Physics
Semester I
Final Review
ConcepTest 3.2a
Vector Components I
1) it doubles
If each component of a
vector is doubled, what
happens to the angle of
that vector?
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
1) it doubles
If each component of a
vector is doubled, what
happens to the angle of
that vector?
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 3.4a
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?
Firing Balls I
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
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?
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.
Firing Balls I
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
ConcepTest 3.4b
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?
Firing Balls II
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
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?
Firing Balls II
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 3.4c
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?
Firing Balls III
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
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?
Firing Balls III
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 3.5
You drop a package from
a plane flying at constant
speed in a straight line.
Dropping a Package
1) quickly lag behind the plane
while falling
2) remain vertically under the
plane while falling
Without air resistance,
3) move ahead of the plane while
falling
the package will:
4) not fall at all
ConcepTest 3.5
You drop a package from
a plane flying at constant
speed in a straight line.
Dropping a Package
1) quickly lag behind the plane
while falling
2) remain vertically under the
plane while falling
Without air resistance,
3) move ahead of the plane while
falling
the package will:
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 3.6a
From the same height
(and at the same time),
one ball is dropped and
another ball is fired
horizontally. Which
one will hit the ground
first?
Dropping the Ball I
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
ConcepTest 3.6a
From the same height
(and at the same time),
one ball is dropped and
another ball is fired
horizontally. Which one
will hit the ground first?
Dropping the Ball I
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 3.6b
In the previous
Dropping the Ball II
1) the “dropped” ball
2) the “fired” ball
problem, which ball
has the greater velocity
at ground level?
3) neither – they both have the
same velocity on impact
4) it depends on how hard the
ball was thrown
ConcepTest 3.6b
In the previous problem,
which ball has the
greater velocity at
ground level?
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
Both balls have the same vertical velocity
when they hit the ground (since they are
both acted on by gravity for the same
time). However, the “fired” ball also has a
horizontal velocity. When you add the two
components vectorially, the “fired” ball
has a larger net velocity when it hits the
ground.
Follow-up: What would you have to do to have them
both reach the same final velocity at ground level?
ConcepTest 3.6c
A projectile is
launched from the
ground at an angle of
30o. At what point in
its trajectory does
this projectile have
the least speed?
Dropping the Ball III
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
ConcepTest 3.6c
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?
The speed is smallest at
the highest point of its
flight path because the ycomponent of the velocity
is zero.
Dropping the Ball III
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
ConcepTest 4.1a Newton’s First Law I
A book is lying at
1) there is a net force but the book has too
much inertia
rest on a table.
2) there are no forces acting on it at all
The book will
3) it does move, but too slowly to be seen
remain there at
4) there is no net force on the book
rest because:
5) there is a net force, but the book is too
heavy to move
ConcepTest 4.1a Newton’s First Law I
A book is lying at
1) there is a net force but the book has too
much inertia
rest on a table.
2) there are no forces acting on it at all
The book will
3) it does move, but too slowly to be seen
remain there at
4) there is no net force on the book
rest because:
5) there is a net force, but the book is too
heavy to move
There are forces acting on the book, but the only
forces acting are in the y-direction. Gravity acts
downward, but the table exerts an upward force
that is equally strong, so the two forces cancel,
leaving no net force.
ConcepTest 4.1b Newton’s 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
ConcepTest 4.1b Newton’s 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?
ConcepTest 4.7a Gravity and Weight I
What can you
say about the
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
force of
gravity Fg
acting on a
stone and a
feather?
5) Fg is zero on both always
ConcepTest 4.7a Gravity and Weight I
What can you say
1) Fg is greater on the feather
2) Fg is greater on the stone
about the force of
3) Fg is zero on both due to vacuum
gravity Fg acting
4) Fg is equal on both always
5) Fg is zero on both always
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 4.7b Gravity and Weight II
What can you
say about the
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
acceleration of
gravity acting
on the stone
and the
feather?
5) it is zero on both always
ConcepTest 4.7b Gravity and Weight II
What can you say
1) it is greater on the feather
about the acceleration
2) it is greater on the stone
of gravity acting on
the stone and the
3) it is zero on both due to vacuum
4) it is equal on both always
5) it is zero on both always
feather?
The acceleration is given by F/m so
here the mass divides out. Since we
know that the force of gravity (weight)
is mg, then we end up with acceleration
g for both objects.
Follow-up: Which one hits the bottom first?
ConcepTest 4.9a Going Up I
A block of mass m rests on the floor of
1) N > mg
an elevator that is moving upward at
2) N = mg
constant speed. What is the
relationship between the force due to
3) N < mg (but not zero)
gravity and the normal force on the
4) N = 0
block?
5) depends on the size of the
elevator
v
m
ConcepTest 4.9a Going Up I
A block of mass m rests on the floor of
1) N > mg
an elevator that is moving upward at
2) N = mg
constant speed. What is the
relationship between the force due to
3) N < mg (but not zero)
gravity and the normal force on the
4) N = 0
block?
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
v
on it are N (up) and mg (down), so N = mg,
just like the block at rest on a table.
m
ConcepTest 4.9b Going Up II
A block of mass m rests
1) N > mg
on the floor of an
2) N = mg
elevator that is
accelerating upward.
What is the relationship
3) N < mg (but not zero)
4) N = 0
5) depends on the size of the
elevator
between the force due to
gravity and the normal
a
force on the block?
m
ConcepTest 4.9b Going Up II
A block of mass m rests on the
1) N > mg
floor of an elevator that is
2) N = mg
accelerating upward. What is
3) N < mg (but not zero)
the relationship between the
4) N = 0
force due to gravity and the
5) depends on the size of the
elevator
normal force on the block?
The block is accelerating upward, so
it must have a net upward force. The
N
m
a>0
forces on it are N (up) and mg (down),
so N must be greater than mg in order
to give the net upward force!
Follow-up: What is the normal force if
the elevator is in free fall downward?
mg
S F = N – mg = ma > 0
\ N > mg
ConcepTest 4.10 Normal Force
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
Case 1
Case 2
ConcepTest 4.10 Normal Force
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
Case 1
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.
Case 2
ConcepTest 4.11 On an Incline
Consider two identical blocks,
1) case A
one resting on a flat surface
2) case B
and the other resting on an
incline. For which case is the
normal force greater?
3) both the same (N = mg)
4) both the same (0 < N < mg)
5) both the same (N = 0)
ConcepTest 4.11 On an Incline
Consider two identical blocks,
1) case A
one resting on a flat surface
2) case B
and the other resting on an
incline. For which case is the
normal force greater?
3) both the same (N = mg)
4) both the same (0 < N < mg)
5) both the same (N = 0)
In Case A, we know that N = W.
y
In Case B, due to the angle of
the incline, N < W. In fact, we
N
f
can see that N = W cos(q).
q
q
W
Wy
x
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
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
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
rope by doing that??
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 4.14a Collision Course I
1) the car
A small car
2) the truck
collides with a
3) both the same
4) it depends on the velocity of each
large truck.
Which
experiences the
greater impact
force?
5) it depends on the mass of each
ConcepTest 4.14a Collision Course I
A small car collides
1) the car
with a large truck.
2) the truck
Which experiences
the greater impact
3) both the same
4) it depends on the velocity of each
5) it depends on the mass of each
force?
According to Newton’s Third Law, both vehicles
experience the same magnitude of force.
ConcepTest 4.14b Collision Course II
1) the car
In the collision
2) the truck
between the
3) both the same
car and the
truck, which
has the greater
acceleration?
4) it depends on the velocity of each
5) it depends on the mass of each
ConcepTest 4.14b Collision Course II
In the collision
between the car and
1) the car
2) the truck
3) both the same
the truck, which has
4) it depends on the velocity of each
the greater
5) it depends on the mass of each
acceleration?
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
Your little sister
1) pushing her from behind
wants you to give
2) pulling her from the front
her a ride on her
sled. On level
3) both are equivalent
4) it is impossible to move the sled
5) tell her to get out and walk
ground, what is
the easiest way to
accomplish this?
1
2
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
1
is pulling up, against gravity, so the
normal force is lessened. Recall that
the frictional force is proportional to
the normal force.
2
ConcepTest 4.22 Will it Budge?
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?
1) moves to the left
2) moves to the right
3) moves up
4) moves down
5) the box does not move
Static friction
(ms = 0.4 )
m
T
ConcepTest 4.22 Will it Budge?
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?
1) moves to the left
2) moves to the right
3) moves up
4) moves down
5) the box does not move
The static friction force has a
maximum of msN = 40 N. The
tension in the rope is only 30 N.
Static friction
(ms = 0.4 )
m
T
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?
ConcepTest 4.23a Sliding Down I
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?
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
Normal
Net Force
Weight
ConcepTest 4.23a Sliding Down I
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?

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
As the angle increases, the component
of weight parallel to the plane increases
and the component perpendicular to the
Normal
plane decreases (and so does the normal
force). Since friction depends on normal
Net Force
force, we see that the friction force gets
smaller and the force pulling the box
down the plane gets bigger.
Weight
ConcepTest 5.1 To Work or Not to
Work
Is it possible to do work on an
1) yes
object that remains at rest?
2) no
ConcepTest 5.1 To Work or Not to
Work
Is it possible to do work on an
1) yes
object that remains at rest?
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 5.2a Friction and Work
I
A box is being
1) friction does no work at all
pulled across a
2) friction does negative work
rough floor at a
3) friction does positive work
constant speed.
What can you
say about the
work done by
friction?
ConcepTest 5.2a Friction and Work I
A box is being pulled
across a rough floor at a
1) friction does no work at all
constant speed. What
2) friction does negative work
can you say about the
3) friction does positive work
work done by friction?
Friction acts in the opposite
N displacement
direction to the displacement, so
the work is negative. Or using the
Pull
f
definition of work (W = F d cos q ),
since q = 180o, then W < 0.
mg
ConcepTest 5.2b Friction and Work II
Can friction ever
do positive work?
1) yes
2) no
ConcepTest 5.2b Friction and Work II
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 5.2c Play Ball!
In a baseball game, the
catcher stops a 90-mph
1) catcher has done positive work
pitch. What can you say
2) catcher has done negative work
about the work done by
3) catcher has done zero work
the catcher on the ball?
ConcepTest 5.2c Play Ball!
In a baseball game, the
catcher stops a 90-mph
1) catcher has done positive work
pitch. What can you say
2) catcher has done negative work
about the work done by
3) catcher has done zero work
the catcher on the ball?
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 q = 180o, then W < 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?
ConcepTest 5.2d Tension and Work
A ball tied to a
1) tension does no work at all
string is being
2) tension does negative work
whirled around in
3) tension does positive work
a circle. What
can you say
about the work
done by tension?
ConcepTest 5.2d Tension and Work
A ball tied to a string is
being whirled around in
1) tension does no work at all
a circle. What can you
2) tension does negative work
say about the work done 3) tension does positive work
by tension?
No work is done because the force
acts in a perpendicular direction to
the displacement. Or using the
definition of work (W = F d cos q ),
since q = 180o, then W < 0.
T
v
Follow-up: Is there a force in the direction of the velocity?
ConcepTest 5.3 Force and Work
1) one force
A box is being pulled
2) two forces
up a rough incline by a
3) three forces
rope connected to a
4) four forces
pulley. How many
5) no forces are doing work
forces are doing work
on the box?
ConcepTest 5.3 Force and Work
A box is being pulled up a
1) one force
rough incline by a rope
2) two forces
connected to a pulley.
3) three forces
How many forces are
4) four forces
doing work on the box?
5) no forces are doing work
Any force not perpendicular
to the motion will do work:
N does no work
N
T
T does positive work
f
f does negative work
mg does negative work
mg
ConcepTest 5.8a Slowing Down
If a car traveling 60
1) 20 m
km/hr can brake to a
2) 30 m
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.
3) 40 m
4) 60 m
5) 80 m
ConcepTest 5.8a Slowing Down
If a car traveling 60 km/hr can
brake to a stop within 20 m,
what is its stopping distance if
1) 20 m
2) 30 m
3) 40 m
it is traveling 120 km/hr?
4) 60 m
Assume that the braking force
5) 80 m
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 5.13 Up the Hill
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?
1) the same
2) twice as much
3) four times as much
4) half as much
5) you gain no PE in either
case
ConcepTest 5.13 Up the Hill
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?
1) the same
2) twice as much
3) four times as much
4) half as much
5) you gain no PE in either
case
Since your vertical position (height) changes by the
same amount in each case, the gain in potential
energy is the same.
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
2
3
4) same speed
for all balls
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?
4) same speed
for all balls
1
2
3
All of the balls have the same initial gravitational PE,
since they are all at the same height (PE = mgh). Thus,
when they get to the bottom, they all have the same final
KE, and hence the same speed (KE = 1/2 mv2).
Follow-up: Which ball takes longer to get down the ramp?
ConcepTest 5.18a Water Slide I
Paul and Kathleen start from rest at
1) Paul
the same time on frictionless water
2) Kathleen
slides with different shapes. At the
3) both the same
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
1) Paul
rest at the same time on
2) Kathleen
frictionless water slides with
3) both the same
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!
ConcepTest 5.21a Time for Work I
Mike applied 10 N of
1) Mike
force over 3 m in 10
2) Joe
3) both did the same work
seconds. Joe applied
the same force over
the same distance in 1
minute. Who did
more work?
ConcepTest 5.21a Time for Work I
Mike applied 10 N
1) Mike
of force over 3 m
2) Joe
in 10 seconds.
3) both did the same work
Joe applied the
same force over
the same
Both exerted the same force over the same
distance in 1
displacement. Therefore, both did the same
minute. Who did
amount of work. Time does not matter for
more work?
determining the work done.
ConcepTest 5.21b Time for Work II
Mike performed 5 J of work in
1) Mike produced more power
10 secs. Joe did 3 J of work
2) Joe produced more power
in 5 secs. Who produced the
3) both produced the same
greater power?
amount of power
ConcepTest 5.21b Time for Work II
Mike performed 5 J of work in
1) Mike produced more power
10 secs. Joe did 3 J of work
2) Joe produced more power
in 5 secs. Who produced the
3) both produced the same
greater power?
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 5.22b Energy
Consumption
Which contributes
1) hair dryer
more to the cost of
2) microwave oven
your electric bill each
3) both contribute equally
month, a 1500-Watt
4) depends upon what you
cook in the oven
hair dryer or a 600-
5) depends upon how long
each one is on
Watt microwave
600 W
oven?
1500 W
ConcepTest 5.22b Energy
Consumption
1) hair dryer
Which contributes more to
2) microwave oven
the cost of your electric bill
3) both contribute equally
each month, a 1500-Watt
4) depends upon what you
cook in the oven
hair dryer or a 600-Watt
5) depends upon how long
each one is on
microwave oven?
We already saw that what you actually pay for
600 W
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.
1500 W
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
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 6.3b 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
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 6.4 Collision Course
1) the car
A small car and a
2) the truck
large truck collide
3) they both have the same
momentum change
head-on and stick
4) can’t tell without knowing the
final velocities
together. Which
one has the larger
momentum
change?
ConcepTest 6.4 Collision Course
A small car and a large
1) the car
truck collide head-on
2) the truck
and stick together.
3) they both have the same
momentum change
Which one has the larger
momentum change?
4) can’t tell without knowing the
final velocities
Since the total momentum of the
system is conserved, that means that
Dp = 0 for the car and truck combined.
Therefore, Dpcar must be equal and
opposite to that of the truck (–Dptruck) in
order for the total momentum change
to be zero. Note that this conclusion
also follows from Newton’s 3rd Law.
Follow-up: Which one feels
the larger acceleration?
ConcepTest 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 headon). 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!
ConcepTest 6.6 Watch Out!
You drive around a curve in a narrow 1) hit the other car
one-way street at 30 mph when you see 2) hit the wall
an identical car heading straight toward 3) makes no difference
you at 30 mph. You have two options: 4) call your physics
teacher!
hit the car head-on or swerve into a
massive concrete wall (also head-on). 5) get insurance!
What should you do?
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 6.7 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
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
1) the beanbag
2) the rubber ball
3) both the same
impulse to the floor when it hits?
Both objects reach the same speed at the floor. However, while
the beanbag comes to rest on the floor, the ball bounces back
up with nearly the same speed as it hit. Thus, the change in
momentum for the ball is greater, because of the rebound.
The impulse delivered by the ball is twice that of the beanbag.
For the beanbag:
For the rubber ball:
Dp = pf – pi = 0 – (–mv ) = mv
Dp = pf – pi = mv – (–mv ) = 2mv
Follow-up: Which one imparts the larger force to the floor?
ConcepTest 6.9a 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
p
p
ConcepTest 6.9a Going Bowling I
A bowling ball and a ping-pong
ball are rolling toward you with
the same momentum. If you
exert the same force to stop each
one, which takes a longer time to
bring to rest?
We know:
Dp
Fav =
Dt
1) the bowling ball
2) same time for both
3) the ping-pong ball
4) impossible to say
so Dp = Fav Dt
p
Here, F and Dp are the same for both balls!
It will take the same amount of time
to stop them.
p
ConcepTest
6.9ba Going Bowling II
A bowling
ball and
ping-pong ball are
rolling toward you
with the same
1) the bowling ball
2) same distance for both
3) the ping-pong ball
4) impossible to say
momentum. If you
exert the same force
to stop each one, for
p
which is the stopping
distance greater?
p
ConcepTest 6.9b Going Bowling II
A bowling ball and a ping-pong
ball are rolling toward you with
1) the bowling ball
2) same distance for both
the same momentum. If you exert
3) the ping-pong ball
the same force to stop each one,
4) impossible to say
for which is the stopping
distance greater?
Use the work-energy theorem: W = DKE.
The ball with less mass has the greater
speed (why?), and thus the greater KE (why
again?). In order to remove that KE, work
must be done, where W = Fd. Since the
force is the same in both cases, the
distance needed to stop the less massive
ball must be bigger.
p
p
ConcepTest 6.10a Elastic
Collisions I
Consider two elastic collisions:
1)
1) a golf ball with speed v hits a
2)
stationary bowling ball head-on.
3)
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?
situation 1
situation 2
both the same
at rest
v
at rest
1
v
2
ConcepTest 6.10a Elastic
Collisions I
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!
1) situation 1
2) situation 2
3) both the same
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.
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.
2v
v
2
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
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
1) zero
the velocity of the smaller ball after the
basketball hits the ground, reverses direction
and then collides with small rubber ball?
4) 3v
2) v
3) 2v
5) 4v
• Remember that relative
3v
m
velocity has to be equal
v
v
before and after collision!
Before the collision, the
v
v
M
basketball bounces up
v
with v and the rubber ball
is coming down with v,
(a)
(b)
(c)
so their relative velocity is
–2v. After the collision, it Follow-up: With initial drop height h, how
therefore has to be +2v!!
high does the small rubber ball bounce up?
ConcepTest 6.14b Recoil Speed II
A cannon sits on a
1) 0 m/s
stationary railroad
2) 0.5 m/s to the right
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?
3) 1 m/s to the right
4) 20 m/s to the right
5) 50 m/s to the right
ConcepTest 6.14b Recoil Speed II
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?
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
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
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 6.16a Crash Cars I
If all three collisions
below are totally
inelastic, which one(s)
will bring the car on
the left to a complete
halt?
1) I
2) II
3) I and II
4) II and III
5) all three
ConcepTest 6.16a Crash Cars I
If all three collisions below
1) I
are totally inelastic, which
2) II
one(s) will bring the car on
the left to a complete halt?
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.
3) I and II
4) II and III
5) all three
ConcepTest 6.16b Crash Cars II
1) I
If all three collisions
below are totally
inelastic, which
terms of lost
energy)?
3) III
4) II and III
5) all three
one(s) will cause the
most damage
2) II
(in
ConcepTest 6.16b Crash Cars II
If all three collisions below are
totally inelastic, which one(s)
1) I
2) II
3) III
will cause the most damage
4) II and III
(in terms of lost energy)?
5) all three
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.
ConcepTest 6.17 Shut the Door!
You are lying in bed and
1) the superball
you want to shut your
2) the blob of clay
bedroom door. You have a
3) it doesn’t matter -- they
will be equally effective
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?
4) you are just too lazy to
throw anything
ConcepTest 6.17 Shut the Door!
You are lying in bed and you want to 1) the superball
shut your bedroom door. You have a 2) the blob of clay
superball and a blob of clay (both
3) it doesn’t matter -- they
with the same mass) sitting next to
you. Which one would be more
effective
to throw at your door to
will be equally effective
4) you are just too lazy to
throw anything
close it?
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.