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If each component of a
vector is doubled, what
happens to the angle of
that vector?
1) it doubles
2) it increases, but by less than double
3) it does not change
4) it is reduced by half
5) it decreases, but not as much as half
ConcepTest 3.2a Vector Components I
If each component of a
vector is doubled, what
happens to the angle of
that vector?
1) it doubles
2) it increases, but by less than double
3) it does not change
4) it is reduced by half
5) it decreases, but not as much as half
The magnitude of the vector clearly doubles if each of its
components is doubled. But the angle of the vector is given by tan
q = 2y/2x, which is the same as tan q = y/x (the original angle).
Follow-up: If you double one component and not the other, how would the angle change?
ConcepTest 3.2a Vector Components I
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
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
when viewed from
train
when viewed from
ground
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.
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
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.
ConcepTest 3.4b Firing Balls II
The same small cart is now rolling down an inclined track 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
ConcepTest 3.4c Firing Balls III
The same small cart is now rolling down an inclined track 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
Because the track is inclined, the cart accelerates. However, the ball has the same component of acceleration along the track as the cart does! This is essentially the component of g acting parallel to the inclined track. So the ball is effectively accelerating down the incline, just as the cart is, and it falls back into the cart.
ConcepTest 3.4c Firing Balls III
ConcepTest 3.5 Dropping a Package
You drop a package from
a plane flying at constant
speed in a straight line.
Without air resistance,
the package will:
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:
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
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 were present?
ConcepTest 3.5 Dropping a Package
ConcepTest 3.6a Dropping the Ball I
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?
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?
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
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 3.6a Dropping the Ball I
ConcepTest 3.6b Dropping the Ball II
In the previous
problem, which ball
has the greater velocity
at ground level?
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?
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
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 3.6b Dropping the Ball II
ConcepTest 3.6c Dropping the Ball III
A projectile is
launched from the
ground at an angle of
30o. At what point in
its trajectory does
this projectile have
the least speed?
1) just after it is launched
2) at the highest point in its flight
3) just before it hits the ground
4) halfway between the ground and
the highest point
5) speed is always constant
A projectile is launched
from the ground at an
angle of 30o. At what
point in its trajectory
does this projectile
have the least speed?
1) just after it is launched
2) at the highest point in its flight
3) just before it hits the ground
4) halfway between the ground and
the highest point
5) speed is always constant
The speed is smallest at
the highest point of its
flight path because the y-
component of the velocity
is zero.
ConcepTest 3.6c Dropping the Ball III
ConcepTest 4.1a Newton’s First Law I1) 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.
ConcepTest 4.1a Newton’s First Law I1) 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:
ConcepTest 4.1b Newton’s First Law II
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
A hockey
puck slides
on ice at
constant
velocity.
What is the
net force
acting on
the puck?
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.
ConcepTest 4.1b Newton’s First Law II
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
A hockey puck
slides on ice at
constant velocity.
What is the net
force acting on the
puck?
Follow-up: Are there any forces acting on the puck? What are they?
ConcepTest 4.7a Gravity and Weight I
1) Fg is greater on the feather
2) Fg is greater on the stone
3) Fg is zero on both due to vacuum
4) Fg is equal on both always
5) Fg is zero on both always
What can you
say about the
force of
gravity Fg
acting on a
stone and a
feather?
The force of gravity (weight) depends
on the mass of the object!! The stone
has more mass, therefore more weight.
ConcepTest 4.7a Gravity and Weight I
1) Fg is greater on the feather
2) Fg is greater on the stone
3) Fg is zero on both due to vacuum
4) Fg is equal on both always
5) Fg is zero on both always
What can you say
about the force of
gravity Fg acting
on a stone and a
feather?
1) it is greater on the feather
2) it is greater on the stone
3) it is zero on both due to vacuum
4) it is equal on both always
5) it is zero on both always
What can you
say about the
acceleration of
gravity acting
on the stone
and the
feather?
ConcepTest 4.7b Gravity and Weight II
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.
1) it is greater on the feather
2) it is greater on the stone
3) it is zero on both due to vacuum
4) it is equal on both always
5) it is zero on both always
What can you say
about the acceleration
of gravity acting on
the stone and the
feather?
ConcepTest 4.7b Gravity and Weight II
Follow-up: Which one hits the bottom first?
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 > mg
2) N = mg
3) N < mg (but not zero)
4) N = 0
5) depends on the size of the elevator
m
v
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.
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 > mg
2) N = mg
3) N < mg (but not zero)
4) N = 0
5) depends on the size of the elevator
m
v
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 > mg
2) N = mg
3) N < mg (but not zero)
4) N = 0
5) depends on the size of the elevator
ConcepTest 4.9b Going Up II
m
a
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!
1) N > mg
2) N = mg
3) N < mg (but not zero)
4) N = 0
5) depends on the size of the elevator
S F = N – mg = ma >
0
\ N > mg
m a > 0
mg
N
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?
ConcepTest 4.9b Going Up II
Follow-up: What is the normal force if the elevator is in free fall downward?
ConcepTest 4.10 Normal Force
Case 1
Case 2
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?
1) case 1
2) case 2
3) it’s the same for both
4) depends on the magnitude of the force F
5) depends on the ice surface
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.
ConcepTest 4.10 Normal Force
Case 1
Case 2
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?
1) case 1
2) case 2
3) it’s the same for both
4) depends on the magnitude of the force F
5) depends on the ice surface
ConcepTest 4.11 On an Incline
1) case A
2) case B
3) both the same (N = mg)
4) both the same (0 < N < mg)
5) both the same (N = 0)
Consider two identical blocks,
one resting on a flat surface
and the other resting on an
incline. For which case is the
normal force greater?
1) case A
2) case B
3) both the same (N = mg)
4) both the same (0 < N < mg)
5) both the same (N = 0)
N
WWy
x
y
f
q
q
ConcepTest 4.11 On an Incline
Consider two identical blocks,
one resting on a flat surface
and the other resting on an
incline. For which case is the
normal force greater?
In Case A, we know that N = W.
In Case B, due to the angle of
the incline, N < W. In fact, we
can see that N = W cos(q).
ConcepTest 4.12 Climbing the Rope
When you climb up a
rope, the first thing
you do is pull down
on the rope. How do
you manage to go up
the rope by doing
that??
1) this slows your initial velocity, which is already upward
2) you don’t go up, you’re too heavy
3) you’re not really pulling down – it just seems that way
4) the rope actually pulls you up
5) 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 Third Law.
ConcepTest 4.12 Climbing the RopeWhen you climb up a
rope, the first thing you
do is pull down on the
rope. How do you
manage to go up the
rope by doing that??
1) this slows your initial velocity, which is already upward
2) you don’t go up, you’re too heavy
3) you’re not really pulling down – it just seems that way
4) the rope actually pulls you up
5) you are pulling the ceiling down
ConcepTest 4.14a Collision Course I
A small car
collides with a
large truck.
Which
experiences the
greater impact
force?
1) the car
2) the truck
3) both the same
4) it depends on the velocity of each
5) it depends on the mass of each
ConcepTest 4.14a Collision Course I
A small car collides
with a large truck.
Which experiences
the greater impact
force?
1) the car
2) the truck
3) both the same
4) it depends on the velocity of each
5) it depends on the mass of each
According to Newton’s Third Law, both vehicles
experience the same magnitude of force.
1) the car
2) the truck
3) both the same
4) it depends on the velocity of each
5) it depends on the mass of each
In the collision
between the
car and the
truck, which
has the greater
acceleration?
ConcepTest 4.14b Collision Course II
1) the car
2) the truck
3) both the same
4) it depends on the velocity of each
5) it depends on the mass of each
In the collision
between the car and
the truck, which has
the greater
acceleration?
ConcepTest 4.14b Collision Course II
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 4.21 Going Sledding
1
2
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
Your little sister
wants you to give
her a ride on her
sled. On level
ground, what is
the easiest way to
accomplish this?
ConcepTest 4.21 Going Sledding
1
2
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.
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
Your little sister wants
you to give her a ride
on her sled. On level
ground, what is the
easiest way to
accomplish this?
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?
Tm
Static friction (ms = 0.4 )
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.
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?
Tm
Static friction (ms = 0.4 )
Follow-up: What happens if the tension is 35 N? What about 45 N?
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?
Net Force
Normal
Weight
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?
Net Force
Normal
Weight
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.
ConcepTest 4.23a Sliding Down I
Is it possible to do work on an
object that remains at rest?
1) yes
2) no
ConcepTest 5.1 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.
ConcepTest 5.1 To Work or Not to Work
ConcepTest 5.2a Friction and Work I
1) friction does no work at all
2) friction does negative work
3) friction does positive work
A box is being
pulled across a
rough floor at a
constant speed.
What can you
say about the
work done by
friction?
f
N
mg
displacement
Pull
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 < 0.
ConcepTest 5.2a Friction and Work I
1) friction does no work at all
2) friction does negative work
3) friction does positive work
A box is being pulled
across a rough floor at a
constant speed. What
can you say about the
work done by friction?
Can friction ever
do positive work? 1) yes
2) 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 5.2b Friction and Work II
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
ConcepTest 5.2c 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 < 0.
Note that because the work done on the ball is negative, its
speed decreases.
ConcepTest 5.2c Play Ball!
Follow-up: What about the work done by the ball on the catcher?
ConcepTest 5.2d Tension and Work
1) tension does no work at all
2) tension does negative work
3) tension does positive work
A ball tied to a
string is being
whirled around in
a circle. What
can you say
about the work
done by tension?
ConcepTest 5.2d Tension and Work
1) tension does no work at all
2) tension does negative work
3) tension does positive work
A ball tied to a string is
being whirled around in
a circle. What can you
say about the work done
by tension?
v
T
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 = 180o, then W < 0.
Follow-up: Is there a force in the direction of the velocity?
ConcepTest 5.3 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?
ConcepTest 5.3 Force and Work
N
f
T
mg
displacementAny force not perpendicular
to the motion will do work:
N does no work
T does positive work
f does negative work
mg does negative 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?
ConcepTest 5.8a Slowing Down
1) 20 m
2) 30 m
3) 40 m
4) 60 m
5) 80 m
If a car traveling 60
km/hr can brake to a
stop within 20 m,
what is its stopping
distance if it is
traveling 120 km/hr?
Assume that the
braking force is the
same in both cases.
F d = Wnet = DKE = 0 – 1/2 mv2
thus: |F| d = 1/2 mv2
Therefore, if the speed doubles,
the stopping distance gets four
times larger.
ConcepTest 5.8a Slowing Down
1) 20 m
2) 30 m
3) 40 m
4) 60 m
5) 80 m
If a car traveling 60 km/hr can
brake to a stop within 20 m,
what is its stopping distance if
it is traveling 120 km/hr?
Assume that the braking force
is the same in both cases.
ConcepTest 5.13 Up the Hill
1) the same
2) twice as much
3) four times as much
4) half as much
5) you gain no PE in either case
Two paths lead to the top
of a big hill. One is steep
and direct, while the
other is twice as long but
less steep. How much
more potential energy
would you gain if you
take the longer path?
Since your vertical position (height) changes by the
same amount in each case, the gain in potential
energy is the same.
ConcepTest 5.13 Up the Hill
1) the same
2) twice as much
3) four times as much
4) half as much
5) you gain no PE in either case
Two paths lead to the top of a big
hill. One is steep and direct, while
the other is twice as long but less
steep. How much more potential
energy would you gain if you take
the longer path?
Follow-up: How much more work do you do in taking the steeper path?
Follow-up: Which path would you rather take? Why?
ConcepTest 5.16 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?
1
4) same speed
for all balls2 3
ConcepTest 5.16 Down the Hill
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).
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?
1
4) same speed
for all balls2 3
Follow-up: Which ball takes longer to get down the ramp?
ConcepTest 5.18a Water Slide I
1) Paul
2) Kathleen
3) both the same
Paul and Kathleen start from rest at
the same time on frictionless water
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.
ConcepTest 5.18b Water Slide II
Paul and Kathleen
start from rest at
the same time on
frictionless water
slides with
different shapes.
Who makes it to
the bottom first?
1) Paul
2) Kathleen
3) both the same
ConcepTest 5.18b Water Slide II
Paul and Kathleen start from
rest at the same time on
frictionless water slides with
different shapes. Who makes it
to the bottom first?
Even though they both have
the same final velocity,
Kathleen is at a lower height
than Paul for most of her ride.
Thus she always has a larger
velocity during her ride and
therefore arrives earlier!
1) Paul
2) Kathleen
3) both the same
ConcepTest 5.21a Time for Work I
1) Mike
2) Joe
3) both did the same work
Mike applied 10 N of
force over 3 m in 10
seconds. Joe applied
the same force over
the same distance in 1
minute. Who did
more work?
Both exerted the same force over the same
displacement. Therefore, both did the same
amount of work. Time does not matter for
determining the work done.
ConcepTest 5.21a Time for Work I
1) Mike
2) Joe
3) both did the same work
Mike applied 10 N
of force over 3 m
in 10 seconds.
Joe applied the
same force over
the same
distance in 1
minute. Who did
more work?
Mike performed 5 J of work in
10 secs. Joe did 3 J of work
in 5 secs. Who produced the
greater power?
1) Mike produced more power
2) Joe produced more power
3) both produced the same
amount of power
ConcepTest 5.21b Time for Work II
Mike performed 5 J of work in
10 secs. Joe did 3 J of work
in 5 secs. Who produced the
greater power?
1) Mike produced more power
2) Joe produced more power
3) both produced the same
amount of power
Since power = work / time, we see that Mike produced 0.5 W
and Joe produced 0.6 W of power. Thus, even though Mike
did more work, he required twice the time to do the work, and
therefore his power output was lower.
ConcepTest 5.21b Time for Work II
ConcepTest 5.22b Energy Consumption
Which contributes
more to the cost of
your electric bill each
month, a 1500-Watt
hair dryer or a 600-
Watt microwave
oven?
1) hair dryer
2) microwave oven
3) both contribute equally
4) depends upon what you cook in the oven
5) depends upon how long each one is on
1500 W
600 W
We already saw that what you actually pay for
is energy. To find the energy consumption of
an appliance, you must know more than just
the power rating—you have to know how long
it was running.
ConcepTest 5.22b Energy Consumption
Which contributes more to
the cost of your electric bill
each month, a 1500-Watt hair
dryer or a 600-Watt
microwave oven?
1) hair dryer
2) microwave oven
3) both contribute equally
4) depends upon what you cook in the oven
5) depends upon how long each one is on
1500 W
600 W
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?
1) greater than
2) less than
3) equal to
ConcepTest 6.3a 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?
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.
ConcepTest 6.3a Momentum and Force
1) greater than
2) less than
3) equal to
ConcepTest 6.3b 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?
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 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 6.3b 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?
ConcepTest 6.4 Collision Course
1) the car
2) the truck
3) they both have the same
momentum change
4) can’t 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 Newton’s 3rd Law.
ConcepTest 6.4 Collision Course
1) the car
2) the truck
3) they both have the same
momentum change
4) can’t 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?
Follow-up: Which one feels the larger acceleration?
ConcepTest 6.6 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?
1) hit the other car
2) hit the wall
3) makes no difference
4) call your physics
teacher!
5) 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 6.6 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?
1) hit the other car
2) hit the wall
3) makes no difference
4) call your physics
teacher!
5) get insurance!
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
ConcepTest 6.7 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
ConcepTest 6.7 Impulse
Follow-up: Which one imparts the larger force to the floor?
ConcepTest 6.9a Going Bowling I
p
p
1) the bowling ball
2) same time for both
3) the ping-pong ball
4) impossible to say
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?
ConcepTest 6.9a Going Bowling I
We know:
Here, F and Dp are the same for both balls!
It will take the same amount of time to stop them. p
p so Dp = Fav Dt
1) the bowling ball
2) same time for both
3) the ping-pong ball
4) impossible to say
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?
av DtDp
F =
ConcepTest 6.9b Going Bowling II
p
p
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, for
which is the stopping
distance greater?
1) the bowling ball
2) same distance for both
3) the ping-pong ball
4) impossible to say
ConcepTest 6.9b Going Bowling II
p
p
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.
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,
for which is the stopping
distance greater?
1) the bowling ball
2) same distance for both
3) the ping-pong ball
4) impossible to say
ConcepTest 6.10a Elastic Collisions I
v 2
v
1at rest
at rest
1) situation 1
2) situation 2
3) both the same
Consider two elastic collisions: 1) a golf ball with speed v hits a stationary bowling ball head-on.
2) a bowling ball with speed v hits a stationary golf ball head-on. In which case does the golf ball have the greater speed after the collision?
Remember that the magnitude of the relative velocity has to be equal before and after the collision!
ConcepTest 6.10a Elastic Collisions I
v
1
In case 1 the bowling ball will almost remain at rest, and the golf ball will bounce back with speed close to v.
v 2
2v
In case 2 the bowling ball will keep going with speed close to v, hence the golf ball will rebound with speed close to 2v.
1) situation 1
2) situation 2
3) both the same
Consider two elastic collisions: 1) a golf ball with speed v hits a stationary bowling ball head-on. 2) a bowling ball with speed v hits a stationary golf ball head-on. In which case does the golf ball have the greater speed after the collision?
ConcepTest 6.10b Elastic Collisions II
Carefully place a small rubber ball
(mass m) on top of a much bigger
basketball (mass M) and drop these
from some height h. What is the
velocity of the smaller ball after the
basketball hits the ground, reverses
direction and then collides with
small rubber ball?
1) zero
2) v
3) 2v
4) 3v
5) 4v
• Remember that relative velocity has to be equal before and after collision! Before the collision, the basketball bounces up with v and the rubber ball is coming down with v, so their relative velocity is –2v. After the collision, it therefore has to be +2v!!
ConcepTest 6.10b Elastic Collisions II
v
v
v
v
3v
v
(a) (b) (c)
m
M
Carefully place a small rubber ball (mass m)
on top of a much bigger basketball (mass M)
and drop these from some height h. What is
the velocity of the smaller ball after the
basketball hits the ground, reverses direction
and then collides with small rubber ball?
1) zero
2) v
3) 2v
4) 3v
5) 4v
Follow-up: With initial drop height h, how high does the small rubber ball bounce up?
ConcepTest 6.14b Recoil Speed II
1) 0 m/s
2) 0.5 m/s to the right
3) 1 m/s to the right
4) 20 m/s to the right
5) 50 m/s to the right
A cannon sits on a
stationary railroad
flatcar with a total
mass of 1000 kg.
When a 10-kg cannon
ball is fired to the left
at a speed of 50 m/s,
what is the recoil
speed of the flatcar?
ConcepTest 6.14b Recoil Speed II
Since the initial momentum of the system
was zero, the final total momentum must
also be zero. Thus, the final momenta of
the cannon ball and the flatcar must be
equal and opposite.
pcannonball = (10 kg)(50 m/s) = 500 kg-m/s
pflatcar = 500 kg-m/s = (1000 kg)(0.5 m/s)
1) 0 m/s
2) 0.5 m/s to the right
3) 1 m/s to the right
4) 20 m/s to the right
5) 50 m/s to the right
A cannon sits on a stationary
railroad flatcar with a total mass of
1000 kg. When a 10-kg cannon ball
is fired to the left at a speed of 50
m/s, what is the recoil speed of the
flatcar?
When a bullet is fired
from a gun, the bullet
and the gun have equal
and opposite momenta.
If this is true, then why
is the bullet deadly?
(whereas it is safe to
hold the gun while it is
fired)
1) it is much sharper than the gun
2) it is smaller and can penetrate your body
3) it has more kinetic energy than the gun
4) it goes a longer distance and gains speed
5) it has more momentum than the gun
ConcepTest 6.15 Gun Control
When a bullet is fired
from a gun, the bullet
and the gun have equal
and opposite momenta.
If this is true, then why
is the bullet deadly?
(whereas it is safe to
hold the gun while it is
fired)
1) it is much sharper than the gun
2) it is smaller and can penetrate your body
3) it has more kinetic energy than the gun
4) it goes a longer distance and gains speed
5) it has more momentum than the gun
While it is true that the magnitudes of the momenta of the gun and the bullet are equal, the bullet is less massive and so it has a much higher velocity. Since KE is related to v2, the bullet has considerably more KE and therefore can do more damage on impact.
ConcepTest 6.15 Gun Control
ConcepTest 6.16a Crash Cars I
1) I
2) II
3) I and II
4) II and III
5) all three
If all three collisions
below are totally
inelastic, which one(s)
will bring the car on
the left to a complete
halt?
ConcepTest 6.16a Crash Cars I
In case I, the solid wall
clearly stops the car.
In cases II and III, since ptot
= 0 before the collision,
then ptot must also be zero
after the collision, which
means that the car comes
to a halt in all three cases.
1) I
2) II
3) I and II
4) II and III
5) all three
If all three collisions below
are totally inelastic, which
one(s) will bring the car on
the left to a complete halt?
ConcepTest 6.16b Crash Cars II
If all three collisions
below are totally
inelastic, which
one(s) will cause the
most damage (in
terms of lost
energy)?
1) I
2) II
3) III
4) II and III
5) all three
ConcepTest 6.16b Crash Cars II
The car on the left loses
the same KE in all 3 cases,
but in case III, the car on
the right loses the most
KE because KE = 1/2 m v2
and the car in case III
has the largest velocity.
If all three collisions below are
totally inelastic, which one(s)
will cause the most damage
(in terms of lost energy)?
1) I
2) II
3) III
4) II and III
5) all three
ConcepTest 6.17 Shut the Door!
1) the superball
2) the blob of clay
3) it doesn’t matter -- they
will be equally effective
4) you are just too lazy to
throw anything
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?
ConcepTest 6.17 Shut the Door!
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.
1) the superball
2) the blob of clay
3) it doesn’t matter -- they
will be equally effective
4) you are just too lazy to
throw anything
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?
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