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8/9/2019 AP Physics B Ch 7 Review PPT
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Chapter 6 energy
transformations involved
only one object
Chapter 7 momentum is
transferred when 2 or more
objects interact in a collision
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Impulse changes momentum
Bat applies an average
force over a short time
interval to accelerate the
ball
Must stop the ball, change
its direction and send it in
the opposite direction
v F ma mt
F t m v
(! !
(
( ! (g g
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Impulse = Favgy(time
Impulse from the bat changes the
momentum of the ball
Actual force builds to a very highmaximum value and then drops off
We will most often study forces that
have a constant average value
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variable force
constant force
Impulse = area under force time graph
Impulse = vector quantity in
same direction as force vector
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A ball hits a wall and bounces off
at the same speed.
What is the direction of the
impulse acting on the ball?
f iImpulse = p = p - p(
pf
pi
6
(p
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Linear Momentum
Product of an objects mass and velocity
vector quantity with same direction as velocity
vector
Units:
units for momentum are the same for impulse
p mv!ur r
2
m mkg kg s N s
s s
y ! ! y
g g
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Impulse momentum theorem
Impulse = change in momentum
Equivalent or identical?
equivalence means that if you calculate the
impulse you know what the change in
momentum is equal to equivalence means that if you know the mass
and velocity change of the object then you know
the value of the impulse that changed its velocity
0 0f f F t m v mv mv p p py ( ! ( ! ! ! (r r r r r r r
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Airbag-watermelon drop-balloon toss2 identical 1 kg watermelons are dropped from rest from a 3 meter diving board
concrete vf= 0
3 m
conservation of
energy to solve for
velocity just before
collision
211 9.8 3 12
7.7 /
PE KE
v
v m s
!
!
!
g g g g
3 m
water vf= 0
(p for both cases is the same = 0 7.7 kgm/s = - 7.7 kgm/s
Impulses for both water and concrete are both 7.7 kgm/s
Collision time for concrete (t = .001 s Force = - 7700 N (up)
Collision time for water(t = 1 s Force = - 7.7 N
TIME IS THE DETERMINING FACTOR, NOT THE FORCE
+
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Application ofImpulse Momentum Theorem
Airbag principle water balloon toss
2 extremes in changing momentum from large value to
zero
Very high force acting over a very short time
Lower force acting over a longer time
Time is what determines the force NOT force which
determines the time
1000 0.01 10
10 1 10
F t p
N s N s
N s N s
7 y ( ! (
!
!
r r
g g
g g
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Force plate ball drop example
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Conservation ofLinear Momentum
During collision each ball exerts an equal force on the other in the
opposite direction according to Newtons3rd L
aw of MotionTherefore since the time interval is the same for both forces it can be
said that the impulses of A on B and B on A are equal and opposite in
direction
Impulse from A changes Bs momentum; Impulse from B changes As
momentum 12
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Total Linear Momentum stays constant
A B
B A
Bf Bi Af Ai Ai Af
Bf Af Ai Bi
B Bf A Af B Bi A Ai
F t F t
p p
p p p p p p
p p p p
m v m v m v m v
( ! (
( ! (
! !
!
!
r rgr r Impulses are equal and opposite
change in momentums are equal and opposite
Total momentum after the collision equals the total momentum beforethe collision.
Assumes that system is closed and isolated
Isolated = no external forces
Closed = no mass or particles being added or removed from system 13
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Conservation of Momentum Examples
When two particles stick together after the collision thereis only one mass (total of m1 + m2) and only one final
velocity vf
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Momentum is a vector
Total momentum before
collision = 0
Must have + and signs on the
final velocities for total
momentum after the collision =
push to be equal to 0
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7-4 Conservation of Energy and Momentum
in Collisions
Momentum is conserved
in all collisions.
Collisions in which
kinetic energy is
conserved as well are
called elastic collisions,and those in which it is
not are called inelastic.
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Elastic, Inelastic Collisions
Momentum is always conserved for alltypes of collisions, in a closed, isolated
system
However energy has the ability to do work
in the form of deformation of one of the
objects in the collision or to generate heat
Collisions are classified by amount of
kinetic energy that is used up doing workduring collision
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Completely Elastic total KE before = total KE after
Inelastic total KE before > total KE after
some KE used up to compressand expand the ball during
collision Completely Inelastic
objects stick together aftercollision
may or may not be moving
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7-5 Elastic Collisions in One Dimension
Here we have two objects
colliding elastically. We
know the masses and the
initial speeds.
Since both momentumand kinetic energy are
conserved, we can write
two equations. This
allows us to solve for thetwo unknown final
speeds.
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Ballistic Pendulum
They may be a bullet shot
into a block which rises or a
ball which swings down and
strikes a block which then
moves to the right.
Use energy conservation to
solve for speed height
change relationship
Use momentumconservation to solve for
velocities before/after
collision
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Ballistic Pendulum
Completely inelastic collision between
bullet and block
KE of bullet > KE of bullet+block some of bullets KE used to deform block
cannot equate final PE of pendulum with
initial KE of bullet
cannot equate initial and final KEs
momentum is conserved for the collision
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2 dimensional collisions
total initial momentum in x = total final momentum in x
total initial momentum in y = total final momentum in y
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A two dimensional collision
U
J
i f!
r r
xi xf!
1v
1'v
2'v
1 1 1 1 2 2' cos ' cosm v m v m vU!
yi yfP P!
1 1 2 20 ' sin ' sinm v m vU J! 24