ConcepTest 5.1 Tetherball

1
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?

1) toward the top of the pole 2) toward the
ground 3) along the horizontal component of the
tension force 4) along the vertical component of
the tension force 5) tangential to the circle
2
ConcepTest 5.1 Tetherball
1) toward the top of the pole 2) toward the
ground 3) along the horizontal component of the
tension force 4) along the vertical component of
the tension force 5) tangential to the circle

• In the game of tetherball, the struck ball
  whirls around a pole. In what direction does the
  net force on the ball point?

The vertical component of the tension balances
the weight. The horizontal component of tension
provides the centripetal force that points toward
the center of the circle.
3
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?

(1) you are thrown to the right (2) you feel no
particular change (3) you are thrown to the
left (4) you are thrown to the ceiling (5) you
are thrown to the floor
4
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?

(1) you are thrown to the right (2) you feel no
particular change (3) you are thrown to the
left (4) you are thrown to the ceiling (5) you
are thrown to the floor
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.
5
ConcepTest 5.2b Around the Curve II
(1) centrifugal force is pushing you into the
door (2) the door is exerting a leftward force
on you (3) both of the above (4) neither of the
above

• During that sharp left turn, you found yourself
  hitting the passenger door. What is the correct
  description of what is actually happening?

6
ConcepTest 5.2b Around the Curve II
(1) centrifugal force is pushing you into the
door (2) the door is exerting a leftward force
on you (3) both of the above (4) neither of the
above

• During that sharp left turn, you found yourself
  hitting the passenger door. What is the correct
  description of what is actually happening?

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.
7
ConcepTest 5.2c Around the Curve III
(1) cars engine is not strong enough to keep the
car from being pushed out (2) friction between
tires and road is not strong enough to keep car
in a circle (3) car is too heavy to make the
turn (4) a deer caused you to skid (5) none of
the above

• You drive your dads car too fast around a curve
  and the car starts to skid. What is the correct
  description of this situation?

8
ConcepTest 5.2c Around the Curve III
(1) cars engine is not strong enough to keep the
car from being pushed out (2) friction between
tires and road is not strong enough to keep car
in a circle (3) car is too heavy to make the
turn (4) a deer caused you to skid (5) none of
the above

• You drive your dads car too fast around a curve
  and the car starts to skid. What is the correct
  description of this situation?

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?
9
ConcepTest 5.3 Missing Link

• A ping pong ball is shot into a circular tube
  that is lying flat (horizontal) on a tabletop.
  When the ping pong ball leaves the track, which
  path will it follow?

10
ConcepTest 5.3 Missing Link

• A ping pong ball is shot into a circular tube
  that is lying flat (horizontal) on a tabletop.
  When the ping pong ball leaves the track, which
  path will it follow?

• Once the ball leaves the tube, there is no longer
  a force to keep it going in a circle. Therefore,
  it simply continues in a straight line, as
  Newtons First Law requires!

Follow-up What physical force provides the
centripetal force?
11
ConcepTest 5.4 Ball and String
1) T2 1/4 T1 2) T2 1/2 T1 3) T2
T1 4) T2 2 T1 5) T2 4 T1

• Two equal-mass rocks tied to strings are whirled
  in horizontal circles. The radius of circle 2 is
  twice that of circle 1. If the period of motion
  is the same for both rocks, what is the tension
  in cord 2 compared to cord 1?

12
ConcepTest 5.4 Ball and String
1) T2 1/4 T1 2) T2 1/2 T1 3) T2
T1 4) T2 2 T1 5) T2 4 T1

• Two equal-mass rocks tied to strings are whirled
  in horizontal circles. The radius of circle 2 is
  twice that of circle 1. If the period of motion
  is the same for both rocks, what is the tension
  in cord 2 compared to cord 1?

The centripetal force in this case is given by
the tension, so T mv2/r. For the same period,
we find that v2 2v1 (and this term is squared).
However, for the denominator, we see that r2
2r1 which gives us the relation T2 2T1.
13
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?

14
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?
15
ConcepTest 5.6a Going in Circles I

• Youre on a Ferris wheel moving in a vertical
  circle. When the Ferris wheel is at rest, the
  normal force N exerted by your seat is equal to
  your weight mg. How does N change at the top of
  the Ferris wheel when you are in motion?

1) N remains equal to mg 2) N is smaller than
mg 3) N is larger than mg 4) None of the above
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ConcepTest 5.6a Going in Circles I

• Youre on a Ferris wheel moving in a vertical
  circle. When the Ferris wheel is at rest, the
  normal force N exerted by your seat is equal to
  your weight mg. How does N change at the top of
  the Ferris wheel when you are in motion?

1) N remains equal to mg 2) N is smaller than
mg 3) N is larger than mg 4) None of the above
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?
17
ConcepTest 5.6b Going in Circles II
1) Fc N mg 2) Fc mg N 3) Fc T
N mg 4) Fc N 5) Fc mg

• A skier goes over a small round hill with radius
  R. Since she is in circular motion, there has to
  be a centripetal force. At the top of the hill,
  what is Fc of the skier equal to?

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ConcepTest 5.6b Going in Circles II
1) Fc N mg 2) Fc mg N 3) Fc T
N mg 4) Fc N 5) Fc mg

• A skier goes over a small round hill with radius
  R. Since she is in circular motion, there has to
  be a centripetal force. At the top of the hill,
  what is Fc of the skier equal to?

v
Fc points toward the center of the circle, i.e.,
downward in this case. The weight vector points
down and the normal force (exerted by the hill)
points up. The magnitude of the net force,
therefore, is Fc mg N
N
mg
R
Follow-up What happens when the skier goes into
a small dip?
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ConcepTest 5.7c Going in Circles III
1) Fc T mg 2) Fc T N mg 3) Fc
T mg 4) Fc T 5) Fc mg

• You swing a ball at the end of string in a
  vertical circle. Since the ball is in circular
  motion there has to be a centripetal force. At
  the top of the balls path, what is Fc equal to?

20
ConcepTest 5.7c Going in Circles III

• You swing a ball at the end of string in a
  vertical circle. Since the ball is in circular
  motion there has to be a centripetal force. At
  the top of the balls path, what is Fc equal to?

1) Fc T mg 2) Fc T N mg 3) Fc
T mg 4) Fc T 5) Fc mg
Fc points toward the center of the circle, i.e.
downward in this case. The weight vector points
down and the tension (exerted by the string)
also points down. The magnitude of the net
force, therefore, is Fc T mg
v
T
mg
R
Follow-up What is Fc at the bottom of the
balls path?
21
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 fire hydrants. When
you arrive at the park, do you and your dog have
the same displacement?
1) yes 2) no
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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 fire hydrants. When
you arrive at the park, do you and your dog have
the same displacement?
1) yes 2) no
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?
23
ConcepTest 2.3 Position and Speed
1) yes 2) no 3) it depends on the
position
If the position of a car is zero, does its speed
have to be zero?
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ConcepTest 2.3 Position and Speed
1) yes 2) no 3) it depends on the
position
If the position of a car is zero, does its speed
have to be zero?
No, the speed does not depend on position,
it depends on the change of position. Since we
know that the displacement does not depend on the
origin of the coordinate system, an object can
easily start at x 3 and be moving by the time
it gets to x 0.
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ConcepTest 2.4 Odometer
1) distance 2) displacement 3) both
Does the odometer in a car measure distance
or displacement?
26
ConcepTest 2.4 Odometer
1) distance 2) displacement 3) both
Does the odometer in a car measure distance
or displacement?
If you go on a long trip and then return
home, your odometer does not measure zero, but it
records the total miles that you traveled. That
means the odometer records distance.
Follow-up How would you measure displacement in
your car?
27
ConcepTest 3.3 Vector Addition
1) 0 2) 18 3) 37 4) 64 5) 100

• You are adding vectors of length 20 and 40
  units. What is the only possible resultant
  magnitude that you can obtain out of the
  following choices?

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ConcepTest 3.3 Vector Addition
1) 0 2) 18 3) 37 4) 64 5) 100

• You are adding vectors of length 20 and 40
  units. What is the only possible resultant
  magnitude that you can obtain out of the
  following choices?

The minimum resultant occurs when the vectors
are opposite, giving 20 units. The maximum
resultant occurs when the vectors are aligned,
giving 60 units. Anything in between is also
possible, for angles between 0 and 180.
29
ConcepTest 3.4a Firing Balls I

• A small cart is rolling at constant velocity on
  a flat track. It fires a ball straight up into
  the air as it moves. After it is fired, what
  happens to the ball?

1) it depends on how fast the cart is moving 2)
it falls behind the cart 3) it falls in front of
the cart 4) it falls right back into the cart 5)
it remains at rest
30
ConcepTest 3.4a Firing Balls I

• A small cart is rolling at constant velocity on
  a flat track. It fires a ball straight up into
  the air as it moves. After it is fired, what
  happens to the ball?

1) it depends on how fast the cart is moving 2)
it falls behind the cart 3) it falls in front of
the cart 4) it falls right back into the cart 5)
it remains at rest
In the frame of reference of the cart, the ball
only has a vertical component of velocity. So it
goes up and comes back down. To a ground
observer, both the cart and the ball have the
same horizontal velocity, so the ball still
returns into the cart.
31
ConcepTest 3.4b Firing Balls II
Now the cart is being pulled along a horizontal
track by an external force (a weight hanging over
the table edge) and accelerating. It fires a
ball straight out of the cannon as it moves.
After it is fired, what happens to the ball?
1) it depends upon how much the track is
tilted 2) it falls behind the cart 3) it
falls in front of the cart 4) it falls right
back into the cart 5) it remains at rest
32
ConcepTest 3.4b Firing Balls II
Now the cart is being pulled along a horizontal
track by an external force (a weight hanging over
the table edge) and accelerating. It fires a
ball straight out of the cannon as it moves.
After it is fired, what happens to the ball?
1) it depends upon how much the track is
tilted 2) it falls behind the cart 3) it
falls in front of the cart 4) it falls right
back into the cart 5) it remains at rest
Now the acceleration of the cart is completely
unrelated to the ball. In fact, the ball does
not have any horizontal acceleration at all (just
like the first question), so it will lag behind
the accelerating cart once it is shot out of the
cannon.
33
ConcepTest 4.1a Newtons First Law I
1) there is a net force but the book has too
much inertia 2) there are no forces acting on it
at all 3) it does move, but too slowly to be
seen 4) there is no net force on the book 5)
there is a net force, but the book is too heavy
to move

• A book is lying at rest on a table. The book
  will remain there at rest because

34
ConcepTest 4.1a Newtons First Law I
1) there is a net force but the book has too
much inertia 2) there are no forces acting on it
at all 3) it does move, but too slowly to be
seen 4) there is no net force on the book 5)
there is a net force, but the book is too heavy
to move

• A book is lying at rest on a table. The book
  will remain there at rest because

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.
35
ConcepTest 4.1b Newtons First Law II

• A hockey puck slides on ice at constant
  velocity. What is the net force acting on the
  puck?

1) more than its weight 2) equal to its
weight 3) less than its weight but more than
zero 4) depends on the speed of the puck 5) zero
36
ConcepTest 4.1b Newtons First Law II

• A hockey puck slides on ice at constant
  velocity. What is the net force acting on the
  puck?

1) more than its weight 2) equal to its
weight 3) less than its weight but more than
zero 4) depends on the speed of the puck 5) zero
The puck is moving at a constant velocity, and
therefore it is not accelerating. Thus, there
must be no net force acting on the puck.
Follow-up Are there any forces acting on the
puck? What are they?
37
ConcepTest 4.1c Newtons First Law III

• You put your book on the bus seat next to you.
  When the bus stops suddenly, the book slides
  forward off the seat. Why?

1) a net force acted on it 2) no net force
acted on it 3) it remained at rest 4) it did
not move, but only seemed to 5) gravity briefly
stopped acting on it
38
ConcepTest 4.1c Newtons First Law III

• You put your book on the bus seat next to you.
  When the bus stops suddenly, the book slides
  forward off the seat. Why?

1) a net force acted on it 2) no net force
acted on it 3) it remained at rest 4) it did
not move, but only seemed to 5) 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?
39
ConcepTest 6.1 To Work or Not to Work
Is it possible to do work on an object that
remains at rest?
1) yes 2) no
40
ConcepTest 6.1 To Work or Not to Work
Is it possible to do work on an object that
remains at rest?
1) yes 2) 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.
41
ConcepTest 6.2a Friction and Work I

• A box is being pulled across a rough floor at a
  constant speed. What can you say about the work
  done by friction?

1) friction does no work at all 2) friction
does negative work 3) friction does positive work
42
ConcepTest 6.2a Friction and Work I

• A box is being pulled across a rough floor at a
  constant speed. What can you say about the work
  done by friction?

1) friction does no work at all 2) friction
does negative work 3) friction does positive work
Friction acts in the opposite direction to the
displacement, so the work is negative. Or using
the definition of work W F d cos q since ?
180o, then W lt 0.
43
ConcepTest 6.2c Play Ball!
In a baseball game, the catcher stops a 90-mph
pitch. What can you say about the work done by
the catcher on the ball?
1) catcher has done positive work 2) catcher
has done negative work 3) catcher has done zero
work
44
ConcepTest 6.2c Play Ball!
In a baseball game, the catcher stops a 90-mph
pitch. What can you say about the work done by
the catcher on the ball?
1) catcher has done positive work 2) catcher
has done negative work 3) catcher has done zero
work
The force exerted by the catcher is opposite in
direction to the displacement of the ball, so the
work is negative. Or using the definition of
work (W F d cos q ), since ? 180o, then W lt
0. Note that because the work done on the ball
is negative, its speed decreases.
Follow-up What about the work done by the ball
on the catcher?
45
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
boulders momentum compare to the rate of change
of the pebbles momentum?
1) greater than 2) less than 3) equal to
46
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
boulders momentum compare to the rate of change
of the pebbles momentum?
1) greater than 2) less than 3) 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.
47
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
boulders velocity compare to the rate of change
of the pebbles velocity?
1) greater than 2) less than 3) equal to
48
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
boulders velocity compare to the rate of change
of the pebbles velocity?
1) greater than 2) less than 3) equal to
The rate of change of velocity is the
acceleration. Remember that a Dv/Dt. The
acceleration is related to the force by Newtons
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.
49
ConcepTest 7.4 Collision Course
1) the car 2) the truck 3) they both have the
same momentum change 4) cant tell without
knowing the final velocities

• A small car and a large truck collide head-on
  and stick together. Which one has the larger
  momentum change?

50
ConcepTest 7.4 Collision Course
1) the car 2) the truck 3) they both have the
same momentum change 4) cant tell without
knowing the final velocities

• A small car and a large truck collide head-on
  and stick together. Which one has the larger
  momentum change?

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
Newtons 3rd Law.
Follow-up Which one feels the larger
acceleration?
51
ConcepTest 2.5 Speedometer
1) velocity 2) speed 3) both 4)
neither
Does the speedometer in a car measure
velocity or speed?
52
ConcepTest 2.5 Speedometer
1) velocity 2) speed 3) both 4)
neither
Does the speedometer in a car measure
velocity or speed?
The speedometer clearly measures speed, not
velocity. Velocity is a vector (depends on
direction), but the speedometer does not care
what direction you are traveling. It only
measures the magnitude of the velocity, which is
the speed.
Follow-up How would you measure velocity in your
car?
53
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?

1) yes 2) no 3) it depends
54
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?

1) yes 2) no 3) it depends
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!
55
ConcepTest 2.8a Acceleration I
1) yes 2) no 3) depends on the velocity

• If the velocity of a car is non-zero (v ¹ 0),
  can the acceleration of the car be zero?

56
ConcepTest 2.8a Acceleration I
1) yes 2) no 3) depends on the velocity

• If the velocity of a car is non-zero (v ¹ 0),
  can the acceleration of the car be zero?

Sure it can! An object moving with constant
velocity has a non-zero velocity, but it has zero
acceleration since the velocity is not changing.
57
ConcepTest 3.5 Dropping a Package
1) quickly lag behind the plane while falling 2)
remain vertically under the plane while
falling 3) move ahead of the plane while
falling 4) not fall at all

• You drop a package from a plane flying at
  constant speed in a straight line. Without air
  resistance, the package will

58
ConcepTest 3.5 Dropping a Package
1) quickly lag behind the plane while falling 2)
remain vertically under the plane while
falling 3) move ahead of the plane while
falling 4) not fall at all

• You drop a package from a plane flying at
  constant speed in a straight line. Without air
  resistance, the package will

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?
59
ConcepTest 3.6a Dropping the Ball I
(1) the dropped ball (2) the fired
ball (3) they both hit at the same time (4) it
depends on how hard the ball was fired (5) it
depends on the initial height

• 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?

60
ConcepTest 3.6a Dropping the Ball I
(1) the dropped ball (2) the fired
ball (3) they both hit at the same time (4) it
depends on how hard the ball was fired (5) it
depends on the initial height

• 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?

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?
61
ConcepTest 3.6b Dropping the Ball II
1) the dropped ball 2) the fired ball 3)
neither they both have the same velocity on
impact 4) it depends on how hard the ball was
thrown

• In the previous problem, which ball has the
  greater velocity at ground level?

62
ConcepTest 3.6b Dropping the Ball II
1) the dropped ball 2) the fired ball 3)
neither they both have the same velocity on
impact 4) it depends on how hard the ball was
thrown

• In the previous problem, which ball has the
  greater velocity at ground level?

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?
63
ConcepTest 4.1d Newtons First Law IV
1) the force pushing the stone forward finally
stopped pushing on it 2) no net force acted on
the stone 3) a net force acted on it all
along 4) the stone simply ran out of steam 5)
the stone has a natural tendency to be at rest
You kick a smooth flat stone out on a frozen
pond. The stone slides, slows down and
eventually stops. You conclude that
64
ConcepTest 4.1d Newtons First Law IV
1) the force pushing the stone forward finally
stopped pushing on it 2) no net force acted on
the stone 3) a net force acted on it all
along 4) the stone simply ran out of steam 5)
the stone has a natural tendency to be at rest
You kick a smooth flat stone out on a frozen
pond. The stone slides, slows down and
eventually stops. You conclude that
After the stone was kicked, no force was pushing
it along! However, there must have been some
force acting on the stone to slow it down and
stop it. This would be friction!!
Follow-up What would you have to do to keep the
stone moving?
65
ConcepTest 4.2a Cart on Track I

• Consider a cart on a horizontal frictionless
  table. Once the cart has been given a push and
  released, what will happen to the cart?

1) slowly come to a stop 2) continue with
constant acceleration 3) continue with decreasing
acceleration 4) continue with constant
velocity 5) immediately come to a stop
66
ConcepTest 4.2a Cart on Track I

• Consider a cart on a horizontal frictionless
  table. Once the cart has been given a push and
  released, what will happen to the cart?

1) slowly come to a stop 2) continue with
constant acceleration 3) continue with decreasing
acceleration 4) continue with constant
velocity 5) immediately come to a stop
After the cart is released, there is no longer a
force in the x-direction. This does not mean
that the cart stops moving!! It simply means
that the cart will continue moving with the same
velocity it had at the moment of release. The
initial push got the cart moving, but that force
is not needed to keep the cart in motion.
67
ConcepTest 4.2b Cart on Track II

• We just decided that the cart continues with
  constant velocity. What would have to be done in
  order to have the cart continue with constant
  acceleration?

1) push the cart harder before release 2) push
the cart longer before release 3) push the cart
continuously 4) change the mass of the cart 5)
it is impossible to do that
68
ConcepTest 4.2b Cart on Track II

• We just decided that the cart continues with
  constant velocity. What would have to be done in
  order to have the cart continue with constant
  acceleration?

1) push the cart harder before release 2) push
the cart longer before release 3) push the cart
continuously 4) change the mass of the cart 5)
it is impossible to do that
In order to achieve a non-zero acceleration, it
is necessary to maintain the applied force. The
only way to do this would be to continue pushing
the cart as it moves down the track. This will
lead us to a discussion of Newtons Second Law.
69
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?

1) tension does no work at all 2) tension does
negative work 3) tension does positive work
70
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?

1) tension does no work at all 2) tension does
negative work 3) tension does positive work
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 ? 90o, then W 0.
Follow-up Is there a force in the direction of
the velocity?
71
ConcepTest 6.3 Force and Work
1) one force 2) two forces 3) three forces 4)
four forces 5) no forces are doing work

• A box is being pulled up a rough incline by a
  rope connected to a pulley. How many forces are
  doing work on the box?

72
ConcepTest 6.3 Force and Work
1) one force 2) two forces 3) three forces 4)
four forces 5) no forces are doing work

• A box is being pulled up a rough incline by a
  rope connected to a pulley. How many forces are
  doing work on the box?

Any force not perpendicularto the motion will
do work
N does no work
T does positive work
f does negative work
mg does negative work
73
ConcepTest 6.5a Kinetic Energy I
By what factor does the kinetic energy of a car
change when its speed is tripled?
1) no change at all 2) factor of 3 3) factor
of 6 4) factor of 9 5) factor of 12
74
ConcepTest 6.5a Kinetic Energy I
By what factor does the kinetic energy of a car
change when its speed is tripled?
1) no change at all 2) factor of 3 3) factor
of 6 4) factor of 9 5) 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?
75
ConcepTest 7.5a Two Boxes I

• Two boxes, one heavier than the other, are
  initially at rest on a horizontal frictionless
  surface. The same constant force F acts on each
  one for exactly 1 second. Which box has more
  momentum after the force acts?

1) the heavier one 2) the lighter one 3) both
the same
76
ConcepTest 7.5a Two Boxes I

• Two boxes, one heavier than the other, are
  initially at rest on a horizontal frictionless
  surface. The same constant force F acts on each
  one for exactly 1 second. Which box has more
  momentum after the force acts?

1) the heavier one 2) the lighter one 3) both
the same
We know
so impulse Dp Fav Dt.
In this case F and Dt are the same for both
boxes !
Both boxes will have the same final momentum.
77
ConcepTest 7.5b Two Boxes II
In the previous question, which box has the
larger velocity after the force acts?
1) the heavier one 2) the lighter one 3)
both the same
78
ConcepTest 7.5b Two Boxes II
In the previous question, which box has the
larger velocity after the force acts?
1) the heavier one 2) the lighter one 3)
both the same
The force is related to the acceleration by
Newtons 2nd Law (F ma). The lighter box
therefore has the greater acceleration, and will
reach a higher speed after the 1-second time
interval.
Follow-up Which box has gone a larger distance
after the force acts?
Follow-up Which box has gained more KE after
the force acts?
79
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?
1) the beanbag 2) the rubber ball 3) both
the same
80
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?
1) the beanbag 2) the rubber ball 3) both
the same
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
Dp pf pi 0 (mv ) mv For the
rubber ball Dp pf pi mv (mv )
2mv
Follow-up Which one imparts the larger force to
the floor?
81
ConcepTest 2.8b Acceleration II

• When throwing a ball straight up, which of the
  following is true about its velocity v and its
  acceleration a at the highest point in its path?

1) both v 0 and a 0 2) v ¹ 0, but a 0 3)
v 0, but a ¹ 0 4) both v ¹ 0 and a ¹ 0 5) not
really sure
82
ConcepTest 2.8b Acceleration II

• When throwing a ball straight up, which of the
  following is true about its velocity v and its
  acceleration a at the highest point in its path?

1) both v 0 and a 0 2) v ¹ 0, but a 0 3)
v 0, but a ¹ 0 4) both v ¹ 0 and a ¹ 0 5) not
really sure
At the top, clearly v 0 because the ball
has momentarily stopped. But the velocity of the
ball is changing, so its acceleration is
definitely not zero! Otherwise it would remain
at rest!!
Follow-up and the value of a is?
83
ConcepTest 2.9a Free Fall I

• 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?

1) its acceleration is constant everywhere 2) at
the top of its trajectory 3) halfway to the top
of its trajectory 4) just after it leaves your
hand 5) just before it returns to your hand on
the way down
84
ConcepTest 2.9a Free Fall I

• 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?

1) its acceleration is constant everywhere 2) at
the top of its trajectory 3) halfway to the top
of its trajectory 4) just after it leaves your
hand 5) 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.
85
ConcepTest 2.9b Free Fall II
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?
1) Alices ball 2) it depends on how hard the
ball was thrown 3) neither -- they both have the
same acceleration 4) Bills ball
86
ConcepTest 2.9b Free Fall II
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?
1) Alices ball 2) it depends on how hard the
ball was thrown 3) neither -- they both have the
same acceleration 4) Bills ball
Both balls are in free fall once they are
released, therefore they both feel the
acceleration due to gravity (g). This
acceleration is independent of the initial
velocity of the ball.
Follow-up Which one has the greater velocity
when they hit the ground?
87
ConcepTest 3.7a Punts I
Which of the 3 punts has the longest hang time?
88
ConcepTest 3.7a Punts I
Which of the 3 punts has the longest hang time?
The time in the air is determined by the
vertical motion ! Since all of the punts reach
the same height, they all stay in the air for the
same time.
Follow-up Which one had the greater initial
velocity?
89
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 ?

3) both at the same time
90
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 2 goes less high, therefore it stays in
flight for less time than the other shell. Thus,
ship 2 is hit first.
3) both at the same time
Follow-up Which one traveled the greater
distance?
91
ConcepTest 3.8 Cannon on the Moon

• For a cannon on Earth, the cannonball would
  follow path 2. 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?

92
ConcepTest 3.8 Cannon on the Moon

• For a cannon on Earth, the cannonball would
  follow path 2. 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?

The ball will spend more time in the air because
gMoon lt gEarth. With more time, it can travel
farther in the horizontal direction.
Follow-up Which path would it take in outer
space?
93
ConcepTest 4.9a Going Up I

• A block of mass m rests on the floor of an
  elevator that is moving upward at constant speed.
  What is the relationship between the force due
  to gravity and the normal force on the block?

1) N gt mg 2) N mg 3) N lt mg (but not
zero) 4) N 0 5) depends on the size of the
elevator
94
ConcepTest 4.9a Going Up I

• A block of mass m rests on the floor of an
  elevator that is moving upward at constant speed.
  What is the relationship between the force due
  to gravity and the normal force on the block?

1) N gt mg 2) N mg 3) N lt mg (but not
zero) 4) N 0 5) depends on the size of the
elevator
The block is moving at constant speed, so it
must have no net force on it. The forces on it
are N (up) and mg (down), so N mg, just like
the block at rest on a table.
95
ConcepTest 4.9b Going Up II

• A block of mass m rests on the floor of an
  elevator that is accelerating upward. What is
  the relationship between the force due to gravity
  and the normal force on the block?

1) N gt mg 2) N mg 3) N lt mg (but not
zero) 4) N 0 5) depends on the size of the
elevator
96
ConcepTest 4.9b Going Up II

• A block of mass m rests on the floor of an
  elevator that is accelerating upward. What is
  the relationship between the force due to gravity
  and the normal force on the block?

1) N gt mg 2) N mg 3) N lt mg (but not
zero) 4) N 0 5) depends on the size of the
elevator
The block is accelerating upward, so it must
have a net upward force. The forces on it are N
(up) and mg (down), so N must be greater than mg
in order to give the net upward force!
S F N mg ma gt 0 \ N gt mg
Follow-up What is the normal force if the
elevator is in free fall downward?
97
ConcepTest 4.10 Normal Force
1) case 1 2) case 2 3) its the same for
both 4) depends on the magnitude of the force
F 5) depends on the ice surface

• Below you see two cases a physics student
  pulling or pushing a sled with a force F which is
  applied at an angle q. In which case is the
  normal force greater?

98
ConcepTest 4.10 Normal Force
1) case 1 2) case 2 3) its the same for
both 4) depends on the magnitude of the force
F 5) depends on the ice surface

• Below you see two cases a physics student
  pulling or pushing a sled with a force F which is
  applied at an angle q. In which case is the
  normal force greater?

In Case 1, the force F is pushing down (in
addition to mg), so the normal force needs to be
larger. In Case 2, the force F is pulling up,
against gravity, so the normal force is lessened.
99
ConcepTest 6.14 Elastic Potential Energy
How does the work required to stretch a spring 2
cm compare with the work required to stretch it 1
cm?
1) same amount of work 2) twice the work 3)
4 times the work 4) 8 times the work
100
ConcepTest 6.14 Elastic Potential Energy
How does the work required to stretch a spring 2
cm compare with the work required to stretch it 1
cm?
1) same amount of work 2) twice the work 3)
4 times the work 4) 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.
101
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 springs potential
energy (PEs) and the gravitational potential
energy (PEg) of the mass?
1) both PEs and PEg decrease 2) PEs
increases and PEg decreases 3) both PEs and
PEg increase 4) PEs decreases and PEg
increases 5) PEs increases and PEg is constant
102
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 springs potential
energy (PEs) and the gravitational potential
energy (PEg) of the mass?
1) both PEs and PEg decrease 2) PEs
increases and PEg decreases 3) both PEs and
PEg increase 4) PEs decreases and PEg
increases 5) 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.
103
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?

4) same speed for all balls
2
3
1
104
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?

4) same speed for all balls
2
3
1
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?
105
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?

1) the bowling ball 2) same time for both 3)
the ping-pong ball 4) impossible to say
106
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?

1) the bowling ball 2) same time for both 3)
the ping-pong ball 4) impossible to say
We know
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.
107
ConcepTest 7.12a Inelastic Collisions I
1) 10 m/s 2) 20 m/s 3) 0 m/s 4) 15 m/s 5) 5
m/s

• A box slides with initial velocity 10 m/s on a
  frictionless surface and collides inelastically
  with an identical box. The boxes stick together
  after the collision. What is the final velocity?

108
ConcepTest 7.12a Inelastic Collisions I
1) 10 m/s 2) 20 m/s 3) 0 m/s 4) 15 m/s 5) 5
m/s

• A box slides with initial velocity 10 m/s on a
  frictionless surface and collides inelastically
  with an identical box. The boxes stick together
  after the collision. What is the final velocity?

The initial momentum is M vi
(10) M
109
ConcepTest 7.13a Nuclear Fission I

• A uranium nucleus (at rest) undergoes fission
  and splits into two fragments, one heavy and the
  other light. Which fragment has the greater
  momentum?

1) the heavy one 2) the light one 3) both
have the same momentum 4) impossible to say
110
ConcepTest 7.13a Nuclear Fission I

• A uranium nucleus (at rest) undergoes fission
  and splits into two fragments, one heavy and the
  other light. Which fragment has the greater
  momentum?

1) the heavy one 2) the light one 3) both
have the same momentum 4) impossible to say
The initial momentum of the uranium was zero, so
the final total momentum of the two fragments
must also be zero. Thus the individual momenta
are equal in magnitude and opposite in direction.
111
ConcepTest 2.13a Graphing Velocity I
1) it speeds up all the time 2) it slows down
all the time 3) it moves at constant velocity 4)
sometimes it speeds up and sometimes it slows
down 5) not really sure
The graph of position versus time for a car
is given below. What can you say about the
velocity of the car over time?
112
ConcepTest 2.13a Graphing Velocity I
1) it speeds up all the time 2) it slows down
all the time 3) it moves at constant velocity 4)
sometimes it speeds up and sometimes it slows
down 5) not really sure
The graph of position versus time for a car
is given below. What can you say about the
velocity of the car over time?
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!
113
ConcepTest 2.13b Graphing Velocity II

• 1) it speeds up all the time
• 2) it slows down all the time
• 3) it moves at constant velocity
• 4) sometimes it speeds up and
• sometimes it slows down
• 5) not really sure

The graph of position vs. time for a car is
given below. What can you say about the velocity
of the car over time?
114
ConcepTest 2.13b Graphing Velocity II

• 1) it speeds up all the time
• 2) it slows down all the time
• 3) it moves at constant velocity
• 4) sometimes it speeds up and
• sometimes it slows down
• 5) not really sure

The graph of position vs. time for a car is
given below. What can you say about the velocity
of the car over time?
The car slows down all the time because the slope
of the x vs. t graph is diminishing as time goes
on. Remember that the slope of x vs. t is the
velocity! At large t, the value of the position x
does not change, indicating that the car must be
at rest.
115
ConcepTest 2.14a v versus t graphs I
1) decreases 2) increases 3) stays constant 4)
increases, then decreases 5) decreases, then
increases
Consider the line labeled A in the v versus
t plot. How does the speed change with time for
line A?
116
ConcepTest 2.14a v versus t graphs I
1) decreases 2) increases 3) stays constant 4)
increases, then decreases 5) decreases, then
increases
Consider the line labeled A in the v versus
t plot. How does the speed change with time for
line A?
In case A, the initial velocity is positive
and the magnitude of the velocity continues to
increase with time.
117
ConcepTest 2.14b v versus t graphs II
1) decreases 2) increases 3) stays constant 4)
increases, then decreases 5) decreases, then
increases
Consider the line labeled B in the v versus
t plot. How does the speed change with time for
line B?
118
ConcepTest 2.14b v versus t graphs II
1) decreases 2) increases 3) stays constant 4)
increases, then decreases 5) decreases, then
increases
Consider the line labeled B in the v versus
t plot. How does the speed change with time for
line B?
In case B, the initial velocity is positive but
the magnitude of the velocity decreases toward
zero. After this, the magnitude increases again,
but becomes negative, indicating that the object
has changed direction.
119
ConcepTest 2.15a Rubber Balls I
v
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? (Assume your y-axis is
pointing up.)
120
ConcepTest 2.15a Rubber Balls I
v
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? (Assume your y-axis is
pointing up.)
The ball is dropped from rest, so its initial
velocity is zero. Since the y-axis is pointing
upwards and the ball is falling downwards, its
velocity is negative and becomes more and more
negative as it accelerates downward.
121
ConcepTest 2.15b Rubber Balls II
v
You toss a ball straight up in the air and
catch it again. Right after it leaves your hand
and before you catch it, which of the above plots
represents the v vs. t graph for this motion?
(Assume your y-axis is pointing up.)
122
ConcepTest 2.15b Rubber Balls II
v
You toss a ball straight up in the air and
catch it again. Right after it leaves your hand
and before you catch it, which of the above plots
represents the v vs. t graph for this motion?
(Assume your y-axis is pointing up.)
The ball has an initial velocity that is
positive but diminishing as it slows. It stops
at the top (v 0), and then its velocity
becomes negative and becomes more and more
negative as it accelerates downward.
123
ConcepTest 3.9 Spring-Loaded Gun
The spring-loaded gun can launch projectiles at
different angles with the same launch speed. At
what angle should the projectile be launched in
order to travel the greatest distance before
landing?
1) 15 2) 30 3) 45 4) 60 5) 75
124
ConcepTest 3.9 Spring-Loaded Gun
The spring-loaded gun can launch projectiles at
different angles with the same launch speed. At
what angle should the projectile be launched in
order to travel the greatest distance before
landing?
1) 15 2) 30 3) 45 4) 60 5) 75
A steeper angle lets the projectile stay in the
air longer, but it does not travel so far because
it has a small x-component of velocity. On the
other hand, a shallow angle gives a large
x-velocity, but the projectile is not in the air
for very long. The compromise comes at 45,
although this result is best seen in a
calculation of the range formula as shown in
the textbook.
125
ConcepTest 4.21 Going Sledding

• Your little sister wants you to give her a ride
  on her sled. On level ground, what is the
  easiest way to accomplish this?

1) pushing her from behind 2) pulling her from
the front 3) both are equivalent 4) it is
impossible to move the sled 5) tell her to get
out and walk
126
ConcepTest 4.21 Going Sledding

• Your little sister wants you to give her a ride
  on her sled. On level ground, what is the
  easiest way to accomplish this?

1) pushing her from behind 2) pulling her from
the front 3) both are equivalent 4) it is
impossible to move the sled 5) tell her to get
out and walk
In Case 1, the force F is pushing down (in
addition to mg), so the normal force is larger.
In Case 2, the force F is pulling up, against
gravity, so the normal force is lessened. Recall
that the frictional force is proportional to the
normal force.
127
ConcepTest 4.22 Will It Budge?
1) moves to the left 2) moves to the right 3)
moves up 4) moves down 5) the box does not
move

• A box of weight 100 N is at rest on a floor
  where ms 0.5. A rope is attached to the box
  and pulled horizontally with tension T 30 N.
  Which way does the box move?

128
ConcepTest 4.22 Will It Budge?
1) moves to the left 2) moves to the right 3)
moves up 4) moves down 5) the box does not
move

• A box of weight 100 N is at rest on a floor
  where ms 0.5. A rope is attached to the box
  and pulled horizontally with tension T 30 N.
  Which way does the box move?

The static friction force has a maximum of msN
40 N. The tension in the rope is only 30 N.
So the pulling force is not big enough to
overcome friction.
Follow-up What happens if the tension is 35 N?
What about 45 N?
129
ConcepTest 4.23a Sliding Down I
1) component of the gravity force parallel to
the plane increased 2) coeff. of static friction
decreased 3) normal force exerted by the board
decreased 4) both 1 and 3 5) all of 1, 2,
and 3

• A box sits on a flat board. You lift one end of
  the board, making an angle with the floor. As
  you increase the angle, the box will eventually
  begin to slide down. Why?

130
ConcepTest 4.23a Sliding Down I
1) component of the gravity force parallel to
the plane increased 2) coeff. of static friction
decreased 3) normal force exerted by the board
decreased 4) both 1 and 3 5) all of 1, 2,
and 3

• A box sits on a flat board. You lift one end of
  the board, making an angle with the floor. As
  you increase the angle, the box will eventually
  begin to slide down. Why?

• As the angle increases, the component of weight
  parallel to the plane increases and the component
  perpendicular to the plane decreases (and so does
  the Normal force). Since friction depends on
  Normal force, we see that the friction force gets
  smaller and the force pulling the box down the
  plane gets bigger.

131
ConcepTest 6.17b Runaway Box

• A box sliding on a frictionless flat surface
  runs into a fixed spring, which compresses a
  distance x to stop the box. If the initial
  speed of the box were doubled, how much would the
  spring compress in this case?

132
ConcepTest 6.17b Runaway Box

• A box sliding on a frictionless flat surface
  runs into a fixed spring, which compresses a
  distance x to stop the box. If the initial
  speed of the box were doubled, how much would the
  spring compress in this case?

Use energy conservation initial energy Ei
KE 1/2 mv2 final energy Ef PEs
1/2 kx2 Conservation of Energy Ei 1/2
mv2 Ef 1/2 kx2 therefore mv2 kx2
So if v doubles, x doubles!
133
ConcepTest 6.19 Cart on a Hill
1) 4 m/s 2) 5 m/s 3) 6 m/s 4) 7 m/s 5) 25 m/s

• A cart starting from rest rolls down a hill and
  at the bottom has a speed of 4 m/s. If the cart
  were given an initial push, so its initial speed
  at the top of the hill was 3 m/s, what wo