so a common quantity is now 750 ml.
a. How many liters are in a fifth?
b. How many milliliters are in a fifth?
c. Which is larger, 750 ml or a fifth of a gallon?
SP3.) An energy-efficient bulb claims to have the brightness of a
75W bulb but only uses 15W of electrical power.
a. If you have this light bulb on for 5 hours a day, for 350
days during a year, how many hours is it on?
b. A kilowatt is 1000 watts. The kilowatt-hour is a com-
mon unit for energy, obtained by multiplying the power
in kilowatts by the time used in hours. How many kilo-
watt-hours (kWh) will you use when burning the 75W
bulb for the year?
c. How many kilowatt-hours (kWh) will you use when
burning the 15W bulb for the year?
d. Assuming that the cost of electricity is 15° per kWh,
what is the cost of using the 75W bulb for the year?
e. Assuming this same cost, what is the cost of using the
15W bulb for the year?
f. How much do you save by using the 15W bulb?
g. How much would you save if you replaced 20 of the
75W bulbs with the 15W bulbs?
home anoniments and honotions
14
Chapter 1 Physics, the Fundamental Science
questions
* = more open-ended questions, requiring lengthier responses, suitable
for group discussion
Q = sample responses are available in appendix D
Q = sample responses are available on the website
*Q1. Which of these criteria best distinguish between explana-
tions provided by science and those provided by religion:
truth, testability, or appeal to authority? How do religious
explanations differ from scientific explanations?
Q2. A person claiming to have paranormal powers states that
she can predict which card will come up next in a shuffled
deck of cards simply by exercising her mental powers. Is
this a testable claim? Explain.
Q3. Historians sometimes develop theories to explain observed
patterns in the history of different countries. Are these theo-
ries testable in the same sense as a theory in physics?
Explain.
*Q4. Over the years, there have been several credible claims by
experienced observers of sightings of Unidentified Flying
Objects (UFOs). Despite this, scientists have shied away
from taking up serious study of UFOs, although there are
ongoing searches for signals from extraterrestrial intelligent
beings. Can you think of reasons why scientists have not
taken UFOs seriously? What problems can you see in try-
ing to study UFOs?
Q5. Suppose that your car will not start and you form the hy-
pothesis that the battery is dead. How would you test this
hypothesis? Explain.
Q6. Suppose that your phone has not rung in several days, but a
friend tells you he has tried to call. Develop two hypothe-
ses that could explain why the phone has not rung and state
how you would test these hypotheses.
*Q7. Suppose that a friend states the hypothesis that the color of
socks that he wears on a given day, brown or black, will
determine whether the stock market will go up or down. He
can cite several instances in which this hypothesis has been
apparently verified. How would you go about evaluating
this hypothesis?
Q8. Which of the three science fields: biology, chemistry, or
physics, would you say is the most fundamental? Explain
by describing in what sense one of these fields may be
more fundamental than the others.
Q9. Based upon the brief descriptions provided in table 1.2,
which subfield of physics would you say is involved in the
explanation of rainbows? Which subfield is involved in
describing how an acorn falls? Explain.
Q10. Based upon the descriptions provided in table 1.2, which
subfields of physics are involved in explaining why an ice
cube melts? Which subfields are involved in explaining
how an airplane flies? Explain.
(Q11. Suppose that you are told that speed is defined by the rela-
tionship s = d/t, where s represents speed, d represents dis-
tance, and t represents time. State this relationship in
words, using no mathematical symbols.
Q12. Impulse is defined as the average force acting on an object
multiplied by the time the force acts. If we let I represent
impulse, F the average force, and the time, is 1 = Flt a
correct way of expressing this definition? Explain.
Q13. The distance that an object travels when it starts from rest
and undergoes constant acceleration is one-half the acceler-
ation multiplied by the square of the time. Invent your own
symbols and express this statement in symbolic form.
Q14. What are the primary advantages of the metric system of
units over the older English system of units? Explain.
Q15. What are the advantages, if any, of continuing to use the
English system of units in industry and commerce rather
than converting to the metric system? Explain.
Q16. Which system of units, the metric system or English sys-
tem, is used more widely throughout the world? Explain.
Q17. The width of a man’s hand was used as a common unit of
length several hundred years ago. What are the advantages
and disadvantages of using such a unit? Explain.
Q18. A pirate map indicates that a treasure is buried 50 paces
due east and 120 paces due north of a big rock. Will you
know where to dig? Explain.
Q19. List the following volumes in descending order: gallon, quart,
liter, milliliter. The conversion factors given on the inside
front cover may be useful.
Q20. List the following lengths in descending order: kilometer,
feet, mile, centimeter, inch. The conversion factors given on
the inside front cover may be useful.
exercises
E1. Suppose that a pancake recipe designed to feed three peo-
ple calls for 600 mL of flour. How many milliliters of flour
would you use if you wanted to extend the recipe to feed
five people?
E2. Suppose that a cupcake recipe designed to produce twelve
cupcakes calls for 900 mL of flour. How many milliliters
of flour would you use if you wanted to make only eight
cupcakes?
E3. It is estimated that six large pizzas are about right to serve
a physics club meeting of 30 students. How many pizzas
would be required if the group grows to 50 students?
E4 A man uses his hand to measure the width of a tabletop. If
his hand has a width of 12 cm at its widest point, and he
finds the tabletop to be 10.5 hands wide, what is the width
of the tabletop in cm? In meters?
34
Chapter 2 Describing Motion
4 Graphing motion. Graphs of distance, speed, velocity,
and acceleration plotted against time can illustrate relationships
between these quantities. Instantaneous velocity is equal to the
slope of the distance-time graph. Instantaneous acceleration is
equal to the slope of the velocity-time graph. The distance trav-
eled is equal to the area under the velocity-time graph.
5 Uniform acceleration. When an object accelerates at
a constant rate producing a constant-slope graph of velocity versus
time, we say that it is uniformly accelerated. Graphs help us to
understand the two formulas describing how velocity and distance
traveled vary with time for this important special case.
du
Wh
VO
V = V0 + at
d= vot+ jat2
key terms
Speed, 19
Average speed, 19
Rate, 20
Instantaneous speed, 21
Velocity, 22
Magnitude, 23
Vector, 24
Vector quantity, 24
Instantaneous velocity, 24
Acceleration, 25
Average acceleration, 25
Instantaneous acceleration, 26
Slope, 28
Uniform acceleration, 31
questions
* = more open-ended questions, requiring lengthier responses,
suitable for group discussion
Q = sample responses are available in appendix D
Q = sample responses are available on the website
Q1. Suppose that critters are discovered on Mars who measure
distance in boogles and time in bops.
a. What would the units of speed be in this system?
Explain.
b. What would the units of velocity be? Explain.
c. What would the units of acceleration be? Explain.
Q2. Suppose that we choose inches as our basic unit of dis-
tance and days as our basic unit of time.
a. What would the units of velocity and acceleration be in
this system? Explain.
b. Would this be a good choice of units for measuring the
acceleration of an automobile? Explain.
whereas the tortoise plods along steadily and finishes the
race ahead of the hare.
a. Which of the two racers has the greater average speed
over the duration of the race? Explain.
b. Which of the two racers is likely to reach the greatest
instantaneous speed during the race? Explain.
Q5.) A driver states that she was doing 80 when stopped by the
police. Is that a clear statement? Would this be interpreted
differently in England than it would be in the United
States? Explain.
Q6. Does the speedometer on a car measure average speed or
instantaneous speed? Explain.
Q7. Is the average speed over several minutes more likely to
be close to the instantaneous speed at anytime for a car
traveling in freely flowing, low-density traffic or for one
traveling in high-density traffic? Explain.
*Q8. The highway patrol sometimes uses radar guns to identify
possible speeders and at other times uses associates in air-
planes who note the time taken for a car to pass between
two marks some distance apart on the highway. What do each
of these methods measure, average speed or instantaneous
Q3. What units would have an appropriate size for measuring
the rate at which fingernails grow? Explain.
Q4. A tortoise and a hare cover the same distance in a race. The
hare goes very fast for brief intervals, but stops frequently,
36
Chapter 2 Describing Motion
Q26. The velocity-versus-time graph of an object curves as
shown in the diagram. Is the acceleration of the object
constant? Explain.
v
less than the distance covered during the second 5 sec-
onds? Explain.
Q29. A car starts from rest, accelerates uniformly for 5 seconds,
travels at constant velocity for 5 seconds, and finally decel-
erates uniformly for 5 seconds. Sketch graphs of velocity
versus time and acceleration versus time for this situation.
Q30. Suppose that two runners run a 100-meter dash, but the
first runner reaches maximum speed more quickly than the
second runner. Both runners maintain constant speed once
they have reached their maximum speed and cross the fin-
ish line at the same time. Which runner has the larger
maximum speed? Explain.
Q31. Sketch a graph showing velocity-versus-time curves for the
two runners described in question 30. (Sketch both curves
on the same graph, so that the differences are apparent.)
*Q32. A physics instructor walks with increasing speed across
the front of the room then suddenly reverses direction and
walks backward with constant speed. Sketch graphs of
velocity and acceleration consistent with this description.
t
Q26 Diagram
Q27. For a uniformly accelerated car, is the average acceleration
equal to the instantaneous acceleration? Explain.
Q28. A car traveling in the forward direction experiences a neg-
ative uniform acceleration for 10 seconds. Is the distance
covered during the first 5 seconds equal to, greater than, or
exercises
E1. A traveler covers a distance of 460 miles in a time of 8 hours.
What is the average speed for this trip?
E2. A walker covers a distance of 1.8 km in a time of 30 min-
utes. What is the average speed of the walker for this dis-
tance in km/h?
E3. Grass clippings are found to have an average length of
4.8 cm when a lawn is mowed 12 days after the previous
mowing. What is the average speed of growth of this grass
in cm/day?
E4. A driver drives for 2.5 hours at an average speed of 54 MPH.
What distance does she travel in this time?
E5. A woman walks a distance of 240 m with an average speed
of 1.2 m/s. What time was required to walk this distance?
E6. A person in a hurry averages 62 MPH on a trip covering
a distance of 300 miles. What time was required to travel
that distance?
E12. The velocity of a car decreases from 30 m/s to 18 m/s in a
time of 4 seconds. What is the average acceleration of the
car in this process?
E13) A car traveling with an initial velocity of 12 m/s acceler-
ates at a constant rate of 2.5 m/s2 for a time of 2 seconds.
a. What is its velocity at the end of this time?
b. What distance does the car travel during this process?
E14. A runner traveling with an initial velocity of 2.0 m/s accel-
erates at a constant rate of 1.2 m/s2 for a time of 2 seconds.
a. What is his velocity at the end of this time?
b. What distance does the runner cover during this process?
E15. A car moving with an initial velocity of 30 m/s slows down
at a constant rate of – 3 m/s2.
a. What is its velocity after 3 seconds of deceleration?
b. What distance does the car cover in this time?
E16. A runner moving with an initial velocity of 4.0 m/s slows
down at a constant rate of -1.5 m/s2 over a period of
2 seconds.
a. What is her velocity at the end of this time?
b. What distance does she travel during this process?
E17. If a world-class sprinter ran a distance of 100 meters start-
ing at his top speed of 11 m/s and running with constant
speed throughout, how long would it take him to cover the
distance?
E18. Starting from rest, a car accelerates at a constant rate of
3.0 m/s2 for a time of 5 seconds.
a. Compute the velocity of the car at 1 s, 2 s, 3 s, 4 s, and
5 s and plot these velocity values against time.
b. Compute the distance traveled by the car for these same
times and plot the distance values against time.
E7) A hiker walks with an average speed of 1.2 m/s. What
distance in kilometers does the hiker travel in a time of
1 hour?
E8. A car travels with an average speed of 22 m/s.
a. What is this speed in km/s?
b. What is this speed in km/h?
E9. A car travels with an average speed of 58 MPH. What is
this speed in km/h? (See example box 2.1.)
E10. Starting from rest and moving in a straight line, a runner
achieves a velocity of 7 m/s in a time of 2 s. What is the
average acceleration of the runner?
E11. Starting from rest, a car accelerates at a rate of 4.2 m/s2 for
a time of 5 seconds. What is its velocity at the end of this
time?
4
Questions
35
Q19. A car moves along a straight line so that its position (dis-
tance from some starting point) varies with time as de-
scribed by the graph shown here.
a. Does the car ever go backward? Explain.
b. Is the instantaneous velocity at point A greater or less
than that at point B? Explain.
da
B
Q19 Diagram
speed? Can you think of situations in which either one
of these methods might unfairly penalize a driver? Explain.
29. A ball is thrown against a wall and bounces back toward
the thrower with the same speed as it had before hitting the
wall. Does the velocity of the ball change in this process?
Explain.
Q10. A ball attached to a string is whirled in a horizontal circle
such that it moves with constant speed.
a. Does the velocity of the ball change in this process?
Explain.
b. Is the acceleration of the ball equal to zero? Explain.
*Q11. A ball tied to a string fastened at the other end to a rigid
support forms a pendulum. If we pull the ball to one side
and release it, the ball moves back and forth along an arc
determined by the string length.
a. Is the velocity constant in this process? Explain.
b. Is the speed likely to be constant in this process? What
happens to the speed when the ball reverses direction?
Q12. A dropped ball gains speed as it falls. Can the velocity of
the ball be constant in this process? Explain.
Q13) A driver of a car steps on the brakes, causing the velocity
of the car to decrease. According to the definition of accel-
eration provided in this chapter, does the car accelerate in
this process? Explain.
Q14. At a given instant in time, two cars are traveling at different
velocities, one twice as large as the other. Based upon this
information is it possible to say which of these two cars
has the larger acceleration at this instant in time? Explain.
Q15. A car just starting up from a stop sign has zero velocity at
the instant that it starts. Must the acceleration of the car
also be zero at this instant? Explain.
Q16. A car traveling with constant speed rounds a curve in the
highway. Is the acceleration of the car equal to zero in this
situation? Explain.
Q17. A racing sports car traveling with a constant velocity of
100 MPH due west startles a turtle by the side of the road
who begins to move out of the way. Which of these two
objects is likely to have the larger acceleration at that
instant? Explain.
Q18. In the graph shown here, velocity is plotted as a function
of time for an object traveling in a straight line.
a. Is the velocity constant for any time interval shown?
Explain.
b. During which time interval shown does the object have
the greatest acceleration? Explain.
Q20. For the car whose distance is plotted against time in ques-
tion 19, is the velocity constant during any time interval
shown in the graph? Explain.
Q21. A car moves along a straight section of road so that its
velocity varies with time as shown in the graph.
a. Does the car ever go backward? Explain.
b. At which of the labeled points on the graph, A, B, or
C, is the magnitude of the acceleration the greatest?
Explain.
V
B
с
A
2
4
6
t(s)
Q21 Diagram
VA
D
Q22. For the car whose velocity is plotted in question 21, in
which of the equal time segments 0-2 seconds, 2-4 sec-
onds, or 4-6 seconds, is the distance traveled by the car
the greatest? Explain.
Q23. Look again at the velocity-versus-time graph for the toy
car shown in figure 2.15.
a. Is the instantaneous speed greater at any time during
this motion than the average speed for the entire trip?
Explain.
b. Is the car accelerated when the direction of the car is
reversed at 1 = 50 s? Explain.
Q24. Suppose that the acceleration of a car increases with time.
Could we use the relationship v = v. + at in this situation?
Explain.
Q25. When a car accelerates uniformly from rest, which of these
quantities increases with time: acceleration, velocity, and/or
distance traveled? Explain.
2
4
6
8
t(s)
Q18 Diagram
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