ConcepTest 2.1
Walking the Dog
You and your dog go for a walk to the
park. On the way, your dog takes many
side trips to chase squirrels or examine
a) yes
fire hydrants. When you arrive at the
park, do you and your dog have the same
displacement?
b) no
ConcepTest 2.1
Walking the Dog
You and your dog go for a walk to the
park. On the way, your dog takes many
side trips to chase squirrels or examine
a) yes
fire hydrants. When you arrive at the
park, do you and your dog have the same
b) no
displacement?
Yes, you have the same displacement. Since you and your dog had the
same initial position and the same final position, then you have (by
definition) the same displacement.
Follow-up: Have you and your dog traveled the same distance?
ConcepTest 2.7
Velocity in One Dimension
If the average velocity is non-zero over
some time interval, does this mean that
the instantaneous velocity is never zero
during the same interval?
a) yes
b) no
c) it depends
ConcepTest 2.7
Velocity in One Dimension
If the average velocity is non-zero over
some time interval, does this mean that
the instantaneous velocity is never zero
a) yes
b) no
c) it depends
during the same interval?
No!!! For example, your average velocity for a trip home
might be 60 mph, but if you stopped for lunch on the way
home, there was an interval when your instantaneous
velocity was zero, in fact!
ConcepTest 2.9a
You throw a ball straight
up into the air. After it
leaves your hand, at what
point in its flight does it
have the maximum value
of acceleration?
Free Fall I
a) its acceleration is constant
everywhere
b) at the top of its trajectory
c) halfway to the top of its trajectory
d) just after it leaves your hand
e) just before it returns to your
hand on the way down
ConcepTest 2.9a
You throw a ball straight
up into the air. After it
leaves your hand, at what
point in its flight does it
have the maximum value
of acceleration?
Free Fall I
a) its acceleration is constant
everywhere
b) at the top of its trajectory
c) halfway to the top of its trajectory
d) just after it leaves your hand
e) just before it returns to your
hand on the way down
The ball is in free fall once it is released. Therefore, it is entirely under
the influence of gravity, and the only acceleration it experiences is g,
which is constant at all points.
ConcepTest 2.9b
Alice and Bill are at the top of a
building. Alice throws her ball
downward. Bill simply drops
his ball. Which ball has the
greater acceleration just after
release?
Free Fall II
a) Alice’s ball
b) it depends on how hard
the ball was thrown
c) neither—they both have
the same acceleration
d) Bill’s ball
Alice
v0
vA
Bill
vB
ConcepTest 2.9b
Alice and Bill are at the top of a
building. Alice throws her ball
downward. Bill simply drops
his ball. Which ball has the
greater acceleration just after
release?
Both balls are in free fall once they are
released, therefore they both feel the
Free Fall II
a) Alice’s ball
b) it depends on how hard
the ball was thrown
c) neither—they both have
the same acceleration
d) Bill’s ball
Alice
v0
Bill
acceleration due to gravity (g). This
acceleration is independent of the initial
vA
velocity of the ball.
Follow-up: Which one has the greater velocity when they hit
the ground?
vB
ConcepTest 2.12a
You drop a rock off a
bridge. When the rock
has fallen 4 m, you drop
a second rock. As the
two rocks continue to
fall, what happens to
their separation?
Throwing Rocks I
a) the separation increases as they fall
b) the separation stays constant at 4 m
c) the separation decreases as they fall
d) it is impossible to answer without more
information
ConcepTest 2.12a
You drop a rock off a
bridge. When the rock
has fallen 4 m, you drop
a second rock. As the
two rocks continue to
fall, what happens to
their separation?
Throwing Rocks I
a) the separation increases as they fall
b) the separation stays constant at 4 m
c) the separation decreases as they fall
d) it is impossible to answer without more
information
At any given time, the first rock always has a greater velocity than the
second rock, therefore it will always be increasing its lead as it falls.
Thus, the separation will increase.
ConcepTest 2.12b
You drop a rock off a
bridge. When the rock
has fallen 4 m, you drop
a second rock. As the
two rocks continue to
fall, what happens to
their velocities?
Throwing Rocks II
a) both increase at the same rate
b) the velocity of the first rock increases
faster than the velocity of the second
c) the velocity of the second rock increases
faster than the velocity of the first
d) both velocities stay constant
ConcepTest 2.12b
You drop a rock off a
bridge. When the rock
has fallen 4 m, you drop
a second rock. As the
two rocks continue to
fall, what happens to
their velocities?
Throwing Rocks II
a) both increase at the same rate
b) the velocity of the first rock increases
faster than the velocity of the second
c) the velocity of the second rock increases
faster than the velocity of the first
d) both velocities stay constant
Both rocks are in free fall, thus under the influence of gravity only.
That means they both experience the constant acceleration of gravity.
Since acceleration is defined as the change of velocity, both of their
velocities increase at the same rate.
Follow-up: What happens when air resistance is present?
ConcepTest 2.13a
Graphing Velocity I
a) it speeds up all the time
The graph of position versus
time for a car is given below.
What can you say about the
velocity of the car over time?
b) it slows down all the time
c) it moves at constant velocity
d) sometimes it speeds up and
sometimes it slows down
e) not really sure
x
t
ConcepTest 2.13a
Graphing Velocity I
a) it speeds up all the time
The graph of position versus
time for a car is given below.
What can you say about the
velocity of the car over time?
b) it slows down all the time
c) it moves at constant velocity
d) sometimes it speeds up and
sometimes it slows down
e) not really sure
x
The car moves at a constant velocity
because the x vs. t plot shows a straight
line. The slope of a straight line is
constant. Remember that the slope of x
versus t is the velocity!
t
v ConcepTest 2.15a
a)
c)
t
t
v
b)
v
d)
t
You drop a rubber ball. Right
after it leaves your hand and
before it hits the floor, which
of the above plots
represents the v vs. t graph
for this motion?
v
Rubber Balls I
(Assume
your y-axis is pointing up.)
t
v ConcepTest 2.15a
a)
v
Rubber Balls I
c)
t
t
v
b)
v
d)
t
You drop a rubber ball. Right
after it leaves your hand and
before it hits the floor, which
The ball is dropped from rest, so its
initial velocity is zero. Since the yaxis is pointing upwards and the ball
of the above plots
represents the v vs. t graph
for this motion?
t
(Assume
your y-axis is pointing up.)
is falling downwards, its velocity is
negative and becomes more and more
negative as it accelerates downward.
ConcepTest 3.1a
If two vectors are given
Vectors I
a) same magnitude, but can be in any
direction
such that A + B = 0, what b) same magnitude, but must be in the
same direction
can you say about the
magnitude and direction
of vectors A and B?
c) different magnitudes, but must be in the
same direction
d) same magnitude, but must be in opposite
directions
e) different magnitudes, but must be in
opposite directions
ConcepTest 3.1a
If two vectors are given
Vectors I
a) same magnitude, but can be in any
direction
such that A + B = 0, what b) same magnitude, but must be in the
same direction
can you say about the
magnitude and direction
of vectors A and B?
c) different magnitudes, but must be in the
same direction
d) same magnitude, but must be in opposite
directions
e) different magnitudes, but must be in
opposite directions
The magnitudes must be the same, but one vector must be pointing in
the opposite direction of the other, in order for the sum to come out to
zero. You can prove this with the tip-to-tail method.
ConcepTest 3.5
You drop a package from
a plane flying at constant
speed in a straight line.
Dropping a Package
a) quickly lag behind the plane
while falling
b) remain vertically under the
plane while falling
Without air resistance, the
c) move ahead of the plane while
falling
package will:
d) not fall at all
ConcepTest 3.5
You drop a package from
a plane flying at constant
speed in a straight line.
Dropping a Package
a) quickly lag behind the plane
while falling
b) remain vertically under the
plane while falling
Without air resistance, the
c) move ahead of the plane while
falling
package will:
d) not fall at all
Both the plane and the package have
the same horizontal velocity at the
moment of release. They will maintain
this velocity in the x-direction, so they
stay aligned.
Follow-up: What would happen if air resistance is present?
ConcepTest 3.6a
From the same height (and
at the same time), one ball
is dropped and another ball
is fired horizontally. Which
one will hit the ground
first?
Dropping the Ball I
a) the “dropped” ball
b) the “fired” ball
c) they both hit at the same time
d) it depends on how hard the ball
was fired
e) it depends on the initial height
ConcepTest 3.6a
From the same height (and
at the same time), one ball
is dropped and another ball
is fired horizontally. Which
one will hit the ground
first?
Dropping the Ball I
a) the “dropped” ball
b) the “fired” ball
c) they both hit at the same time
d) it depends on how hard the ball
was fired
e) it depends on the initial height
Both of the balls are falling vertically under the influence of
gravity. They both fall from the same height. Therefore, they will
hit the ground at the same time. The fact that one is moving
horizontally is irrelevant—remember that the x and y motions are
completely independent!!
Follow-up: Is that also true if there is air resistance?
ConcepTest 3.6b
Dropping the Ball II
a) the “dropped” ball
In the previous problem,
b) the “fired” ball
which ball has the greater
c) neither—they both have the
same velocity on impact
velocity at ground level?
d) it depends on how hard the
ball was thrown
ConcepTest 3.6b
Dropping the Ball II
a) the “dropped” ball
In the previous problem,
b) the “fired” ball
which ball has the greater
c) neither—they both have the
same velocity on impact
velocity at ground level?
d) it depends on how hard the
ball was thrown
Both balls have the same vertical velocity
when they hit the ground (since they are
both acted on by gravity for the same
time). However, the “fired” ball also has a
horizontal velocity. When you add the two
components vectorially, the “fired” ball
has a larger net velocity when it hits the
ground.
Follow-up: What would you have to do to have them
both reach the same final velocity at ground level?
ConcepTest 3.6c
A projectile is launched
from the ground at an
angle of 30°. At what point
in its trajectory does this
projectile have the least
speed?
Dropping the Ball III
a) just after it is launched
b) at the highest point in its flight
c) just before it hits the ground
d) halfway between the ground and
the highest point
e) speed is always constant
ConcepTest 3.6c
A projectile is launched
from the ground at an
angle of 30°. At what
point in its trajectory does
this projectile have the
least speed?
Dropping the Ball III
a) just after it is launched
b) at the highest point in its flight
c) just before it hits the ground
d) halfway between the ground and
the highest point
e) speed is always constant
The speed is smallest at
the highest point of its
flight path because the ycomponent of the velocity
is zero.
ConcepTest 3.7b
Punts II
A battleship simultaneously fires two shells at two enemy
submarines. The shells are launched with the same initial
velocity. If the shells follow the trajectories shown, which
submarine gets hit first?
a)
c) both at the same time
b)
ConcepTest 3.7b
Punts II
A battleship simultaneously fires two shells at two enemy
submarines. The shells are launched with the same initial
velocity. If the shells follow the trajectories shown, which
submarine gets hit first?
The flight time is fixed by the
motion in the y-direction. The
higher an object goes, the longer
it stays in flight. The shell hitting
ship b goes less high, therefore it
stays in flight for less time than
the other shell. Thus, ship b is
hit first.
a)
c) both at the same time
Follow-up: Which one traveled the greater distance?
b)
ConcepTest 3.8
Cannon on the Moon
For a cannon on Earth, the cannonball would follow path b.
Instead, if the same cannon were on the Moon, where g = 1.6
m/s2, which path would the cannonball take in the same
situation?
a)
b)
c)
d)
ConcepTest 3.10a
Shoot the Monkey I
You are trying to hit a friend with a
water balloon. He is sitting in the
window of his dorm room directly
across the street. You aim straight
at him and shoot. Just when you
shoot, he falls out of the window!
Does the water balloon hit him?
a) yes, it hits
b) maybe—it depends on
the speed of the shot
c) no, it misses
d) the shot is impossible
e) not really sure
Assume that the shot does have
enough speed to reach the dorm
across the street.
ConcepTest 3.10a
Shoot the Monkey I
You are trying to hit a friend with a
water balloon. He is sitting in the
window of his dorm room directly
across the street. You aim straight
at him and shoot. Just when you
shoot, he falls out of the window!
Does the water balloon hit him?
Your friend falls under the
influence of gravity, just like the
water balloon. Thus, they are
both undergoing free fall in the
y-direction. Since the slingshot
was accurately aimed at the
right height, the water balloon
will fall exactly as your friend
does, and it will hit him!!
a) yes, it hits
b) maybe—it depends on
the speed of the shot
c) no, it misses
d) the shot is impossible
e) not really sure
Assume that the shot does have
enough speed to reach the dorm
across the street.
ConcepTest 4.1a Newton’s First Law I
A book is lying at
rest on a table.
The book will
remain there at
rest because:
a) there is a net force but the book has too
much inertia
b) there are no forces acting on it at all
c) it does move, but too slowly to be seen
d) there is no net force on the book
e) there is a net force, but the book is too
heavy to move
ConcepTest 4.1a Newton’s First Law I
A book is lying at
rest on a table.
The book will
remain there at
rest because:
a) there is a net force but the book has too
much inertia
b) there are no forces acting on it at all
c) it does move, but too slowly to be seen
d) there is no net force on the book
e) there is a net force, but the book is too
heavy to move
There are forces acting on the book, but the only
forces acting are in the y-direction. Gravity acts
downward, but the table exerts an upward force
that is equally strong, so the two forces cancel,
leaving no net force.
ConcepTest 4.1c Newton’s First Law III
You put your book on
the bus seat next to
you. When the bus
a) a net force acted on it
b) no net force acted on it
stops suddenly, the
c) it remained at rest
book slides forward off
d) it did not move, but only seemed to
the seat. Why?
e) gravity briefly stopped acting on it
ConcepTest 4.1c Newton’s First Law III
You put your book on
the bus seat next to
you. When the bus
a) a net force acted on it
b) no net force acted on it
stops suddenly, the
c) it remained at rest
book slides forward off
d) it did not move, but only seemed to
the seat. Why?
e) gravity briefly stopped acting on it
The book was initially moving forward (since it was
on a moving bus). When the bus stopped, the book
continued moving forward, which was its initial state
of motion, and therefore it slid forward off the seat.
Follow-up: What is the force that usually keeps the book on the seat?
ConcepTest 4.3 Truck on Frozen Lake
A very large truck sits on a
frozen lake. Assume there
is no friction between the
tires and the ice. A fly
suddenly smashes against
the front window. What
will happen to the truck?
a) it is too heavy, so it just sits there
b) it moves backward at const. speed
c) it accelerates backward
d) it moves forward at const. speed
e) it accelerates forward
ConcepTest 4.3 Truck on Frozen Lake
A very large truck sits on a
frozen lake. Assume there
is no friction between the
tires and the ice. A fly
suddenly smashes against
the front window. What
will happen to the truck?
a) it is too heavy, so it just sits there
b) it moves backward at const. speed
c) it accelerates backward
d) it moves forward at const. speed
e) it accelerates forward
When the fly hit the truck, it exerted a force on the truck
(only for a fraction of a second). So, in this time period,
the truck accelerated (backwards) up to some speed.
After the fly was squashed, it no longer exerted a force,
and the truck simply continued moving at constant speed.
Follow-up: What is the truck doing 5 minutes after the fly hit it?
ConcepTest 4.7a Gravity and Weight I
What can you say
a) Fg is greater on the feather
about the force of
b) Fg is greater on the stone
gravity Fg acting on a
stone and a feather?
c) Fg is zero on both due to vacuum
d) Fg is equal on both always
e) Fg is zero on both always
ConcepTest 4.7a Gravity and Weight I
What can you say
a) Fg is greater on the feather
about the force of
b) Fg is greater on the stone
gravity Fg acting on a
stone and a feather?
c) Fg is zero on both due to vacuum
d) Fg is equal on both always
e) Fg is zero on both always
The force of gravity (weight) depends
on the mass of the object!! The stone
has more mass, therefore more weight.
ConcepTest 4.7b Gravity and Weight II
What can you say
a) it is greater on the feather
about the acceleration
b) it is greater on the stone
of gravity acting on the
c) it is zero on both due to vacuum
stone and the feather?
d) it is equal on both always
e) it is zero on both always
ConcepTest 4.7b Gravity and Weight II
What can you say
a) it is greater on the feather
about the acceleration
b) it is greater on the stone
of gravity acting on the
c) it is zero on both due to vacuum
stone and the feather?
d) it is equal on both always
e) it is zero on both always
The acceleration is given by F/m so
here the mass divides out. Since we
know that the force of gravity (weight)
is mg, then we end up with acceleration
g for both objects.
Follow-up: Which one hits the bottom first?
ConcepTest 4.8 On the Moon
An astronaut on Earth kicks
a bowling ball and hurts his
foot. A year later, the same
astronaut kicks a bowling
a) more
b) less
c) the same
ball on the Moon with the
same force. His foot hurts...
Ouch!
ConcepTest 4.8 On the Moon
An astronaut on Earth kicks
a bowling ball and hurts his
foot. A year later, the same
astronaut kicks a bowling
a) more
b) less
c) the same
ball on the Moon with the
same force. His foot hurts...
Ouch!
The masses of both the bowling ball
and the astronaut remain the same, so
his foot feels the same resistance and
hurts the same as before.
Follow-up: What is different about
the bowling ball on the Moon?
ConcepTest 4.11 On an Incline
Consider two identical blocks,
a) case A
one resting on a flat surface,
b) case B
and the other resting on an
incline. For which case is the
normal force greater?
c) both the same (N = mg)
d) both the same (0 < N < mg)
e) both the same (N = 0)
ConcepTest 4.11 On an Incline
Consider two identical blocks,
a) case A
one resting on a flat surface,
b) case B
and the other resting on an
incline. For which case is the
normal force greater?
c) both the same (N = mg)
d) both the same (0 < N < mg)
e) both the same (N = 0)
In Case A, we know that N = W.
y
In Case B, due to the angle of
the incline, N < W. In fact, we
N
f
can see that N = W cos(q).
q Wy
q
W
x
ConcepTest 4.12 Climbing the Rope
When you climb up a rope,
a) this slows your initial velocity which
is already upward
the first thing you do is pull
b) you don’t go up, you’re too heavy
down on the rope. How do
c) you’re not really pulling down—it
just seems that way
you manage to go up the
rope by doing that?
d) the rope actually pulls you up
e) you are pulling the ceiling down
ConcepTest 4.12 Climbing the Rope
When you climb up a rope,
a) this slows your initial velocity which
is already upward
the first thing you do is pull
b) you don’t go up, you’re too heavy
down on the rope. How do
c) you’re not really pulling down—it
just seems that way
you manage to go up the
rope by doing that?
d) the rope actually pulls you up
e) you are pulling the ceiling down
When you pull down on the rope, the rope pulls up on
you!! It is actually this upward force by the rope that
makes you move up! This is the “reaction” force (by the
rope on you) to the force that you exerted on the rope.
And voilá, this is Newton’s 3rd Law.
ConcepTest 4.13a Bowling vs. Ping-Pong I
In outer space, a bowling
ball and a ping-pong ball
attract each other due to
gravitational forces. How
do the magnitudes of these
attractive forces compare?
a) the bowling ball exerts a greater
force on the ping-pong ball
b) the ping-pong ball exerts a greater
force on the bowling ball
c) the forces are equal
d) the forces are zero because they
cancel out
e) there are actually no forces at all
F12
F21
ConcepTest 4.13a Bowling vs. Ping-Pong I
In outer space, a bowling
ball and a ping-pong ball
attract each other due to
gravitational forces. How
do the magnitudes of these
attractive forces compare?
a) the bowling ball exerts a greater
force on the ping-pong ball
b) the ping-pong ball exerts a greater
force on the bowling ball
c) the forces are equal
d) the forces are zero because they
cancel out
e) there are actually no forces at all
The forces are equal and
opposite by Newton’s 3rd
Law!
F12
F21
ConcepTest 4.13b Bowling vs. Ping-Pong II
In outer space, gravitational
a) they do not accelerate because
they are weightless
forces exerted by a bowling
b) accels. are equal, but not opposite
ball and a ping-pong ball on
c) accelerations are opposite, but
bigger for the bowling ball
each other are equal and
opposite. How do their
accelerations compare?
d) accelerations are opposite, but
bigger for the ping-pong ball
e) accels. are equal and opposite
F12
F21
ConcepTest 4.13b Bowling vs. Ping-Pong II
In outer space, gravitational
a) they do not accelerate because
they are weightless
forces exerted by a bowling
b) accels. are equal, but not opposite
ball and a ping-pong ball on
c) accelerations are opposite, but
bigger for the bowling ball
each other are equal and
opposite. How do their
accelerations compare?
d) accelerations are opposite, but
bigger for the ping-pong ball
e) accels. are equal and opposite
The forces are equal and opposite—
this is Newton’s 3rd Law!! But the
acceleration is F/m and so the smaller
mass has the bigger acceleration.
Follow-up: Where will the balls meet if
they are released from this position?
F12
F21
ConcepTest 4.14a Collision Course I
a) the car
A small car collides with
b) the truck
a large truck. Which
c) both the same
experiences the greater
impact force?
d) it depends on the velocity of each
e) it depends on the mass of each
ConcepTest 4.14a Collision Course I
a) the car
A small car collides with
b) the truck
a large truck. Which
c) both the same
experiences the greater
impact force?
d) it depends on the velocity of each
e) it depends on the mass of each
According to Newton’s 3rd Law, both vehicles experience
the same magnitude of force.
ConcepTest 4.14b Collision Course II
In the collision between
a) the car
the car and the truck,
b) the truck
which has the greater
c) both the same
acceleration?
d) it depends on the velocity of each
e) it depends on the mass of each
ConcepTest 4.14b Collision Course II
In the collision between
a) the car
the car and the truck,
b) the truck
which has the greater
c) both the same
acceleration?
d) it depends on the velocity of each
e) it depends on the mass of each
We have seen that both
vehicles experience the
same magnitude of force.
But the acceleration is
given by F/m so the car
has the larger acceleration,
since it has the smaller
mass.
ConcepTest 4.16b Tension II
Two tug-of-war opponents each
a) 0 N
pull with a force of 100 N on
b) 50 N
opposite ends of a rope. What
c) 100 N
is the tension in the rope?
d) 150 N
e) 200 N
ConcepTest 4.16b Tension II
Two tug-of-war opponents each
a) 0 N
pull with a force of 100 N on
b) 50 N
opposite ends of a rope. What
c) 100 N
is the tension in the rope?
d) 150 N
e) 200 N
This is literally the identical situation to the
previous question. The tension is not 200 N!!
Whether the other end of the rope is pulled by a
person, or pulled by a tree, the tension in the rope
is still 100 N!!
ConcepTest 4.16c Tension III
You and a friend can
each pull with a force of
20 N. If you want to rip
a rope in half, what is
the best way?
a) you and your friend each pull on
opposite ends of the rope
b) tie the rope to a tree, and you both
pull from the same end
c) it doesn’t matter—both of the above
are equivalent
d) get a large dog to bite the rope
ConcepTest 4.16c Tension III
You and a friend can
each pull with a force of
20 N. If you want to rip
a rope in half, what is
the best way?
a) you and your friend each pull on
opposite ends of the rope
b) tie the rope to a tree, and you both
pull from the same end
c) it doesn’t matter—both of the above
are equivalent
d) get a large dog to bite the rope
Take advantage of the fact that the tree can
pull with almost any force (until it falls down,
that is!). You and your friend should team up
on one end, and let the tree make the effort on
the other end.
ConcepTest 4.20 Antilock Brakes
Antilock brakes keep the
car wheels from locking
and skidding during a
sudden stop. Why does
this help slow the car
down?
a) mk > ms so sliding friction is better
b) mk > ms so static friction is better
c) ms > mk so sliding friction is better
d) ms > mk so static friction is better
e) none of the above
ConcepTest 4.20 Antilock Brakes
Antilock brakes keep the
car wheels from locking
and skidding during a
sudden stop. Why does
this help slow the car
down?
a) mk > ms so sliding friction is better
b) mk > ms so static friction is better
c) ms > mk so sliding friction is better
d) ms > mk so static friction is better
e) none of the above
Static friction is greater than sliding friction, so
by keeping the wheels from skidding, the static
friction force will help slow the car down more
efficiently than the sliding friction that occurs
during a skid.
ConcepTest 4.1a Newton’s First Law I
A book is lying at
rest on a table.
The book will
remain there at
rest because:
a) there is a net force but the book has too
much inertia
b) there are no forces acting on it at all
c) it does move, but too slowly to be seen
d) there is no net force on the book
e) there is a net force, but the book is too
heavy to move
ConcepTest 4.1a Newton’s First Law I
A book is lying at
rest on a table.
The book will
remain there at
rest because:
a) there is a net force but the book has too
much inertia
b) there are no forces acting on it at all
c) it does move, but too slowly to be seen
d) there is no net force on the book
e) there is a net force, but the book is too
heavy to move
There are forces acting on the book, but the only
forces acting are in the y-direction. Gravity acts
downward, but the table exerts an upward force
that is equally strong, so the two forces cancel,
leaving no net force.
ConcepTest 4.1c Newton’s First Law III
You put your book on
the bus seat next to
you. When the bus
a) a net force acted on it
b) no net force acted on it
stops suddenly, the
c) it remained at rest
book slides forward off
d) it did not move, but only seemed to
the seat. Why?
e) gravity briefly stopped acting on it
ConcepTest 4.1c Newton’s First Law III
You put your book on
the bus seat next to
you. When the bus
a) a net force acted on it
b) no net force acted on it
stops suddenly, the
c) it remained at rest
book slides forward off
d) it did not move, but only seemed to
the seat. Why?
e) gravity briefly stopped acting on it
The book was initially moving forward (since it was
on a moving bus). When the bus stopped, the book
continued moving forward, which was its initial state
of motion, and therefore it slid forward off the seat.
Follow-up: What is the force that usually keeps the book on the seat?
ConcepTest 4.3 Truck on Frozen Lake
A very large truck sits on a
frozen lake. Assume there
is no friction between the
tires and the ice. A fly
suddenly smashes against
the front window. What
will happen to the truck?
a) it is too heavy, so it just sits there
b) it moves backward at const. speed
c) it accelerates backward
d) it moves forward at const. speed
e) it accelerates forward
ConcepTest 4.3 Truck on Frozen Lake
A very large truck sits on a
frozen lake. Assume there
is no friction between the
tires and the ice. A fly
suddenly smashes against
the front window. What
will happen to the truck?
a) it is too heavy, so it just sits there
b) it moves backward at const. speed
c) it accelerates backward
d) it moves forward at const. speed
e) it accelerates forward
When the fly hit the truck, it exerted a force on the truck
(only for a fraction of a second). So, in this time period,
the truck accelerated (backwards) up to some speed.
After the fly was squashed, it no longer exerted a force,
and the truck simply continued moving at constant speed.
Follow-up: What is the truck doing 5 minutes after the fly hit it?
ConcepTest 4.7a Gravity and Weight I
What can you say
a) Fg is greater on the feather
about the force of
b) Fg is greater on the stone
gravity Fg acting on a
stone and a feather?
c) Fg is zero on both due to vacuum
d) Fg is equal on both always
e) Fg is zero on both always
ConcepTest 4.7a Gravity and Weight I
What can you say
a) Fg is greater on the feather
about the force of
b) Fg is greater on the stone
gravity Fg acting on a
stone and a feather?
c) Fg is zero on both due to vacuum
d) Fg is equal on both always
e) Fg is zero on both always
The force of gravity (weight) depends
on the mass of the object!! The stone
has more mass, therefore more weight.
ConcepTest 4.7b Gravity and Weight II
What can you say
a) it is greater on the feather
about the acceleration
b) it is greater on the stone
of gravity acting on the
c) it is zero on both due to vacuum
stone and the feather?
d) it is equal on both always
e) it is zero on both always
ConcepTest 4.7b Gravity and Weight II
What can you say
a) it is greater on the feather
about the acceleration
b) it is greater on the stone
of gravity acting on the
c) it is zero on both due to vacuum
stone and the feather?
d) it is equal on both always
e) it is zero on both always
The acceleration is given by F/m so
here the mass divides out. Since we
know that the force of gravity (weight)
is mg, then we end up with acceleration
g for both objects.
Follow-up: Which one hits the bottom first?
ConcepTest 4.8 On the Moon
An astronaut on Earth kicks
a bowling ball and hurts his
foot. A year later, the same
astronaut kicks a bowling
a) more
b) less
c) the same
ball on the Moon with the
same force. His foot hurts...
Ouch!
ConcepTest 4.8 On the Moon
An astronaut on Earth kicks
a bowling ball and hurts his
foot. A year later, the same
astronaut kicks a bowling
a) more
b) less
c) the same
ball on the Moon with the
same force. His foot hurts...
Ouch!
The masses of both the bowling ball
and the astronaut remain the same, so
his foot feels the same resistance and
hurts the same as before.
Follow-up: What is different about
the bowling ball on the Moon?
ConcepTest 4.11 On an Incline
Consider two identical blocks,
a) case A
one resting on a flat surface,
b) case B
and the other resting on an
incline. For which case is the
normal force greater?
c) both the same (N = mg)
d) both the same (0 < N < mg)
e) both the same (N = 0)
ConcepTest 4.11 On an Incline
Consider two identical blocks,
a) case A
one resting on a flat surface,
b) case B
and the other resting on an
incline. For which case is the
normal force greater?
c) both the same (N = mg)
d) both the same (0 < N < mg)
e) both the same (N = 0)
In Case A, we know that N = W.
y
In Case B, due to the angle of
the incline, N < W. In fact, we
N
f
can see that N = W cos(q).
q Wy
q
W
x
ConcepTest 4.12 Climbing the Rope
When you climb up a rope,
a) this slows your initial velocity which
is already upward
the first thing you do is pull
b) you don’t go up, you’re too heavy
down on the rope. How do
c) you’re not really pulling down—it
just seems that way
you manage to go up the
rope by doing that?
d) the rope actually pulls you up
e) you are pulling the ceiling down
ConcepTest 4.12 Climbing the Rope
When you climb up a rope,
a) this slows your initial velocity which
is already upward
the first thing you do is pull
b) you don’t go up, you’re too heavy
down on the rope. How do
c) you’re not really pulling down—it
just seems that way
you manage to go up the
rope by doing that?
d) the rope actually pulls you up
e) you are pulling the ceiling down
When you pull down on the rope, the rope pulls up on
you!! It is actually this upward force by the rope that
makes you move up! This is the “reaction” force (by the
rope on you) to the force that you exerted on the rope.
And voilá, this is Newton’s 3rd Law.
ConcepTest 4.13a Bowling vs. Ping-Pong I
In outer space, a bowling
ball and a ping-pong ball
attract each other due to
gravitational forces. How
do the magnitudes of these
attractive forces compare?
a) the bowling ball exerts a greater
force on the ping-pong ball
b) the ping-pong ball exerts a greater
force on the bowling ball
c) the forces are equal
d) the forces are zero because they
cancel out
e) there are actually no forces at all
F12
F21
ConcepTest 4.13a Bowling vs. Ping-Pong I
In outer space, a bowling
ball and a ping-pong ball
attract each other due to
gravitational forces. How
do the magnitudes of these
attractive forces compare?
a) the bowling ball exerts a greater
force on the ping-pong ball
b) the ping-pong ball exerts a greater
force on the bowling ball
c) the forces are equal
d) the forces are zero because they
cancel out
e) there are actually no forces at all
The forces are equal and
opposite by Newton’s 3rd
Law!
F12
F21
ConcepTest 4.13b Bowling vs. Ping-Pong II
In outer space, gravitational
a) they do not accelerate because
they are weightless
forces exerted by a bowling
b) accels. are equal, but not opposite
ball and a ping-pong ball on
c) accelerations are opposite, but
bigger for the bowling ball
each other are equal and
opposite. How do their
accelerations compare?
d) accelerations are opposite, but
bigger for the ping-pong ball
e) accels. are equal and opposite
F12
F21
ConcepTest 4.13b Bowling vs. Ping-Pong II
In outer space, gravitational
a) they do not accelerate because
they are weightless
forces exerted by a bowling
b) accels. are equal, but not opposite
ball and a ping-pong ball on
c) accelerations are opposite, but
bigger for the bowling ball
each other are equal and
opposite. How do their
accelerations compare?
d) accelerations are opposite, but
bigger for the ping-pong ball
e) accels. are equal and opposite
The forces are equal and opposite—
this is Newton’s 3rd Law!! But the
acceleration is F/m and so the smaller
mass has the bigger acceleration.
Follow-up: Where will the balls meet if
they are released from this position?
F12
F21
ConcepTest 4.14a Collision Course I
a) the car
A small car collides with
b) the truck
a large truck. Which
c) both the same
experiences the greater
impact force?
d) it depends on the velocity of each
e) it depends on the mass of each
ConcepTest 4.14a Collision Course I
a) the car
A small car collides with
b) the truck
a large truck. Which
c) both the same
experiences the greater
impact force?
d) it depends on the velocity of each
e) it depends on the mass of each
According to Newton’s 3rd Law, both vehicles experience
the same magnitude of force.
ConcepTest 4.14b Collision Course II
In the collision between
a) the car
the car and the truck,
b) the truck
which has the greater
c) both the same
acceleration?
d) it depends on the velocity of each
e) it depends on the mass of each
ConcepTest 4.14b Collision Course II
In the collision between
a) the car
the car and the truck,
b) the truck
which has the greater
c) both the same
acceleration?
d) it depends on the velocity of each
e) it depends on the mass of each
We have seen that both
vehicles experience the
same magnitude of force.
But the acceleration is
given by F/m so the car
has the larger acceleration,
since it has the smaller
mass.
ConcepTest 4.16b Tension II
Two tug-of-war opponents each
a) 0 N
pull with a force of 100 N on
b) 50 N
opposite ends of a rope. What
c) 100 N
is the tension in the rope?
d) 150 N
e) 200 N
ConcepTest 4.16b Tension II
Two tug-of-war opponents each
a) 0 N
pull with a force of 100 N on
b) 50 N
opposite ends of a rope. What
c) 100 N
is the tension in the rope?
d) 150 N
e) 200 N
This is literally the identical situation to the
previous question. The tension is not 200 N!!
Whether the other end of the rope is pulled by a
person, or pulled by a tree, the tension in the rope
is still 100 N!!
ConcepTest 4.16c Tension III
You and a friend can
each pull with a force of
20 N. If you want to rip
a rope in half, what is
the best way?
a) you and your friend each pull on
opposite ends of the rope
b) tie the rope to a tree, and you both
pull from the same end
c) it doesn’t matter—both of the above
are equivalent
d) get a large dog to bite the rope
ConcepTest 4.16c Tension III
You and a friend can
each pull with a force of
20 N. If you want to rip
a rope in half, what is
the best way?
a) you and your friend each pull on
opposite ends of the rope
b) tie the rope to a tree, and you both
pull from the same end
c) it doesn’t matter—both of the above
are equivalent
d) get a large dog to bite the rope
Take advantage of the fact that the tree can
pull with almost any force (until it falls down,
that is!). You and your friend should team up
on one end, and let the tree make the effort on
the other end.
ConcepTest 4.20 Antilock Brakes
Antilock brakes keep the
car wheels from locking
and skidding during a
sudden stop. Why does
this help slow the car
down?
a) mk > ms so sliding friction is better
b) mk > ms so static friction is better
c) ms > mk so sliding friction is better
d) ms > mk so static friction is better
e) none of the above
ConcepTest 4.20 Antilock Brakes
Antilock brakes keep the
car wheels from locking
and skidding during a
sudden stop. Why does
this help slow the car
down?
a) mk > ms so sliding friction is better
b) mk > ms so static friction is better
c) ms > mk so sliding friction is better
d) ms > mk so static friction is better
e) none of the above
Static friction is greater than sliding friction, so
by keeping the wheels from skidding, the static
friction force will help slow the car down more
efficiently than the sliding friction that occurs
during a skid.
ConcepTest 5.1 Tetherball
In the game of tetherball,
a) toward the top of the pole
b) toward the ground
the struck ball whirls
c) along the horizontal component of
the tension force
around a pole. In what
d) along the vertical component of the
tension force
direction does the net
force on the ball point?
e) tangential to the circle
T
W
ConcepTest 5.1 Tetherball
In the game of tetherball,
the struck ball whirls
around a pole. In what
direction does the net
force on the ball point?
a) toward the top of the pole
b) toward the ground
c) along the horizontal component of
the tension force
d) along the vertical component of the
tension force
e) tangential to the circle
The vertical component of the
tension balances the weight. The
horizontal component of tension
W
T
T
provides the centripetal force that
points toward the center of the
circle.
W
ConcepTest 5.2a Around the Curve I
You are a passenger in a
car, not wearing a seat
belt. The car makes a
sharp left turn. From
your perspective in the
car, what do you feel is
happening to you?
a) you are thrown to the right
b) you feel no particular change
c) you are thrown to the left
d) you are thrown to the ceiling
e) you are thrown to the floor
ConcepTest 5.2a Around the Curve I
You are a passenger in a
car, not wearing a seat
belt. The car makes a
sharp left turn. From
your perspective in the
car, what do you feel is
happening to you?
The passenger has the tendency
to continue moving in a straight
line. From your perspective in the
car, it feels like you are being
thrown to the right, hitting the
passenger door.
a) you are thrown to the right
b) you feel no particular change
c) you are thrown to the left
d) you are thrown to the ceiling
e) you are thrown to the floor
ConcepTest 5.2b Around the Curve II
During that sharp left turn,
you found yourself hitting
the passenger door. What
is the correct description of
what is actually happening?
a) centrifugal force is pushing you
into the door
b) the door is exerting a leftward
force on you
c) both of the above
d) neither of the above
ConcepTest 5.2b Around the Curve II
During that sharp left turn,
you found yourself hitting
the passenger door. What
is the correct description of
what is actually happening?
a) centrifugal force is pushing you
into the door
b) the door is exerting a leftward
force on you
c) both of the above
d) neither of the above
The passenger has the tendency
to continue moving in a straight
line. There is a centripetal force,
provided by the door, that forces
the passenger into a circular path.
ConcepTest 5.2c Around the Curve III
You drive your dad’s car
too fast around a curve
and the car starts to skid.
What is the correct
description of this
situation?
a) car’s engine is not strong enough to
keep the car from being pushed out
b) friction between tires and road is not
strong enough to keep car in a circle
c) car is too heavy to make the turn
d) a deer caused you to skid
e) none of the above
ConcepTest 5.2c Around the Curve III
You drive your dad’s car
too fast around a curve
and the car starts to skid.
What is the correct
description of this
situation?
a) car’s engine is not strong enough to
keep the car from being pushed out
b) friction between tires and road is not
strong enough to keep car in a circle
c) car is too heavy to make the turn
d) a deer caused you to skid
e) none of the above
The friction force between tires and
road provides the centripetal force
that keeps the car moving in a circle.
If this force is too small, the car
continues in a straight line!
Follow-up: What could be done to
the road or car to prevent skidding?
ConcepTest 5.5 Barrel of Fun
A rider in a “barrel of fun”
finds herself stuck with
her back to the wall.
Which diagram correctly
shows the forces acting
on her?
ConcepTest 5.5 Barrel of Fun
A rider in a “barrel of fun”
finds herself stuck with
her back to the wall.
Which diagram correctly
shows the forces acting
on her?
The normal force of the wall on the
rider provides the centripetal force
needed to keep her going around
in a circle. The downward force of
gravity is balanced by the upward
frictional force on her, so she does
not slip vertically.
Follow-up: What happens if the rotation of the ride slows down?
ConcepTest 5.6a Going in Circles I
You’re on a Ferris wheel moving in a
vertical circle. When the Ferris wheel is
at rest, the normal force N exerted by
a) N remains equal to mg
b) N is smaller than mg
your seat is equal to your weight mg.
c) N is larger than mg
How does N change at the top of the
d) None of the above
Ferris wheel when you are in motion?
ConcepTest 5.6a Going in Circles I
You’re on a Ferris wheel moving in a
vertical circle. When the Ferris wheel is
at rest, the normal force N exerted by
a) N remains equal to mg
b) N is smaller than mg
your seat is equal to your weight mg.
c) N is larger than mg
How does N change at the top of the
d) None of the above
Ferris wheel when you are in motion?
You are in circular motion, so there
has to be a centripetal force pointing
inward. At the top, the only two
forces are mg (down) and N (up), so
N must be smaller than mg.
Follow-up: Where is N larger than mg?
ConcepTest 5.8a Earth and Moon I
Which is stronger,
Earth’s pull on the
Moon, or the
Moon’s pull on
Earth?
a) the Earth pulls harder on the Moon
b) the Moon pulls harder on the Earth
c) they pull on each other equally
d) there is no force between the Earth and
the Moon
e) it depends upon where the Moon is in
its orbit at that time
ConcepTest 5.8a Earth and Moon I
Which is stronger,
Earth’s pull on the
Moon, or the
Moon’s pull on
Earth?
a) the Earth pulls harder on the Moon
b) the Moon pulls harder on the Earth
c) they pull on each other equally
d) there is no force between the Earth and
the Moon
e) it depends upon where the Moon is in
its orbit at that time
By Newton’s 3rd Law, the forces are
equal and opposite.
ConcepTest 5.12 In the Space Shuttle
a) They are so far from Earth that Earth’s gravity
doesn’t act any more.
Astronauts in the
space shuttle
float because:
b) Gravity’s force pulling them inward is cancelled
by the centripetal force pushing them outward.
c) While gravity is trying to pull them inward, they
are trying to continue on a straight-line path.
d) Their weight is reduced in space so the force of
gravity is much weaker.
ConcepTest 5.12 In the Space Shuttle
a) They are so far from Earth that Earth’s gravity
doesn’t act any more.
Astronauts in the
space shuttle
float because:
b) Gravity’s force pulling them inward is cancelled
by the centripetal force pushing them outward.
c) While gravity is trying to pull them inward, they
are trying to continue on a straight-line path.
d) Their weight is reduced in space so the force of
gravity is much weaker.
Astronauts in the space shuttle float because
they are in “free fall” around Earth, just like a
satellite or the Moon. Again, it is gravity that
provides the centripetal force that keeps them
in circular motion.
Follow-up: How weak is the value of g at an altitude of 300 km?
ConcepTest 6.1 To Work or Not to Work
Is it possible to do work on an
a) yes
object that remains at rest?
b) no
ConcepTest 6.1 To Work or Not to Work
Is it possible to do work on an
a) yes
object that remains at rest?
b) no
Work requires that a force acts over a distance.
If an object does not move at all, there is no
displacement, and therefore no work done.
ConcepTest 6.2a Friction and Work I
A box is being pulled
across a rough floor
a) friction does no work at all
at a constant speed.
b) friction does negative work
What can you say
c) friction does positive work
about the work done
by friction?
ConcepTest 6.2a Friction and Work I
A box is being pulled
across a rough floor
a) friction does no work at all
at a constant speed.
b) friction does negative work
What can you say
c) friction does positive work
about the work done
by friction?
Friction acts in the opposite
N displacement
direction to the displacement, so
the work is negative. Or using the
Pull
f
definition of work: W = F d cos q
since q = 180o, then W < 0.
mg
ConcepTest 6.2b Friction and Work II
Can friction ever
do positive work?
a) yes
b) no
ConcepTest 6.2b Friction and Work II
Can friction ever
do positive work?
a) yes
b) no
Consider the case of a box on the back of a pickup truck.
If the box moves along with the truck, then it is actually
the force of friction that is making the box move.
ConcepTest 6.2d Tension and Work
A ball tied to a string is
being whirled around in
a circle. What can you
say about the work
done by tension?
a) tension does no work at all
b) tension does negative work
c) tension does positive work
ConcepTest 6.2d Tension and Work
A ball tied to a string is
being whirled around in
a circle. What can you
say about the work
a) tension does no work at all
b) tension does negative work
c) tension does positive work
done by tension?
No work is done because the force
acts in a perpendicular direction to
the displacement. Or using the
definition of work: W = F d cos q
since q = 90o, then W = 0.
T
v
Follow-up: Is there a force in the direction of the velocity?
ConcepTest 6.3 Force and Work
A box is being pulled up a rough
a) one force
incline by a rope connected to a
b) two forces
pulley. How many forces are
c) three forces
doing work on the box?
d) four forces
e) no forces are doing work
ConcepTest 6.3 Force and Work
A box is being pulled up a rough
a) one force
incline by a rope connected to a
b) two forces
pulley. How many forces are
c) three forces
doing work on the box?
d) four forces
e) no forces are doing work
Any force not perpendicular
to the motion will do work:
N does no work
N
T
T does positive work
f
f does negative work
mg does negative work
mg
ConcepTest 6.5a Kinetic Energy I
By what factor does the
a) no change at all
kinetic energy of a car
b) factor of 3
change when its speed
c) factor of 6
is tripled?
d) factor of 9
e) factor of 12
ConcepTest 6.5a Kinetic Energy I
By what factor does the
a) no change at all
kinetic energy of a car
b) factor of 3
change when its speed
c) factor of 6
is tripled?
d) factor of 9
e) factor of 12
Since the kinetic energy is 1/2 mv2, if the speed increases
by a factor of 3, then the KE will increase by a factor of 9.
Follow-up: How would you achieve a KE increase of a factor of 2?
ConcepTest 6.5b Kinetic Energy II
Car #1 has twice the mass of
a) 2 v1 = v2
car #2, but they both have the
b)  2 v1 = v2
same kinetic energy. How do
c) 4 v1 = v2
their speeds compare?
d) v1 = v2
e) 8 v1 = v2
ConcepTest 6.5b Kinetic Energy II
Car #1 has twice the mass of
a) 2 v1 = v2
car #2, but they both have the
b)  2 v1 = v2
same kinetic energy. How do
c) 4 v1 = v2
their speeds compare?
d) v1 = v2
e) 8 v1 = v2
Since the kinetic energy is 1/2 mv2, and the mass of car #1 is
greater, then car #2 must be moving faster. If the ratio of m1/m2
is 2, then the ratio of v2 values must also be 2. This means that
the ratio of v2/v1 must be the square root of 2.
ConcepTest 6.10 Sign of the Energy I
Is it possible for the
a) yes
kinetic energy of an
b) no
object to be negative?
ConcepTest 6.10 Sign of the Energy I
Is it possible for the
a) yes
kinetic energy of an
b) no
object to be negative?
The kinetic energy is 1/2 mv2. The mass and
the velocity squared will always be positive,
so KE must always be positive.
ConcepTest 6.11 Sign of the Energy II
Is it possible for the
a) yes
gravitational potential
b) no
energy of an object to
be negative?
ConcepTest 6.11 Sign of the Energy II
Is it possible for the
a) yes
gravitational potential
b) no
energy of an object to
be negative?
Gravitational PE is mgh, where height h is measured relative to
some arbitrary reference level where PE = 0. For example, a
book on a table has positive PE if the zero reference level is
chosen to be the floor. However, if the ceiling is the zero level,
then the book has negative PE on the table. It is only differences
(or changes) in PE that have any physical meaning.
ConcepTest 6.14 Elastic Potential Energy
How does the work required to
a) same amount of work
stretch a spring 2 cm compare
b) twice the work
with the work required to
c) 4 times the work
stretch it 1 cm?
d) 8 times the work
ConcepTest 6.14 Elastic Potential Energy
How does the work required to
a) same amount of work
stretch a spring 2 cm compare
b) twice the work
with the work required to
c) 4 times the work
stretch it 1 cm?
d) 8 times the work
The elastic potential energy is 1/2 kx2. So in the second case,
the elastic PE is 4 times greater than in the first case. Thus,
the work required to stretch the spring is also 4 times greater.
ConcepTest 6.15 Springs and Gravity
A mass attached to a vertical
spring causes the spring to
stretch and the mass to
move downwards. What can
you say about the spring’s
potential energy (PEs) and
the gravitational potential
energy (PEg) of the mass?
a) both PEs and PEg decrease
b) PEs increases and PEg decreases
c) both PEs and PEg increase
d) PEs decreases and PEg increases
e) PEs increases and PEg is constant
ConcepTest 6.15 Springs and Gravity
A mass attached to a vertical
spring causes the spring to
stretch and the mass to
move downwards. What can
you say about the spring’s
potential energy (PEs) and
the gravitational potential
energy (PEg) of the mass?
a) both PEs and PEg decrease
b) PEs increases and PEg decreases
c) both PEs and PEg increase
d) PEs decreases and PEg increases
e) PEs increases and PEg is constant
The spring is stretched, so its elastic PE increases,
since PEs = 1/2 kx2. The mass moves down to a
lower position, so its gravitational PE decreases,
since PEg = mgh.
ConcepTest 6.16 Down the Hill
Three balls of equal mass start from rest and roll down different
ramps. All ramps have the same height. Which ball has the
greater speed at the bottom of its ramp?
d) same speed
for all balls
a
b
c
ConcepTest 6.16 Down the Hill
Three balls of equal mass start from rest and roll down different
ramps. All ramps have the same height. Which ball has the
greater speed at the bottom of its ramp?
d) same speed
for all balls
a
b
c
All of the balls have the same initial gravitational PE,
since they are all at the same height (PE = mgh). Thus,
when they get to the bottom, they all have the same final
KE, and hence the same speed (KE = 1/2 mv2).
Follow-up: Which ball takes longer to get down the ramp?
ConcepTest 6.18a Water Slide I
Paul and Corinne start from rest at
a) Paul
the same time on frictionless water
b) Corinne
slides with different shapes. At the
bottom, whose velocity is greater?
c) both the same
ConcepTest 6.18a Water Slide I
Paul and Corinne start from rest at
a) Paul
the same time on frictionless water
b) Corinne
slides with different shapes. At the
bottom, whose velocity is greater?
Conservation of Energy:
Ei = mgH = Ef = 1/2 mv2
therefore: gH = 1/2 v2
Since they both start from the
same height, they have the
same velocity at the bottom.
c) both the same
ConcepTest 7.2c Momentum and KE III
Two objects are known to have
the same momentum. Do these
a) yes
two objects necessarily have the
b) no
same kinetic energy?
ConcepTest 7.2c Momentum and KE III
Two objects are known to have
the same momentum. Do these
a) yes
two objects necessarily have the
b) no
same kinetic energy?
If object #1 has mass m and speed v, and object #2
has mass 1/2 m and speed 2v, they will both have the
same momentum. However, since KE = 1/2 mv2, we
see that object #2 has twice the kinetic energy of
object #1, due to the fact that the velocity is squared.
ConcepTest 7.3a Momentum and Force
A net force of 200 N acts on a 100-kg
boulder, and a force of the same
magnitude acts on a 130-g pebble.
How does the rate of change of the
boulder’s momentum compare to
the rate of change of the pebble’s
momentum?
a) greater than
b) less than
c) equal to
ConcepTest 7.3a Momentum and Force
A net force of 200 N acts on a 100-kg
boulder, and a force of the same
magnitude acts on a 130-g pebble.
How does the rate of change of the
boulder’s momentum compare to
the rate of change of the pebble’s
momentum?
a) greater than
b) less than
c) equal to
The rate of change of momentum is, in fact, the force.
Remember that F = Dp/Dt. Since the force exerted on
the boulder and the pebble is the same, then the rate
of change of momentum is the same.
ConcepTest 7.3b Velocity and Force
A net force of 200 N acts on a 100-kg
boulder, and a force of the same
magnitude acts on a 130-g pebble.
How does the rate of change of the
boulder’s velocity compare to the
rate of change of the pebble’s
velocity?
a) greater than
b) less than
c) equal to
ConcepTest 7.3b Velocity and Force
A net force of 200 N acts on a 100 kg
boulder, and a force of the same
magnitude acts on a 130-g pebble.
How does the rate of change of the
boulder’s velocity compare to the
rate of change of the pebble’s
velocity?
a) greater than
b) less than
c) equal to
The rate of change of velocity is the acceleration.
Remember that a = Dv/Dt. The acceleration is related
to the force by Newton’s 2nd Law (F = ma), so the
acceleration of the boulder is less than that of the
pebble (for the same applied force) because the
boulder is much more massive.
ConcepTest 7.4 Collision Course
a) the car
A small car and a large truck
collide head-on and stick
together. Which one has the
larger momentum change?
b) the truck
c) they both have the same
momentum change
d) can’t tell without knowing
the final velocities
ConcepTest 7.4 Collision Course
a) the car
A small car and a large truck
collide head-on and stick
together. Which one has the
larger momentum change?
b) the truck
c) they both have the same
momentum change
d) can’t tell without knowing
the final velocities
Since the total momentum of the
system is conserved, that means that
Dp = 0 for the car and truck combined.
Therefore, Dpcar must be equal and
opposite to that of the truck (–Dptruck) in
order for the total momentum change
to be zero. Note that this conclusion
also follows from Newton’s 3rd Law.
Follow-up: Which one feels
the larger acceleration?
ConcepTest 7.6 Watch Out!
You drive around a curve in a narrow
one-way street at 30 mph when you see
an identical car heading straight toward
you at 30 mph. You have two options:
hit the car head-on or swerve into a
massive concrete wall (also head-on).
What should you do?
a) hit the other car
b) hit the wall
c) makes no difference
d) call your physics prof!!
e) get insurance!
ConcepTest 7.6 Watch Out!
You drive around a curve in a narrow
one-way street at 30 mph when you see
an identical car heading straight toward
you at 30 mph. You have two options:
hit the car head-on or swerve into a
massive concrete wall (also head-on).
What should you do?
a) hit the other car
b) hit the wall
c) makes no difference
d) call your physics prof!!
e) get insurance!
In both cases your momentum will decrease to zero in the collision.
Given that the time Dt of the collision is the same, then the force
exerted on YOU will be the same!!
If a truck is approaching at 30 mph, then you’d be better off hitting
the wall in that case. On the other hand, if it’s only a mosquito, well,
you’d be better off running him down...
ConcepTest 7.7 Impulse
A small beanbag and a bouncy
rubber ball are dropped from the
same height above the floor.
They both have the same mass.
Which one will impart the greater
impulse to the floor when it hits?
a) the beanbag
b) the rubber ball
c) both the same
ConcepTest 7.7 Impulse
A small beanbag and a bouncy
rubber ball are dropped from the
same height above the floor.
They both have the same mass.
Which one will impart the greater
a) the beanbag
b) the rubber ball
c) both the same
impulse to the floor when it hits?
Both objects reach the same speed at the floor. However, while
the beanbag comes to rest on the floor, the ball bounces back
up with nearly the same speed as it hit. Thus, the change in
momentum for the ball is greater, because of the rebound.
The impulse delivered by the ball is twice that of the beanbag.
For the beanbag:
For the rubber ball:
Dp = pf – pi = 0 – (–mv ) = mv
Dp = pf – pi = mv – (–mv ) = 2mv
Follow-up: Which one imparts the larger force to the floor?
ConcepTest 7.8 Singing in the Rain
A person stands under an umbrella
during a rainstorm. Later the rain
turns to hail, although the number
of “drops” hitting the umbrella per
time and their speed remains the
same. Which case requires more
force to hold the umbrella?
a) when it is hailing
b) when it is raining
c) same in both cases
ConcepTest 7.8 Singing in the Rain
A person stands under an umbrella
during a rainstorm. Later the rain
turns to hail, although the number
of “drops” hitting the umbrella per
time and their speed remains the
same. Which case requires more
force to hold the umbrella?
a) when it is hailing
b) when it is raining
c) same in both cases
When the raindrops hit the umbrella, they tend to splatter and run off,
whereas the hailstones hit the umbrella and bounce back upwards.
Thus, the change in momentum (impulse) is greater for the hail. Since
Dp = F Dt, more force is required in the hailstorm. This is similar to
the situation with the bouncy rubber ball in the previous question.
ConcepTest 7.9a Going Bowling I
A bowling ball and a ping-pong
ball are rolling toward you with
the same momentum. If you exert
the same force to stop each one,
which takes a longer time to bring
to rest?
a) the bowling ball
b) same time for both
c) the ping-pong ball
d) impossible to say
p
p
ConcepTest 7.9a Going Bowling I
A bowling ball and a ping-pong
ball are rolling toward you with
the same momentum. If you exert
the same force to stop each one,
which takes a longer time to bring
to rest?
We know:
Dp
Fav =
Dt
a) the bowling ball
b) same time for both
c) the ping-pong ball
d) impossible to say
so Dp = Fav Dt
Here, F and Dp are the same for both balls!
It will take the same amount of time
to stop them.
p
p
ConcepTest 7.9b Going Bowling II
A bowling ball and a ping-pong
ball are rolling toward you with the
same momentum. If you exert the
a) the bowling ball
b) same distance for both
same force to stop each one, for
c) the ping-pong ball
which is the stopping distance
d) impossible to say
greater?
p
p
ConcepTest 7.9b Going Bowling II
A bowling ball and a ping-pong
ball are rolling toward you with the
same momentum. If you exert the
a) the bowling ball
b) same distance for both
same force to stop each one, for
c) the ping-pong ball
which is the stopping distance
d) impossible to say
greater?
Use the work-energy theorem: W = DKE.
The ball with less mass has the greater
speed (why?), and thus the greater KE (why
again?). In order to remove that KE, work
must be done, where W = Fd. Since the
force is the same in both cases, the
distance needed to stop the less massive
ball must be bigger.
p
p
ConcepTest 7.14a Recoil Speed I
Amy (150 lbs) and Gwen (50 lbs) are
standing on slippery ice and push off
each other. If Amy slides at 6 m/s,
what speed does Gwen have?
a) 2 m/s
b) 6 m/s
c) 9 m/s
d) 12 m/s
e) 18 m/s
150 lbs
50 lbs
ConcepTest 7.14a Recoil Speed I
Amy (150 lbs) and Gwen (50 lbs) are
standing on slippery ice and push off
each other. If Amy slides at 6 m/s,
what speed does Gwen have?
a) 2 m/s
b) 6 m/s
c) 9 m/s
d) 12 m/s
e) 18 m/s
The initial momentum is zero,
so the momenta of Amy and
Gwen must be equal and
opposite. Since p = mv,
then if Amy has 3 times
more mass, we see that
Gwen must have 3 times
more speed.
150 lbs
50 lbs
ConcepTest 7.17 Shut the Door!
You are lying in bed and you want to
shut your bedroom door. You have a
superball and a blob of clay (both with
the same mass) sitting next to you.
Which one would be more effective
to throw at your door to close it?
a) the superball
b) the blob of clay
c) it doesn’t matter—they
will be equally effective
d) you are just too lazy to
throw anything
ConcepTest 7.17 Shut the Door!
You are lying in bed and you want to
shut your bedroom door. You have a
superball and a blob of clay (both with
the same mass) sitting next to you.
Which one would be more effective
to throw at your door to close it?
a) the superball
b) the blob of clay
c) it doesn’t matter—they
will be equally effective
d) you are just too lazy to
throw anything
The superball bounces off the door with almost no loss of
speed, so its Dp (and that of the door) is 2mv.
The clay sticks to the door and continues to move along with
it, so its Dp is less than that of the superball, and therefore
it imparts less Dp to the door.
ConcepTest 7.18 Baseball Bat
Where is center of mass
of a baseball bat located?
a) at the midpoint
b) closer to the thick end
c) closer to the thin end (near handle)
d) it depends on how heavy the bat is
ConcepTest 7.18 Baseball Bat
Where is center of mass
of a baseball bat located?
a) at the midpoint
b) closer to the thick end
c) closer to the thin end (near handle)
d) it depends on how heavy the bat is
Since most of the mass of the bat is at the thick end,
this is where the center of mass is located. Only if
the bat were like a uniform rod would its center of
mass be in the middle.