Physics Semester I - RainfordPhysics

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					Physics
Semester I
Final Review
      ConcepTest 3.2a            Vector Components I

                          1) it doubles
If each component of a
                          2) it increases, but by less than double
vector is doubled, what
                          3) it does not change
happens to the angle of
                          4) it is reduced by half
that vector?              5) it decreases, but not as much as half
      ConcepTest 3.2a               Vector Components I

                             1) it doubles
If each component of a
                             2) it increases, but by less than double
vector is doubled, what
                             3) it does not change
happens to the angle of
                             4) it is reduced by half
that vector?                 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              Firing Balls I
A small cart is          1) it depends on how fast the cart is
                             moving
rolling at constant      2) it falls behind the cart
velocity on a flat track. it falls in front of the cart
                         3)
It fires a ball straight 4) it falls right back into the cart
up into the air as it    5) it remains at rest

moves. After it is
fired, what happens
to the ball?
           ConcepTest 3.4a                     Firing Balls I
    A small cart is rolling at        1) it depends on how fast the cart is
    constant velocity on a flat           moving
    track. It fires a ball straight   2) it falls behind the cart
    up into the air as it moves.      3) it falls in front of the cart
    After it is fired, what happens
                                      4) it falls right back into the cart
    to the ball?
                                      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
                                    when                          when
cart and the ball have the       viewed from                  viewed from
same horizontal velocity,
                    velocity         train                       ground
so the ball still returns into
the cart.
               ConcepTest 3.4b                 Firing Balls II
Now the cart is being pulled        1) it depends upon how much the
along a horizontal track by an           track is tilted
external force (a weight
hanging over the table edge)        2) it falls behind the cart
and accelerating. It fires a ball   3) it falls in front of the cart
straight out of the cannon as it
moves. After it is fired, what      4) it falls right back into the cart
happens to the ball?                5) it remains at rest
               ConcepTest 3.4b                 Firing Balls II
Now the cart is being pulled        1) it depends upon how much the
along a horizontal track by an           track is tilted
external force (a weight
hanging over the table edge)        2) it falls behind the cart
and accelerating. It fires a ball   3) it falls in front of the cart
straight out of the cannon as it
moves. After it is fired, what      4) it falls right back into the cart
happens to the ball?                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                     Firing Balls III
The same small cart is
now rolling down an        1) it depends upon how much the track is tilted
inclined track and
                           2) it falls behind the cart
accelerating. It fires a
ball straight out of the   3) it falls in front of the cart
cannon as it moves.
                           4) it falls right back into the cart
After it is fired, what
happens to the ball?       5) it remains at rest
         ConcepTest 3.4c                     Firing Balls III
The same small cart is
now rolling down an        1) it depends upon how much the track is tilted
inclined track and
                           2) it falls behind the cart
accelerating. It fires a
ball straight out of the   3) it falls in front of the cart
cannon as it moves.
                           4) it falls right back into the cart
After it is fired, what
happens to the ball?       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         Dropping a Package
You drop a package from      1) quickly lag behind the plane
                                 while falling
a plane flying at constant
                             2) remain vertically under the
speed in a straight line.        plane while falling
                             3) move ahead of the plane while
Without air resistance,         falling
the package will:            4) not fall at all
           ConcepTest 3.5              Dropping a Package
 You drop a package from              1) quickly lag behind the plane
                                          while falling
 a plane flying at constant
                                      2) remain vertically under the
 speed in a straight line.                plane while falling
                                      3) move ahead of the plane while
 Without air resistance,                 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.
direction

     Follow-up: What would happen if air resistance were present?
    ConcepTest 3.6a         Dropping the Ball I
                          1) the “dropped” ball
From the same height
                          2) the “fired” ball
(and at the same time),   3) they both hit at the same time
one ball is dropped and   4) it depends on how hard the ball
                             was fired
another ball is fired
                          5) it depends on the initial height
horizontally. Which
one will hit the ground
first?
    ConcepTest 3.6a                  Dropping the Ball I
From the same height
                                  1) the “dropped” ball
(and at the same time),
                                  2) the “fired” ball
one ball is dropped and
                                  3) they both hit at the same time
another ball is fired
                                  4) it depends on how hard the ball
horizontally. Which one              was fired
will hit the ground first?        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       Dropping the Ball II

In the previous problem,1)   the “dropped” ball
                        2) the “fired” ball
which ball has the      3) neither – they both have the
                           same velocity on impact
greater velocity at
                        4) it depends on how hard the
ground level?              ball was thrown
    ConcepTest 3.6b                Dropping the Ball II
 In the previous problem,         1) the “dropped” ball
                                  2) the “fired” ball
 which ball has the
                                  3) neither – they both have the
 greater velocity at                 same velocity on impact

 ground level?                    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            Dropping the Ball III
                        1) just after it is launched
A projectile is
                        2) at the highest point in its flight
launched from the
                        3) just before it hits the ground
ground at an angle of
30o. At what point in   4) halfway between the ground and
                           the highest point
its trajectory does
                        5) speed is always constant
this projectile have
the least speed?
    ConcepTest 3.6c               Dropping the Ball III
                             1) just after it is launched
 A projectile is launched
 from the ground at an       2) at the highest point in its flight
 angle of 30o. At what       3) just before it hits the ground
 point in its trajectory     4) halfway between the ground and
 does this projectile           the highest point
 have the least speed?       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.
   zero
     ConcepTest 4.1a Newton’s First Law I
                     1) there is a net force but the book has too
A book is lying at      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
                     4) there is no net force on the book
remain there at
                     5) there is a net force, but the book is too
rest because:           heavy to move
    ConcepTest 4.1a Newton’s First Law I
                        1) there is a net force but the book has too
A book is lying at         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
                        4) there is no net force on the book
remain there at
                        5) there is a net force, but the book is too
rest because:              heavy to move


        There are forces acting on the book, but the only
                                       book
        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.
                       force
  ConcepTest 4.1b Newton’s First Law II
A hockey        1) more than its weight

puck slides     2) equal to its weight

on ice at       3) less than its weight but more than zero
                4) depends on the speed of the puck
constant
                5) zero
velocity.
What is the
net force
acting on
the puck?
      ConcepTest 4.1b Newton’s First Law II
A hockey puck              1) more than its weight
slides on ice at           2) equal to its weight
constant velocity.         3) less than its weight but more than zero
What is the net            4) depends on the speed of the puck
force acting on the        5) zero
puck?


        The puck is moving at a constant velocity, and
                                         velocity
        therefore it is not accelerating. Thus, there must
                            accelerating
        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
                  1) Fg is greater on the feather
What can you      2) Fg is greater on the stone

say about the     3) Fg is zero on both due to vacuum
                  4) Fg is equal on both always
force of          5) Fg is zero on both always


gravity Fg
acting on a
stone and a
feather?
     ConcepTest 4.7a Gravity and Weight I
                            1) Fg is greater on the feather
What can you say
                            2) Fg is greater on the stone
about the force of          3) Fg is zero on both due to vacuum
                            4) Fg is equal on both always
gravity Fg acting
                            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
                  1) it is greater on the feather
What can you      2) it is greater on the stone

say about the     3) it is zero on both due to vacuum
                  4) it is equal on both always
acceleration of   5) it is zero on both always


gravity acting
on the stone
and the
feather?
     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
                             3) it is zero on both due to vacuum
of gravity acting on
                             4) it is equal on both always
the stone and the            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
      mg
   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
                                          3) N < mg (but not zero)
relationship between the force due to
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
                                           3) N < mg (but not zero)
 relationship between the force due to
 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,
                                       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
                           2) N = mg
on the floor of an
                           3) N < mg (but not zero)
elevator that is
                           4) N = 0
accelerating upward.
                           5) depends on the size of the
What is the relationship     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
normal force on the block?               elevator


The block is accelerating upward, so
                                                     N
it must have a net upward force. The
                          force
                                                    m
forces on it are N (up) and mg (down),                        a>0
                                                     mg
so N must be greater than mg in order
to give the net upward force!
                       force                S F = N – mg = ma > 0
Follow-up: What is the normal force if        \ N > mg
the elevator is in free fall downward?
         ConcepTest 4.10 Normal Force
                         1) case 1
Below you see two
                         2) case 2
cases: a physics
                         3) it’s the same for both
student pulling or
                         4) depends on the magnitude of
pushing a sled with a      the force F
force F which is         5) depends on the ice surface
applied at an angle q.
                                              Case 1
In which case is the
normal force greater?

                                     Case 2
              ConcepTest 4.10 Normal Force
Below you see two cases:                 1) case 1
a physics student pulling or             2) case 2
pushing a sled with a force
                                         3) it’s the same for both
F which is applied at an
                                         4) depends on the magnitude of
angle q. In which case is the              the force F
normal force greater?                    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
                mg
needs to be larger. In Case 2, the force F
            larger
                                                     Case 2
is pulling up, against gravity, so the
           up
normal force is lessened.
                lessened
          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
                                 3) both the same (N = mg)
incline. For which case is the
normal force greater?            4) both the same (0 < N < mg)
                                 5) both the same (N = 0)




                        A                    B
            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
                                   3) both the same (N = mg)
  incline. For which case is the
  normal force greater?            4) both the same (0 < N < mg)
                                   5) both the same (N = 0)


In Case A, we know that N = W.
        A
                                                   y
In Case B, due to the angle of
        B
the incline, N < W. In fact, we                   N                x
                                                              f
can see that N = W cos(q).

                                                          q   Wy
                                                      W
                                           q
    A
      ConcepTest 4.12 Climbing the Rope
                        1) this slows your initial velocity,
When you climb up a       which is already upward
                        2) you don’t go up, you’re too heavy
rope, the first thing   3) you’re not really pulling down – it
                          just seems that way
you do is pull down     4) the rope actually pulls you up

on the rope. How do     5) you are pulling the ceiling down


you manage to go up
the rope by doing
that??
        ConcepTest 4.12 Climbing the Rope
When you climb up a            1) this slows your initial velocity,
                                 which is already upward
rope, the first thing you
                               2) you don’t go up, you’re too heavy
do is pull down on the         3) you’re not really pulling down – it
                                 just seems that way
rope. How do you               4) the rope actually pulls you up
manage to go up the            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
                                      reaction
      rope on you) to the force that you exerted on the rope.
              you                                       rope
      And voilá, this is Newton’s Third Law.
     ConcepTest 4.14a Collision Course I
                    1) the car

A small car         2) the truck
                    3) both the same
collides with a
                    4) it depends on the velocity of each
large truck.        5) it depends on the mass of each
Which
experiences the
greater impact
force?
      ConcepTest 4.14a Collision Course I
A small car collides        1) the car
                            2) the truck
with a large truck.
                            3) both the same
Which experiences
                            4) it depends on the velocity of each
the greater impact          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
                   4) it depends on the velocity of each
car and the        5) it depends on the mass of each
truck, which
has the greater
acceleration?
        ConcepTest 4.14b Collision Course II
                               1) the car
In the collision
                               2) the truck
between the car and            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,
               acceleration
since it has the smaller
mass.
mass
      ConcepTest 4.21 Going Sledding
Your little sister   1) pushing her from behind

wants you to give    2) pulling her from the front
                     3) both are equivalent
her a ride on her
                     4) it is impossible to move the sled
sled. On level       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
                                 1) pushing her from behind
you to give her a ride
                                 2) pulling her from the front
on her sled. On level
                                 3) both are equivalent
ground, what is the
                                 4) it is impossible to move the sled
easiest way to
                                 5) tell her to get out and walk
accomplish this?

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
         larger
                                                         1
is pulling up, against gravity, so the
           up
normal force is lessened. Recall that
                lessened
the frictional force is proportional to
the normal force.                                    2
      ConcepTest 4.22 Will it Budge?

A box of weight        1) moves to the left
100 N is at rest on    2) moves to the right

a floor where ms =     3) moves up
                       4) moves down
0.5. A rope is
                       5) the box does not move
attached to the box
and pulled
                      Static friction
horizontally with       (ms = 0.4 )      m
                                                  T

tension T = 30 N.
Which way does
the box move?
             ConcepTest 4.22 Will it Budge?
A box of weight 100 N is at rest     1) moves to the left
on a floor where ms = 0.5. A
                                     2) moves to the right
rope is attached to the box and
                                     3) moves up
pulled horizontally with
                                     4) moves down
tension T = 30 N. Which way
                                     5) the box does not move
does the box move?


 The static friction force has a
 maximum of msN = 40 N. The
                     N
                                     Static friction            T
 tension in the rope is only 30 N.
                                N      (ms = 0.4 )     m
 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
                       1) component of the gravity force
A box sits on a flat      parallel to the plane increased
board. You lift one    2) coeff. of static friction decreased
end of the board,      3) normal force exerted by the board
                          decreased
making an angle with
                       4) both #1 and #3
the floor. As you      5) all of #1, #2 and #3
increase the angle,
the box will
eventually begin to
                                                  Normal
slide down. Why?
                                                  Net Force

                                    Weight
               ConcepTest 4.23a Sliding Down I
    A box sits on a flat board.
                                      1) component of the gravity force
    You lift one end of the              parallel to the plane increased
    board, making an angle            2) coeff. of static friction decreased
    with the floor. As you            3) normal force exerted by the board
    increase the angle, the box          decreased
    will eventually begin to          4) both #1 and #3
    slide down. Why?                  5) all of #1, #2 and #3

l    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                     Normal
     force). Since friction depends on normal
     force, we see that the friction force gets                  Net Force
     smaller and the force pulling the box         Weight
     down the plane gets bigger.
                         bigger
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.
                                              distance
       If an object does not move at all, there is no
       displacement, and therefore no work done.
       displacement                        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
                                        2) friction does negative work
constant speed. What
                                        3) friction does positive work
can you say about the
work done by friction?

 Friction acts in the opposite
                                                          N displacement
 direction to the displacement, so
                                                f              Pull
 the work is negative. Or using the
             negative
 definition of work (W = F d cos q ),
 since ￿ 180o, then W < 0.
        =                                                 mg
ConcepTest 5.2b Friction and Work II


   Can friction ever      1) yes
   do positive work?
                          2) no
ConcepTest 5.2b Friction and Work II


   Can friction ever                          1) yes
   do positive work?
                                              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
                                 truck
 the force of friction that is making the box move.
                                              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
                                           negative
 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.

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 ),                 T
 since ￿ 180o, then W < 0.
        =
                                                      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
                          5) no forces are doing work
pulley. How many
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
                               4) four forces
How many forces are
                               5) no forces are doing work
doing work on the box?
                                         dis
                                             p    lac
 Any force not perpendicular                         em
                                                        en
 to the motion will do work:                              t        N
                                              T
  N does no work
  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
                        3) 40 m
stop within 20 m,
                        4) 60 m
what is its stopping    5) 80 m
distance if it is
traveling 120 km/hr?
Assume that the
braking force is the
same in both cases.
       ConcepTest 5.8a Slowing Down
   If a car traveling 60 km/hr can
                                      1) 20 m
   brake to a stop within 20 m,
                                      2) 30 m
   what is its stopping distance if
                                      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,
                        doubles
the stopping distance gets four
   times larger.
         larger
  ConcepTest 5.13 Up the Hill
                              1) the same
Two paths lead to the top
                              2) twice as much
of a big hill. One is steep   3) four times as much

and direct, while the         4) half as much
                              5) you gain no PE in either
other is twice as long but       case
less steep. How much
more potential energy
would you gain if you
take the longer path?
      ConcepTest 5.13 Up the Hill
Two paths lead to the top of a big           1) the same
hill. One is steep and direct, while         2) twice as much
the other is twice as long but less          3) four times as much
steep. How much more potential               4) half as much
energy would you gain if you take            5) you gain no PE in either
the longer path?                                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?



                              4) same speed
                                  for all balls
1      2          3
   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,
                                                            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).
       KE


   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
       height
 same velocity at the bottom.
   ConcepTest 5.18b Water Slide II
                         1) Paul
Paul and Kathleen
                         2) Kathleen
start from rest at
                         3) both the same
the same time on
frictionless water
slides with
different shapes.
Who makes it to
the bottom first?
      ConcepTest 5.18b Water Slide II
 Paul and Kathleen start from     1) Paul

 rest at the same time on         2) Kathleen
                                  3) both the same
 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.
                          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
                         2) Joe
force over 3 m in 10
                         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
                                    3) both did the same work
in 10 seconds.
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
                    displacement

minute. Who did     amount of work. Time does not matter for
                              work
                    determining the work done.
                                         done
more work?
    ConcepTest 5.21b Time for Work II

                                1) Mike produced more power
Mike performed 5 J of work in
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

                                    1) Mike produced more power
Mike performed 5 J of work in
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
                          3) both contribute equally
your electric bill each
                          4) depends upon what you
month, a 1500-Watt           cook in the oven
                          5) depends upon how long
hair dryer or a 600-         each one is on
                                          600 W
Watt microwave
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
   energy
an appliance, you must know more than just
the power rating—you have to know how long
it was running.
       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        1) greater than
magnitude acts on a 130-g pebble.
                                        2) less than
How does the rate of change of the
                                        3) equal to
boulder’s momentum compare to
the rate of change of the pebble’s
momentum?
    ConcepTest 6.3a Momentum and
    Force
A net force of 200 N acts on a 100-kg
boulder, and a force of the same               1) greater than
magnitude acts on a 130-g pebble.
                                               2) less than
How does the rate of change of the
                                               3) equal to
boulder’s momentum compare to
the rate of change of the pebble’s
momentum?



      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.       1) greater than
How does the rate of change of the      2) less than
boulder’s velocity compare to the       3) equal to
rate of change of the pebble’s
velocity?
    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.             1) greater than
How does the rate of change of the            2) less than
boulder’s velocity compare to the             3) equal to
rate of change of the pebble’s
velocity?


       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
                      3) they both have the same
large truck collide      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
                                              3) they both have the same
  and stick together.
                                                 momentum change
  Which one has the larger                    4) can’t tell without knowing the
                                                 final velocities
  momentum change?
Since the total momentum of the
system is conserved, that means that
Dp = 0 for the car and truck combined.
                             combined
Therefore, Dpcar must be equal and
             ca
opposite to that of the truck (–Dptruck) in
order for the total momentum change
to be zero. Note that this conclusion            Follow-up: Which one feels
                                                 the larger acceleration?
also follows from Newton’s 3rd Law.
   ConcepTest 6.6 Watch Out!
You drive around a curve in     1) hit the other car

a narrow one-way street at      2) hit the wall
                                3) makes no difference
30 mph when you see an
                                4) call your physics
identical car heading               teacher!
straight toward you at 30       5) get insurance!
mph. You have two options:
hit the car head-on or
swerve into a massive
concrete wall (also head-on).
What should you do?
       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
hit the car head-on or swerve into a        teacher!
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,
                                                            mosquito
   you’d be better off running him down...
                                   down
    ConcepTest 6.7 Impulse
A small beanbag and a bouncy
rubber ball are dropped from the
                                     1) the beanbag
same height above the floor.
                                     2) the rubber ball
They both have the same mass.
Which one will impart the greater    3) both the same
impulse to the floor when it hits?
    ConcepTest 6.7 Impulse
A small beanbag and a bouncy
rubber ball are dropped from the
                                            1) the beanbag
same height above the floor.
                                            2) the rubber ball
They both have the same mass.
Which one will impart the greater           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.
                                                     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?
  ConcepTest 6.9a Going Bowling I
A bowling ball and a
ping-pong ball are       1) the bowling ball
                         2) same time for both
rolling toward you
                         3) the ping-pong ball
with the same            4) impossible to say

momentum. If you
exert the same force
to stop each one,                              p

which takes a longer
time to bring to rest?                     p
       ConcepTest 6.9a Going Bowling I
A bowling ball and a ping-pong
ball are rolling toward you with              1) the bowling ball

the same momentum. If you                     2) same time for both

exert the same force to stop each             3) the ping-pong ball

one, which takes a longer time to             4) impossible to say

bring to rest?


                  Dp
We know:    Fav =         so Dp = Fav Dt
                  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 6.9b
A bowling ball and a Going Bowling II
ping-pong ball are      1) the bowling ball
                        2) same distance for both
rolling toward you      3) the ping-pong ball
with the same           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
                                         1) the bowling ball
ball are rolling toward you with         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. KE
  The ball with less mass has the greater
  speed (why?), and thus the greater KE (why
         (why?)                                                    p
  again?). In order to remove that KE, work
  again?)
  must be done, where W = Fd. Since the
                              Fd
                                                               p
  force is the same in both cases, the
  distance needed to stop the less massive
  ball must be bigger.
                bigger
     ConcepTest 6.10a Elastic
      Collisions I
Consider two elastic collisions:
                                      1)   situation 1
   1) a golf ball with speed v hits a 2)   situation 2
stationary bowling ball head-on.      3)   both the same
   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?


                                                         at rest
                  v      at rest
                                            v
                                   1                               2
     ConcepTest 6.10a Elastic
     Collisions I
   Consider two elastic collisions:
        1) a golf ball with speed v hits a   1) situation 1
   stationary bowling ball head-on.
                                             2) situation 2
        2) a bowling ball with speed v
   hits a stationary golf ball head-on. In   3) both the same
   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      v
and after the collision!                                           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
                                                              2v
will rebound with speed close to 2v.              v
                                                                   2
   ConcepTest 6.10b Elastic
   Collisions II
                                         1) zero
Carefully place a small rubber ball
                                         2) v
(mass m) on top of a much bigger
                                         3) 2v
basketball (mass M) and drop these       4) 3v
from some height h. What is the          5) 4v
velocity of the smaller ball after the
basketball hits the ground, reverses
direction and then collides with
small rubber ball?
       ConcepTest 6.10b Elastic
       Collisions II
Carefully place a small rubber ball (mass m)                  1) zero
on top of a much bigger basketball (mass M)                   2) v
and drop these from some height h. What is                    3) 2v
the velocity of the smaller ball after the                    4) 3v
basketball hits the ground, reverses direction                5) 4v
and then collides with small rubber ball?
• Remember that relative                                       3v
  velocity has to be equal        v        m
                                                 v
  before and after collision!
  Before the collision, the                                    v
  basketball bounces up         v       M      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
  –2v
  therefore has to be +2v!!
                       +2v        high does the small rubber ball bounce up?
  ConcepTest 6.14b Recoil Speed II
A cannon sits on a          1) 0 m/s
                            2) 0.5 m/s to the right
stationary railroad
                            3) 1 m/s to the right
flatcar with a total
                            4) 20 m/s to the right
mass of 1000 kg.            5) 50 m/s to the right
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
A cannon sits on a stationary
                                             1) 0 m/s
railroad flatcar with a total mass of
                                             2) 0.5 m/s to the right
1000 kg. When a 10-kg cannon ball
                                             3) 1 m/s to the right
is fired to the left at a speed of 50
                                             4) 20 m/s to the right
m/s, what is the recoil speed of the
                                             5) 50 m/s to the right
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)
    ConcepTest 6.15 Gun Control
When a bullet is fired
from a gun, the bullet      1) it is much sharper than the gun
and the gun have equal      2) it is smaller and can penetrate your body
and opposite momenta.       3) it has more kinetic energy than the gun
If this is true, then why
                            4) it goes a longer distance and gains speed
is the bullet deadly?
(whereas it is safe to      5) it has more momentum than the gun
hold the gun while it is
fired)
    ConcepTest 6.15 Gun Control
When a bullet is fired
from a gun, the bullet      1) it is much sharper than the gun
and the gun have equal      2) it is smaller and can penetrate your body
and opposite momenta.       3) it has more kinetic energy than the gun
If this is true, then why
                            4) it goes a longer distance and gains speed
is the bullet deadly?
(whereas it is safe to      5) it has more momentum than the gun
hold the gun while it is
fired)


   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       1) I
                              2) II
below are totally             3) I and II
inelastic, which one(s)       4) II and III
                              5) all three
will bring the car on
the left to a complete
halt?
      ConcepTest 6.16a Crash Cars I
 If all three collisions below    1) I
 are totally inelastic, which     2) II
                                  3) I and II
 one(s) will bring the car on
                                  4) II and III
 the left to a complete halt?     5) all three


In case I, the solid wall
clearly stops the car.

In cases II and III, since ptot
= 0 before the collision,
                  collision
then ptot must also be zero
after the collision, which
           collision
means that the car comes
to a halt in all three cases.
    ConcepTest 6.16b Crash Cars II

                            1) I
                            2) II
If all three collisions
                            3) III
below are totally
                            4) II and III
inelastic, which            5) all three
one(s) will cause the
most damage        (in
terms of lost
energy)?
     ConcepTest 6.16b Crash Cars II
                                       1) I
   If all three collisions below are
                                       2) II
   totally inelastic, which one(s)
                                       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
             III
the right loses the most
KE because KE = 1/2 m v2
and the car in case III has
the largest velocity.
            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
                               3) it doesn’t matter -- they
bedroom door. You have a          will be equally effective
superball and a blob of clay   4) you are just too lazy to
(both with the same mass)         throw anything

sitting next to you. Which
one would be more
effective to throw at your
door to close it?
       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              will be equally effective

you. Which one would be more                  4) you are just too lazy to
                                                 throw anything
effective   to throw at your door to
close it?

     The superball bounces off the door with almost no loss of
       speed, so its Dp (and that of the door) is 2mv.
                                                   mv

     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
                                          superball
       imparts less Dp to the door.

				
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