ConcepTest 8.1a
Bonnie and Klyde I
Bonnie sits on the outer rim of a
merry-go-round, and Klyde sits
midway between the center and the
rim. The merry-go-round makes
one complete revolution every two
seconds.
Klyde’s angular velocity is:
a) same as Bonnie’s
b) twice Bonnie’s
c) half of Bonnie’s
d) 1/4 of Bonnie’s
e) four times Bonnie’s
w
Klyde
Bonnie
ConcepTest 8.1a
Bonnie and Klyde I
Bonnie sits on the outer rim of a
merry-go-round, and Klyde sits
midway between the center and the
rim. The merry-go-round makes
one complete revolution every two
seconds.
Klyde’s angular velocity is:
a) same as Bonnie’s
b) twice Bonnie’s
c) half of Bonnie’s
d) 1/4 of Bonnie’s
e) four times Bonnie’s
The angular velocity w of any point
w
on a solid object rotating about a
fixed axis is the same. Both Bonnie
and Klyde go around one revolution
Klyde
(2p radians) every two seconds.
Bonnie
ConcepTest 8.1b
Bonnie and Klyde II
Bonnie sits on the outer rim of a
merry-go-round, and Klyde sits
midway between the center and the
rim. The merry-go-round makes one
revolution every two seconds. Who
has the larger linear (tangential)
velocity?
a) Klyde
b) Bonnie
c) both the same
d) linear velocity is zero
for both of them
w
Klyde
Bonnie
ConcepTest 8.1b
Bonnie and Klyde II
Bonnie sits on the outer rim of a
merry-go-round, and Klyde sits
midway between the center and the
rim. The merry-go-round makes one
revolution every two seconds. Who
has the larger linear (tangential)
velocity?
a) Klyde
b) Bonnie
c) both the same
d) linear velocity is zero
for both of them
Their linear speeds v will be
w
different since v = Rw and
Bonnie is located further out
Klyde
(larger radius R) than Klyde.
1
VKlyde  VBonnie
2
Follow-up: Who has the larger centripetal acceleration?
Bonnie
ConcepTest 8.4
Using a Wrench
You are using a wrench to
loosen a rusty nut. Which
a)
b)
arrangement will be the
most effective in loosening
the nut?
c)
d)
e) all are equally effective
ConcepTest 8.4
Using a Wrench
You are using a wrench to
loosen a rusty nut. Which
a)
b)
arrangement will be the
most effective in loosening
the nut?
Since the forces are all the
same, the only difference is
the lever arm. The
arrangement with the largest
lever arm (case #2) will
provide the largest torque.
c)
d)
e) all are equally effective
Follow-up: What is the difference between arrangement 1 and 4?
ConcepTest 8.6
Closing a Door
In which of the cases shown below
a) FA
is the torque provided by the
b) FC
applied force about the rotation
axis biggest? For all cases the
magnitude of the applied force is
the same.
c) FD
d) all of them
e) none of them
ConcepTest 8.6
Closing a Door
In which of the cases shown below
a) FA
is the torque provided by the
b) FC
applied force about the rotation
axis biggest? For all cases the
magnitude of the applied force is
the same.
c) FD
d) all of them
e) none of them
The torque is: t = F d sin q and
so the force that is at 90° to the
lever arm is the one that will have
the largest torque. Clearly, to
close the door, you want to push
perpendicular!!
Follow-up: How large would the force have to be for FD?
ConcepTest 8.9
Moment of Inertia
Two spheres have the same radius and
equal masses. One is made of solid
aluminum, and the other is made from a
hollow shell of gold.
a) solid aluminum
b) hollow gold
c) same
Which one has the bigger moment of
inertia about an axis through its
center?
hollow
solid
same mass & radius
ConcepTest 8.9
Moment of Inertia
Two spheres have the same radius and
equal masses. One is made of solid
aluminum, and the other is made from a
hollow shell of gold.
a) solid aluminum
b) hollow gold
c) same
Which one has the bigger moment of
inertia about an axis through its
center?
Moment of inertia depends on
mass and distance from axis
squared. It is bigger for the
shell since its mass is located
farther from the center.
hollow
solid
same mass & radius
ConcepTest 8.10
Figure Skater
A figure skater spins with her arms
a) the same
extended. When she pulls in her arms,
she reduces her rotational inertia and b) larger because she’s rotating
faster
spins faster so that her angular
momentum is conserved. Compared to c) smaller because her rotational
her initial rotational kinetic energy, her
inertia is smaller
rotational kinetic energy after she pulls
in her arms must be
ConcepTest 8.10
Figure Skater
A figure skater spins with her arms
a) the same
extended. When she pulls in her arms,
she reduces her rotational inertia and b) larger because she’s rotating
faster
spins faster so that her angular
momentum is conserved. Compared to c) smaller because her rotational
her initial rotational kinetic energy, her
inertia is smaller
rotational kinetic energy after she pulls
in her arms must be
KErot=1/2 I w2 = 1/2 L w (used L= Iw ).
Since L is conserved, larger w
means larger KErot. The “extra”
energy comes from the work she
does on her arms.
Follow-up: Where does the extra energy come from?
ConcepTest 11.1a Harmonic Motion I
A mass on a spring in SHM has
a) 0
amplitude A and period T. What
b) A/2
is the total distance traveled by
c) A
the mass after a time interval T?
d) 2A
e) 4A
ConcepTest 11.1a Harmonic Motion I
A mass on a spring in SHM has
a) 0
amplitude A and period T. What
b) A/2
is the total distance traveled by
c) A
the mass after a time interval T?
d) 2A
e) 4A
In the time interval T (the period), the mass goes
through one complete oscillation back to the starting
point. The distance it covers is: A + A + A + A (4A).
ConcepTest 11.1b Harmonic Motion II
A mass on a spring in SHM has
amplitude A and period T. What is
the net displacement of the mass
after a time interval T?
a) 0
b) A/2
c) A
d) 2A
e) 4A
ConcepTest 11.1b Harmonic Motion II
A mass on a spring in SHM has
amplitude A and period T. What is
the net displacement of the mass
after a time interval T?
a) 0
b) A/2
c) A
d) 2A
e) 4A
The displacement is Dx = x2–x1. Since the
initial and final positions of the mass are the
same (it ends up back at its original position),
then the displacement is zero.
Follow-up: What is the net displacement after a half of a period?
ConcepTest 11.3b Spring Combination II
A spring can be stretched a distance of 60 cm
with an applied force of 1 N. If an identical
spring is connected in series with the first
spring, how much force will be required to
stretch this series combination a distance of
60 cm?
a) 1/4 N
b) 1/2 N
c) 1 N
d) 2 N
e) 4 N
ConcepTest 11.3b Spring Combination II
A spring can be stretched a distance of 60 cm
with an applied force of 1 N. If an identical
spring is connected in series with the first
spring, how much force will be required to
stretch this series combination a distance of
60 cm?
a) 1/4 N
b) 1/2 N
c) 1 N
d) 2 N
e) 4 N
Here, the springs are in series, so each spring is only stretched
30 cm, and only half the force is needed. But also, since the
springs are in a row, the force applied to one spring is transmitted
to the other spring (like tension in a rope). So the overall applied
force of 1/2 N is all that is needed. The combination of two springs
in series behaves like a weaker spring!!
ConcepTest 11.4 To the Center of the Earth
A hole is drilled through the
a) you fall to the center and stop
center of Earth and emerges
on the other side. You jump
into the hole. What happens
to you?
b) you go all the way through and
continue off into space
c) you fall to the other side of
Earth and then return
d) you won’t fall at all
ConcepTest 11.4 To the Center of the Earth
A hole is drilled through the
a) you fall to the center and stop
center of Earth and emerges
on the other side. You jump
into the hole. What happens
to you?
b) you go all the way through and
continue off into space
c) you fall to the other side of
Earth and then return
d) you won’t fall at all
You fall through the hole. When you reach the
center, you keep going because of your inertia.
When you reach the other side, gravity pulls
you back toward the center. This is Simple
Harmonic Motion!
Follow-up: Where is your acceleration zero?
ConcepTest 11.5a Energy in SHM I
A mass oscillates in simple
harmonic motion with amplitude
A. If the mass is doubled, but the
amplitude is not changed, what
will happen to the total energy of
the system?
a) total energy will increase
b) total energy will not change
c) total energy will decrease
ConcepTest 11.5a Energy in SHM I
A mass oscillates in simple
harmonic motion with amplitude
A. If the mass is doubled, but the
amplitude is not changed, what
will happen to the total energy of
the system?
a) total energy will increase
b) total energy will not change
c) total energy will decrease
The total energy is equal to the initial value of the
elastic potential energy, which is PEs = 1/2 kA2. This
does not depend on mass, so a change in mass will
not affect the energy of the system.
Follow-up: What happens if you double the amplitude?
ConcepTest 11.7c Spring on the Moon
A mass oscillates on a vertical
spring with period T. If the whole
setup is taken to the Moon, how
does the period change?
a) period will increase
b) period will not change
c) period will decrease
ConcepTest 11.7c Spring on the Moon
A mass oscillates on a vertical
spring with period T. If the whole
setup is taken to the Moon, how
does the period change?
a) period will increase
b) period will not change
c) period will decrease
The period of simple harmonic motion only depends on the
mass and the spring constant and does not depend on the
acceleration due to gravity. By going to the Moon, the value
of g has been reduced, but that does not affect the period of
the oscillating mass-spring system.
Follow-up: Will the period be the same on any planet?
ConcepTest 11.8a Period of a Pendulum I
Two pendula have the
same length, but different
masses attached to the
string. How do their
periods compare?
a) period is greater for the greater mass
b) period is the same for both cases
c) period is greater for the smaller mass
ConcepTest 11.8a Period of a Pendulum I
Two pendula have the
same length, but different
masses attached to the
string. How do their
periods compare?
a) period is greater for the greater mass
b) period is the same for both cases
c) period is greater for the smaller mass
The period of a pendulum depends on the length and the
acceleration due to gravity, but it does not depend on the
mass of the bob.
T = 2p (L/g)
Follow-up: What happens if the amplitude is doubled?
ConcepTest 11.9 Grandfather Clock
A grandfather clock has a
weight at the bottom of the
pendulum that can be moved
up or down. If the clock is
running slow, what should
you do to adjust the time
properly?
a) move the weight up
b) move the weight down
c) moving the weight will not matter
d) call the repair man
ConcepTest 11.9 Grandfather Clock
A grandfather clock has a
weight at the bottom of the
pendulum that can be moved
up or down. If the clock is
running slow, what should
you do to adjust the time
properly?
a) move the weight up
b) move the weight down
c) moving the weight will not matter
d) call the repair man
The period of the grandfather clock is too long, so we need to
decrease the period (increase the frequency). To do this, the length
must be decreased, so the adjustable weight should be moved up in
order to shorten the pendulum length.
T = 2p (L/g)
ConcepTest 11.11 Damped Pendulum
After a pendulum starts swinging,
its amplitude gradually decreases
with time because of friction.
What happens to the period of the
pendulum during this time?
a) period increases
b) period does not change
c) period decreases
ConcepTest 11.11 Damped Pendulum
After a pendulum starts swinging,
its amplitude gradually decreases
with time because of friction.
a) period increases
b) period does not change
c) period decreases
What happens to the period of the
pendulum during this time?
The period of a pendulum does not depend
on its amplitude, but only on its length and
the acceleration due to gravity.
T  2p
L
g
Follow-up: What is happening to the energy of the pendulum?
ConcepTest 11.13 Sound It Out
Does a longitudinal wave,
a) yes
such as a sound wave,
b) no
have an amplitude ?
c) it depends on the
medium the wave is in
air
pressure
high
normal
low

A
x
ConcepTest 11.13 Sound It Out
Does a longitudinal wave,
a) yes
such as a sound wave,
b) no
have an amplitude ?
c) it depends on the
medium the wave is in
All wave types—transverse,
longitudinal, surface—have
air
pressure

all of these properties:
wavelength, frequency,
amplitude, velocity, period
high
normal
low
A
x
ConcepTest 11.14 The Wave
At a football game, the “wave”
might circulate through the stands
and move around the stadium. In
this wave motion, people stand up
and sit down as the wave passes.
What type of wave would this be
characterized as?
a) polarized wave
b) longitudinal wave
c) lateral wave
d) transverse wave
e) soliton wave
ConcepTest 11.14 The Wave
At a football game, the “wave”
might circulate through the stands
and move around the stadium. In
this wave motion, people stand up
and sit down as the wave passes.
What type of wave would this be
characterized as?
a) polarized wave
b) longitudinal wave
c) lateral wave
d) transverse wave
e) soliton wave
The people are moving up and down, and the wave is
traveling around the stadium. Thus, the motion of the
wave is perpendicular to the oscillation direction of the
people, and so this is a transverse wave.
Follow-up: What type of wave occurs when you toss a pebble in a pond?
ConcepTest 12.2a Speed of Sound I
a) water
Do sound waves travel
faster in water or in ice?
b) ice
c) same speed in both
d) sound can only travel in a gas
ConcepTest 12.2a Speed of Sound I
a) water
Do sound waves travel
faster in water or in ice?
b) ice
c) same speed in both
d) sound can only travel in a gas
Speed of sound depends on the inertia of the medium and
the restoring force. Since ice and water both consist of
water molecules, the inertia is the same for both. However,
the force holding the molecules together is greater in ice
(because it is a solid), so the restoring force is greater.
Since v = (force / inertia), the speed of sound must be
greater in ice !
ConcepTest 12.2b Speed of Sound II
Do you expect an echo to
return to you more quickly
or less quickly on a hot day,
as compared to a cold day?
a) more quickly on a hot day
b) equal times on both days
c) more quickly on a cold day
ConcepTest 12.2b Speed of Sound II
Do you expect an echo to
return to you more quickly
or less quickly on a hot day,
as compared to a cold day?
a) more quickly on a hot day
b) equal times on both days
c) more quickly on a cold day
The speed of sound in a gas increases with temperature.
This is because the molecules are bumping into each
other faster and more often, so it is easier to propagate
the compression wave (sound wave).
ConcepTest 12.2c Speed of Sound III
If you fill your lungs with
helium and then try
talking, you sound like
Donald Duck. What
conclusion can you
reach about the speed
of sound in helium?
a) speed of sound is less in helium
b) speed of sound is the same in helium
c) speed of sound is greater in helium
d) this effect has nothing to do with the
speed in helium
ConcepTest 12.2c Speed of Sound III
If you fill your lungs with
helium and then try
talking, you sound like
Donald Duck. What
conclusion can you
reach about the speed
of sound in helium?
a) speed of sound is less in helium
b) speed of sound is the same in helium
c) speed of sound is greater in helium
d) this effect has nothing to do with the
speed in helium
The higher pitch implies a higher frequency. In turn,
since v = f, this means that the speed of the wave has
increased (as long as the wavelength, determined by
the length of the vocal chords, remains constant).
Follow-up: Why is the speed of sound greater in helium than in air?
ConcepTest 12.4b Sound Intensity II
You hear a fire truck with a certain
intensity, and you are about 1 mile
away. Another person hears the
same fire truck with an intensity
that is about 10 times less.
Roughly how far is the other
person from the fire truck?
a) about the same distance
b) about 3 miles
c) about 10 miles
d) about 30 miles
e) about 100 miles
ConcepTest 12.4b Sound Intensity II
You hear a fire truck with a certain
intensity, and you are about 1 mile
away. Another person hears the
same fire truck with an intensity
that is about 10 times less.
Roughly how far is the other
person from the fire truck?
Remember that intensity
drops with the inverse
square of the distance,
so if intensity drops by a
factor of 10, the other
person must be 10
farther away, which is
about a factor of 3.
a) about the same distance
b) about 3 miles
c) about 10 miles
d) about 30 miles
e) about 100 miles
I
I
2
1

P / 4 pr 2
2
P / 4 pr 2
1

r2
1
r2
2
ConcepTest 12.6a Pied Piper I
You have a long pipe
a) the long pipe
and a short pipe.
b) the short pipe
Which one has the
c) both have the same frequency
higher frequency?
d) depends on the speed of sound
in the pipe
ConcepTest 12.6a Pied Piper I
You have a long pipe
a) the long pipe
and a short pipe.
b) the short pipe
Which one has the
c) both have the same frequency
higher frequency?
d) depends on the speed of sound
in the pipe
A shorter pipe means that the standing wave in the
pipe would have a shorter wavelength. Since the
wave speed remains the same, the frequency has
to be higher in the short pipe.
ConcepTest 12.6b Pied Piper II
A wood whistle has a variable
length. You just heard the tone
from the whistle at maximum
length. If the air column is made
shorter by moving the end stop,
what happens to the frequency?
a) frequency will increase
b) frequency will not change
c) frequency will decrease
ConcepTest 12.6b Pied Piper II
A wood whistle has a variable
length. You just heard the tone
from the whistle at maximum
length. If the air column is made
shorter by moving the end stop,
what happens to the frequency?
a) frequency will increase
b) frequency will not change
c) frequency will decrease
A shorter pipe means that the standing wave in the pipe would
have a shorter wavelength. Since the wave speed remains
the same, and since we know that v = f , then we see that the
frequency has to increase when the pipe is made shorter.
ConcepTest 12.6c Pied Piper III
If you blow across the opening
of a partially filled soda bottle,
you hear a tone. If you take a big
sip of soda and then blow
across the opening again, how
will the frequency of the tone
change?
a) frequency will increase
b) frequency will not change
c) frequency will decrease
ConcepTest 12.6c Pied Piper III
If you blow across the opening
of a partially filled soda bottle,
you hear a tone. If you take a big
sip of soda and then blow
across the opening again, how
will the frequency of the tone
change?
a) frequency will increase
b) frequency will not change
c) frequency will decrease
By drinking some of the soda, you have effectively increased the
length of the air column in the bottle. A longer pipe means that
the standing wave in the bottle would have a longer wavelength.
Since the wave speed remains the same, and since we know that
v = f , then we see that the frequency has to be lower.
Follow-up: Why doesn’t the wave speed change?
ConcepTest 12.7 Open and Closed Pipes
You blow into an open pipe
and produce a tone. What
happens to the frequency
of the tone if you close the
end of the pipe and blow
into it again?
a) depends on the speed of sound
in the pipe
b) you hear the same frequency
c) you hear a higher frequency
d) you hear a lower frequency
ConcepTest 12.7 Open and Closed Pipes
You blow into an open pipe
and produce a tone. What
happens to the frequency
of the tone if you close the
end of the pipe and blow
into it again?
a) depends on the speed of sound
in the pipe
b) you hear the same frequency
c) you hear a higher frequency
d) you hear a lower frequency
In the open pipe, 1/2 of a wave “fits”
into the pipe, while in the closed pipe,
only 1/4 of a wave fits. Because the
wavelength is larger in the closed
pipe, the frequency will be lower.
Follow-up: What would you have to do
to the pipe to increase the frequency?
ConcepTest 12.8 Out of Tune
When you tune a guitar
string, what physical
characteristic of the
string are you actually
changing?
a) the tension in the string
b) the mass per unit length of the string
c) the composition of the string
d) the overall length of the string
e) the inertia of the string
ConcepTest 12.8 Out of Tune
When you tune a guitar
string, what physical
characteristic of the
string are you actually
changing?
a) the tension in the string
b) the mass per unit length of the string
c) the composition of the string
d) the overall length of the string
e) the inertia of the string
By tightening (or loosening) the knobs on the neck of the
guitar, you are changing the tension in the string. This
alters the wave speed, and therefore alters the frequency
of the fundamental standing wave because f = v/2L .
Follow-up: To increase frequency, do you tighten or loosen the strings?
ConcepTest 12.11a Doppler Effect I
Observers A, B, and C listen to a
moving source of sound. The
location of the wave fronts of the
moving source with respect to
the observers is shown below.
Which of the following is true?
a) frequency is highest at A
b) frequency is highest at B
c) frequency is highest at C
d) frequency is the same at all
three points
ConcepTest 12.11a Doppler Effect I
Observers A, B, and C listen to a
moving source of sound. The
location of the wave fronts of the
moving source with respect to
the observers is shown below.
Which of the following is true?
a) frequency is highest at A
b) frequency is highest at B
c) frequency is highest at C
d) frequency is the same at all
three points
The number of wave fronts
hitting observer C per unit time
is greatest—thus the observed
frequency is highest there.
Follow-up: Where is the frequency lowest?
ConcepTest 12.11b Doppler Effect II
You are heading toward an island in a
speedboat and you see your friend
standing on the shore, at the base of
a cliff. You sound the boat’s horn to
alert your friend of your arrival. If the
horn has a rest frequency of f0, what
frequency does your friend hear?
a) lower than f0
b) equal to f0
c) higher than f0
ConcepTest 12.11b Doppler Effect II
You are heading toward an island in a
speedboat and you see your friend
standing on the shore, at the base of
a cliff. You sound the boat’s horn to
alert your friend of your arrival. If the
horn has a rest frequency of f0, what
frequency does your friend hear?
a) lower than f0
b) equal to f0
c) higher than f0
Due to the approach of the source toward the stationary
observer, the frequency is shifted higher. This is the
same situation as depicted in the previous question.
ConcepTest 12.11c Doppler Effect III
In the previous question, the horn
had a rest frequency of f0, and we
found that your friend heard a
higher frequency f1 due to the
Doppler shift. The sound from
the boat hits the cliff behind your
friend and returns to you as an
echo. What is the frequency of
the echo that you hear?
a) lower than f0
b) equal to f0
c) higher than f0 but lower than f1
d) equal to f1
e) higher than f1
ConcepTest 12.11c Doppler Effect III
In the previous question, the horn
had a rest frequency of f0, and we
found that your friend heard a
higher frequency f1 due to the
Doppler shift. The sound from
the boat hits the cliff behind your
friend and returns to you as an
echo. What is the frequency of
the echo that you hear?
a) lower than f0
b) equal to f0
c) higher than f0 but lower than f1
d) equal to f1
e) higher than f1
The sound wave bouncing off the cliff has the same frequency f1
as the one hitting the cliff (what your friend hears). For the echo,
you are now a moving observer approaching the sound wave of
frequency f1 so you will hear an even higher frequency.
ConcepTest 16.1a Electric Charge I
Two charged balls are
repelling each other as
they hang from the ceiling.
What can you say about
their charges?
a) one is positive, the other is
negative
b) both are positive
c) both are negative
d) both are positive or both
are negative
ConcepTest 16.1a Electric Charge I
Two charged balls are
repelling each other as
they hang from the ceiling.
What can you say about
their charges?
a) one is positive, the other is
negative
b) both are positive
c) both are negative
d) both are positive or both
are negative
The fact that the balls repel each other
only can tell you that they have the
same charge, but you do not know the
sign. So they can be either both
positive or both negative.
Follow-up: What does the picture look like if the two balls are oppositely
charged? What about if both balls are neutral?
ConcepTest 16.1b Electric Charge II
From the picture,
what can you
conclude about
the charges?
a)
have opposite charges
b)
have the same charge
c)
all have the same charge
d) one ball must be neutral (no charge)
ConcepTest 16.1b Electric Charge II
From the picture,
what can you
conclude about
the charges?
a)
have opposite charges
b)
have the same charge
c)
all have the same charge
d) one ball must be neutral (no charge)
The GREEN and PINK balls must
have the same charge, since they repel
each other. The YELLOW ball also
repels the GREEN, so it must also
have the same charge as the GREEN
(and the PINK).
ConcepTest 16.2b Conductors II
Two neutral conductors are connected
a)
0
0
by a wire and a charged rod is brought
b)
+
–
c)
–
+
d)
+
+
e)
–
–
near, but does not touch. The wire is
taken away, and then the charged rod
is removed. What are the charges on
the conductors?
0
0
?
?
ConcepTest 16.2b Conductors II
Two neutral conductors are connected
a)
0
0
by a wire and a charged rod is brought
b)
+
–
c)
–
+
d)
+
+
e)
–
–
near, but does not touch. The wire is
taken away, and then the charged rod
is removed. What are the charges on
the conductors?
While the conductors are connected, positive
0
0
?
?
charge will flow from the blue to the green ball
due to polarization. Once disconnected, the
charges will remain on the separate conductors
even when the rod is removed.
Follow-up: What will happen when the
conductors are reconnected with a wire?
ConcepTest 16.3a Coulomb’s Law I
What is the magnitude
a) 1.0 N
b) 1.5 N
of the force F2?
c) 2.0 N
F1 = 3N
Q
Q
F2 = ?
d) 3.0 N
e) 6.0 N
ConcepTest 16.3a Coulomb’s Law I
What is the magnitude
a) 1.0 N
b) 1.5 N
of the force F2?
c) 2.0 N
F1 = 3N
Q
Q
F2 = ?
d) 3.0 N
e) 6.0 N
The force F2 must have the same magnitude as F1. This is due to the
fact that the form of Coulomb’s Law is totally symmetric with
respect to the two charges involved. The force of one on the other of
a pair is the same as the reverse. Note that this sounds suspiciously
like Newton’s 3rd Law!!
ConcepTest 16.3b Coulomb’s Law II
F1 = 3N
Q
Q
F2 = ?
b) 3.0 N
If we increase one charge to 4Q,
what is the magnitude of F1?
F1 = ?
4Q
Q
a) 3/4 N
F2 = ?
c) 12 N
d) 16 N
e) 48 N
ConcepTest 16.3b Coulomb’s Law II
F1 = 3N
Q
Q
F2 = ?
b) 3.0 N
If we increase one charge to 4Q,
what is the magnitude of F1?
F1 = ?
4Q
Q
a) 3/4 N
F2 = ?
c) 12 N
d) 16 N
e) 48 N
Originally we had:
F1 = k(Q)(Q)/r2 = 3 N
Now we have:
F1 = k(4Q)(Q)/r2
which is 4 times bigger than before.
Follow-up: Now what is the magnitude of F2?
ConcepTest 16.3c Coulomb’s Law III
The force between two charges
a) 9 F
separated by a distance d is F. If
b) 3 F
the charges are pulled apart to a
c) F
distance 3d, what is the force on
d) 1/3 F
each charge?
e) 1/9 F
F
F
Q
Q
d
?
?
Q
Q
3d
ConcepTest 16.3c Coulomb’s Law III
The force between two charges
a) 9 F
separated by a distance d is F. If
b) 3 F
the charges are pulled apart to a
c) F
distance 3d, what is the force on
d) 1/3 F
each charge?
e) 1/9 F
F
Originally we had:
F
Q
Q
Fbefore = k(Q)(Q)/d2 = F
Now we have:
Fafter = k(Q)(Q)/(3d)2 = 1/9 F
d
?
?
Q
Q
3d
Follow-up: What is the force if the original distance is halved?
ConcepTest 16.4b Electric Force II
Two balls with charges +Q and +4Q are separated by 3R. Where
should you place another charged ball Q0 on the line between
the two charges such that the net force on Q0 will be zero?
+4Q
+Q
a)
b)
c)
d)
2R
R
3R
e)
ConcepTest 16.5a Proton and Electron I
A proton and an electron are
held apart a distance of 1 m
and then released. As they
approach each other, what
happens to the force between
them?
p
a) it gets bigger
b) it gets smaller
c) it stays the same
e
ConcepTest 16.5a Proton and Electron I
A proton and an electron are
held apart a distance of 1 m
and then released. As they
approach each other, what
happens to the force between
them?
a) it gets bigger
b) it gets smaller
c) it stays the same
By Coulomb’s Law, the force between the two
charges is inversely proportional to the
distance squared. So, the closer they get to
each other, the bigger the electric force
between them gets!
p
e
Follow-up: Which particle feels the larger force at any one moment?
ConcepTest 16.5b Proton and Electron II
A proton and an electron are held
a) proton
apart a distance of 1 m and then
b) electron
released. Which particle has the
c) both the same
larger acceleration at any one
moment?
p
e
ConcepTest 16.5b Proton and Electron II
A proton and an electron are held
a) proton
apart a distance of 1 m and then
b) electron
released. Which particle has the
c) both the same
larger acceleration at any one
moment?
p
The two particles feel the same force. Since F =
ma, the particle with the smaller mass will
have the larger acceleration. This would be
the electron.
e
ConcepTest 16.5c Proton and Electron III
A proton and an electron
are held apart a distance
of 1 m and then let go.
Where would they meet?
a) in the middle
b) closer to the electron’s side
c) closer to the proton’s side
p
e
ConcepTest 16.5c Proton and Electron III
A proton and an electron
are held apart a distance
of 1 m and then let go.
Where would they meet?
a) in the middle
b) closer to the electron’s side
c) closer to the proton’s side
By Newton’s 3rd Law, the electron and proton feel
the same force. But, since F = ma, and since the
proton’s mass is much greater, the proton’s
acceleration will be much smaller!
p
Thus, they will meet closer to the proton’s original
position.
Follow-up: Which particle will be moving faster when they meet?
e
ConcepTest 19.1a
Series Resistors I
a) 12 V
Assume that the voltage of the battery
is 9 V and that the three resistors are
identical. What is the potential
difference across each resistor?
b) zero
c) 3 V
d) 4 V
e) you need to know the actual
value of R
9V
ConcepTest 19.1a
Series Resistors I
a) 12 V
Assume that the voltage of the battery
is 9 V and that the three resistors are
identical. What is the potential
difference across each resistor?
b) zero
c) 3 V
d) 4 V
e) you need to know the actual
value of R
Since the resistors are all equal, the
voltage will drop evenly across the 3
resistors, with 1/3 of 9 V across each
one. So we get a 3 V drop across
each.
9V
Follow-up: What would be the potential difference if R= 1 W,
2 W, 3 W
ConcepTest 19.2a
Parallel Resistors I
a) 10 A
In the circuit below, what is the
b) zero
current through R1?
c) 5 A
d) 2 A
e) 7 A
R2= 2 W
R1= 5 W
10 V
ConcepTest 19.2a
Parallel Resistors I
a) 10 A
In the circuit below, what is the
b) zero
current through R1?
c) 5 A
d) 2 A
e) 7 A
The voltage is the same (10 V) across each resistor
R2= 2 W
because they are in parallel. Thus, we can use
Ohm’s Law, V1 = I1 R1 to find the current I1 = 2
R1= 5 W
A.
10 V
Follow-up: What is the total current through the battery?
ConcepTest 19.2b
Parallel Resistors II
Points P and Q are connected to a
a) increases
battery of fixed voltage. As more
b) remains the same
resistors R are added to the parallel
c) decreases
circuit, what happens to the total
d) drops to zero
current in the circuit?
ConcepTest 19.2b
Parallel Resistors II
Points P and Q are connected to a
a) increases
battery of fixed voltage. As more
b) remains the same
resistors R are added to the parallel
c) decreases
circuit, what happens to the total
d) drops to zero
current in the circuit?
As we add parallel resistors, the overall
resistance of the circuit drops. Since V = IR,
and V is held constant by the battery, when
resistance decreases, the current must increase.
Follow-up: What happens to the current through each resistor?
ConcepTest 19.3a
Current flows through a
lightbulb. If a wire is now
connected across the
bulb, what happens?
Short Circuit
a) all the current continues to flow through the
bulb
b) half the current flows through the wire, the
other half continues through the bulb
c) all the current flows through the wire
d) none of the above
ConcepTest 19.3a
Current flows through a
lightbulb. If a wire is now
connected across the
bulb, what happens?
Short Circuit
a) all the current continues to flow through the
bulb
b) half the current flows through the wire, the
other half continues through the bulb
c) all the current flows through the wire
d) none of the above
The current divides based on the ratio of
the resistances. If one of the resistances
is zero, then ALL of the current will flow
through that path.
Follow-up: Doesn’t the wire have SOME resistance?
ConcepTest 19.3b
Two lightbulbs A and B are
connected in series to a
constant voltage source.
When a wire is connected
across B, bulb A will:
Short Circuit II
a) glow brighter than before
b) glow just the same as before
c) glow dimmer than before
d) go out completely
e) explode
ConcepTest 19.3b
Two lightbulbs A and B are
connected in series to a
constant voltage source.
When a wire is connected
across B, bulb A will:
Short Circuit II
a) glow brighter than before
b) glow just the same as before
c) glow dimmer than before
d) go out completely
e) explode
Since bulb B is bypassed by the wire, the
total resistance of the circuit decreases.
This means that the current through bulb A
increases.
Follow-up: What happens to bulb B?