### 01 Momentum

```Ch 13: Momentum and
Impulse
M Sittig
AP Physics B
Summer Course 2012
2012年AP物理B暑假班
Don’t forget
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One-Minute Drill (and graph)
Momentum
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N3: Forces come in pairs, F12 = F21 (equal in
magnitude, opposite in direction).
When two objects interact for time Δt, we
can write:
F12·Δt = F21·Δt
m1·a1·Δt =
m1·(Δv1/ Δt) ·Δt =
m1·Δv1 = m2·Δv2
Time of collision
Momentum (it’s a vector)
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Momentum is defined as p = m·v.
Momentum is conserved: if one object gains
momentum from interacting with another
object, the other object loses an equal
amount of momentum.
How much momentum is gained or lost in a
collision?
F12·Δt = m1·Δv1
Momentum
p  m v
Momentum
(kg ·m/s)
Mass (kg)
Velocity
(m/s)
Example Problem
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What is the total momentum of the system
that includes spheres 1 and 2 only?
Practice Problem
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What is the total momentum of the system
that includes all three spheres?
Practice Problem
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What is the total momentum of the system
that includes all three spheres?
Practice Problem
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An object of mass m drops from rest and
falls for a time t. Ignore air resistance. After
time t the magnitude of momentum is ___.
Impulse
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F12·Δt = m1·Δv1
If the mass of an object doesn’t change in a
collision, then m·Δv = Δp, so F·Δt = change
in momentum. Let’s give this a name…
impulse!
Impulse
J  F  t  p
Impulse (N·s)
Force (N)
Time (s)
Change in
momentum(k
g·m/s)
Practice Problem
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Two balls of equal mass swing down and hit
identical bricks while traveling at identical
speeds. Ball A bounces back, but ball B stops
immediately upon hitting the brick. Which ball
has a better chance of knocking the brick over?
Practice Problem
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In the diagram, a 40-kg block is moving
along a horizontal frictionless surface, acted
upon by two horizontal forces as shown.
What is the displacement of the block
during a 5-second time interval?
Practice Problem
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In the diagram, a 40-kg block is moving
along a horizontal frictionless surface, acted
upon by two horizontal forces as shown.
What is the change in the momentum of the
block during a 5-second time interval?
Practice Problem
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In the diagram, a 40-kg block is moving
along a horizontal frictionless surface, acted
upon by two horizontal forces as shown.
What is the net impulse delivered to the
block during a 5-second time interval?
Practice Problem
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The diagram shows an object
in its initial state (on the left)
and the final state on the
right.
Which of the following
vectors best describes a
possible direction of the
impulse imparted on the
object between the initial
and the final moments?
Conservation of Momentum
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Within a system, if there are no external
forces acting, total momentum is conserved.
Total Momentumbefore collision =
Total Momentumafter collision
Momentum is a vector, so it’s conserved in
horizontal and vertical directions. You can
resolve momentum into x- and ycomponents.
Example Problem
Practice Problem
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A family which includes a girl with a mass of 20
kg and her younger brother who has a mass of
15 kg is out playing on a pond covered with
frictionless ice.
The girl and her brother are standing next to
each other at rest, when suddenly the boy
reaches out and gives his sister a big shove. As
a result of the push, the girl ends up moving off
at a speed of 3.0 m/s. What is the boy's
resulting motion?
Practice Problem
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A ball of mass m, moving with speed v,
collides with another ball of mass M,
initially at rest. After the collision the balls
stick together, moving with speed V. Find an
expression for V in terms of m, M and v.
Elastic and Inelastic Collisions
Elastic Collisions
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Momentum is conserved.
Kinetic energy is
conserved.
Perfectly elastic collisions:
gas molecules, small
particles.
Inelastic Collisions
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Momentum is conserved.
Kinetic energy is NOT
conserved.
Perfectly inelastic
collision: the two objects
stick together.
Elastic and Inelastic Collisions
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In our daily life, most collisions are
somewhere in between.
Practice Problem