AP Physics Chapter 6 Momentum and Collisions ..

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AP Physics Chapter 6Momentum and
Collisions
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Chapter 6 Momentum and Collisions

• 6.1 Linear Momentum
• 6.2 Impulse
• 6.3 The Conservation of Linear Momentum
• 6.4 Elastic and Inelastic Collisions
• 6.5-6.6 Not Covered

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Learning Objectives

• Impulse and Momentum
• Students will understand impulse and linear
  momentum, so they can
• Relate mass, velocity, and linear momentum for a
  moving object, and calculate the total linear
  momentum of a system of objects.
• Relate impulse to the change in linear momentum
  and the average force acting on an object.
• Calculate the area under a force versus time
  graph and relate it to the change in momentum of
  an object.

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Learning Objectives

• 2. Conservation of Linear Momentum and Collisions
• Students will understand linear momentum
  conservation, so they can
• Identify situations in which linear momentum, or
  a component of the linear momentum vector, is
  conserved.
• Apply linear momentum conservation to
  one-dimensional elastic and inelastic collisions
  and two-dimensional completely inelastic
  collisions.
• Analyze situations in which two or more objects
  are pushed apart by a spring or other agency, and
  calculate how much energy is released in such a
  process.

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Homework for Chapter 6

• Read Chapter 6
• HW 6.A p. 203 1-7, 10, 11, 13, 18, 19, 22, 26,
  29, 31, 33, 34, 35, 37.
• HW 6.B p. 205 38, 40, 41, 43-46, 49. p.206
  54-56, 58, 62, 65, 66.

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6.1 Linear Momentum6.2 Impulse
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Loosen Up! II
Physics Daily WarmUps 91

• Impulse is found by multiplying the force acting
  on an object by the amount of time the force
  acts. The amount of impulse that an object
  experiences is equal to the amount that its
  momentum changes. This means that the same change
  in momentum can be accomplished by exerting a
  large force for a short amount of time or a small
  force for a longer amount of time.
• Seat belts are designed to give a little when
  they are properly fastened. If not, they would
  not work as well at keeping you from injury in an
  accident or sudden stop. Use the concept of
  impulse equaling the change in momentum to
  explain why they need to give.

Solution The time to bring a person to stop is
increased, thereby decreasing the force exerted
on the person by the belt.
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6.1 Linear Momentum
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6.1 Linear Momentum

• The SI unit of momentum is the kgm/s.
• The total linear momentum of a system is the
  vector sum of the momenta of the individual
  particles.
• P p1 p2 p3 ? pi
• i

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6.1 Linear Momentum
Example 6.1 Which has more linear momentum a)
a 1500 kg car moving at 25.0 m/s or b) a 40,000
kg truck moving at 1.00 m/s?
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6.1 Linear Momentum
Example 6.2 Two identical 1500 kg cars are
moving perpendicular to each other. One moves
with a speed of 25.0 m/s due north and the other
moves at 15.0 m/s due east. What is the total
linear momentum of the system?
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6.1 Linear Momentum Check for Understanding
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6.1 Linear Momentum Check for Understanding
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6.1 Linear Momentum Check for Understanding
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6.1 Linear Momentum Check for Understanding
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6.2 Impulse
J
J
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6.2 Impulse
? In fact, Newton used the momentum form of his
second law when he first started formatting
the law.
J
? For a system in which mass is not a constant,
such as rocket propulsion, the momentum form
should be used.
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6.2 Impulse
Example 6.3 A 0.10 kg ball is dropped onto a
table top. The speeds of the ball right before
hitting the table top and right after hitting the
table top are 5.0 m/s and 4.0 m/s respectively.
If the collision between the ball and the
tabletop lasts 0.15 s, what is the average force
exerted on the ball by the table top?
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Change in momentum The change in momentum is
given by the difference in momentum vectors.
a) Here the vector sum is zero, but the
difference, or change in momentum, is not.
b) The change in momentum is found by computing
the change in the components.
Fig. 6.3 in text, p. 177
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6.2 Impulse Check for Understanding
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6.2 Impulse Check for Understanding
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6.2 Impulse Check for Understanding
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6.2 Impulse Check for Understanding
Answer b
J
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6.2 Impulse Check for Understanding
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6.2 Impulse Check for Understanding
J
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Homework for Sections 6.1 6.2

• HW 6.A p. 203 1-7, 10, 11, 13, 18, 19, 22, 26,
  29, 31, 33, 34, 35, 37.

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6.3 The Conservation of Linear Momentum6.4
Elastic and Inelastic Collisions
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Collision Conservation
Physics Daily WarmUps 97

• Momentum is always conserved in any collision, as
  is energy. However, energy usually transformed
  into several different types as a result of the
  collision. In most collisions, a significant
  amount of the kinetic energy is converted into
  other forms, and the colliding objects movements
  are greatly affected. These are called inelastic
  collisions. There are some collisions, like the
  colliding steel balls suspended by strings in a
  Newtons Cradle, in which kinetic energy is
  almost conserved. Since so little energy is lost
  in each collision, they seem to just go on
  bouncing. These collisions represent elastic
  collisions.
• Elastic collisions always seem to catch our
  attention. Because they are so rare, they seem
  unusual to us. Write down a personal experience
  where you witnessed an elastic collision.

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6.3 The Conservation of Linear Momentum
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6.3 The Conservation of Linear Momentum
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Momentum is conserved in an isolated system. The
motion in two dimensions may be analyzed in terms
of the components of momentum, which is also
conserved.
If m1 and m2 are equal, they will split apart at
a 90 degree angle.
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• Conservation of Momentum
• Before the rifle is fired, the total momentum of
  the rifle and the bullet is zero.
• During firing, there are equal and opposite
  internal forces, and the instantaneous total
  momentum of the rifle-bullet system remains zero.
• When the bullet leaves the barrel, the total
  momentum of the system is still zero.

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6.3 The Conservation of Linear Momentum
Example 6.4 A 50 kg pitching machine (excluding
the baseball) is placed on a frozen pond. The
machine fires a 0.40 kg baseball with a speed of
35 m/s in the horizontal direction. What is the
recoil velocity of the pitching machine? (Assume
negligible friction.)
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6.3 The Conservation of Linear Momentum
Example 6.5 A 10 gram bullet moving at 300 m/s
is fired into a 1.0 kg block. The bullet emerges
(does not stay embedded in the block) with half
of its original speed. What is the velocity of
the block right after the collision?
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6.3 The Conservation of Linear Momentum Check
for Understanding
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6.3 The Conservation of Linear Momentum Check
for Understanding
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6.3 The Conservation of Linear Momentum Check
for Understanding
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6.3 The Conservation of Linear Momentum Check
for Understanding
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6.4 Elastic and Inelastic Collisions
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6.4 Elastic and Inelastic Collisions
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6.4 Elastic and Inelastic Collisions
Elastic Collisions For an elastic collision
between two bodies, one of which is initially at
rest, the velocities after the collision depend
on the relative masses of the bodies.
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6.4 Elastic and Inelastic Collisions
a) When a moving object collides elastically with
a stationary object of equal mass, there is a
complete exchange of momentum and energy.
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b) When a very massive moving object collides
elastically with a much less massive stationary
object, the very massive object continues to move
essentially as before, and the less massive
object is given a velocity almost twice the
initial velocity of the large mass.
Special cases of head-on elastic collisions
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6.4 Elastic and Inelastic Collisions
Special cases of head-on elastic collisions
v1o
m1
m2
Before (v2o 0)
c) When a moving object of small mass collides
elastically with a very massive stationary
object, the incoming object recoils in the
opposite direction with approximately the same
speed and the very massive object remains
essentially stationary. c) m1 ltlt m2
m2
m1
Collision
v1o -v1o
m1
After
m2
v2 0
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6.4 Elastic and Inelastic Collisions
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6.4 Elastic and Inelastic Collisions
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Inelastic collisions In inelastic collisions,
momentum is conserved but kinetic energy is not.
Collisions like the ones shown here, in which
the objects stick together , are called
completely inelastic collisions. The maximum
amount of kinetic energy lost is consistent with
the conservation of momentum.
6.4 Elastic and Inelastic Collisions
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6.4 Elastic and Inelastic Collisions

• Example 6.6 While standing on skates on a frozen
  pond, a student of mass 70.0 kg catches a 2.00 kg
  ball travelling horizontally at 15.0 m/s toward
  him.
• What is the speed of the student and the ball
  immediately after he catches it?
• How much kinetic energy is lost in the process?

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6.4 Elastic and Inelastic Collisions
Example 6.7 A rubber ball with a speed of 5.0
m/s collides head on elastically with an
identical ball at rest. Find the velocity of each
object after the collision.
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6.4 Elastic and Inelastic Collisions Check for
Understanding
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6.4 Elastic and Inelastic Collisions Check for
Understanding
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6.4 Elastic and Inelastic Collisions Check for
Understanding
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6.4 Elastic and Inelastic Collisions Check for
Understanding
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6.4 Elastic and Inelastic Collisions Check for
Understanding
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6.4 Elastic and Inelastic Collisions Check for
Understanding
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6.4 Elastic and Inelastic Collisions Check for
Understanding
(Hint See Special Case b)
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6.4 Elastic and Inelastic Collisions Check for
Understanding
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6.4 Elastic and Inelastic Collisions Check for
Understanding
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6.4 Elastic and Inelastic Collisions
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Homework for Sections 6.3 6.4

• HW 6.B p. 205 38, 40, 41, 43-46, 49. p.206
  54-56, 58, 62, 65, 66.

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End of Chapter 6