IMPULSE AND MOMENTUM

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IMPULSE AND MOMENTUM   The impulse F ?t is a
vector quantity equal in magnitude to the product
of the force and the time interval in which it
acts. Its direction is the same as that of the
force. F ?t Units newton.second (N.s)
The momentum p of a particle is a vector quantity
equal in magnitude to the product of its mass m
and its velocity v. p m v Units
(kg.m/s)
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Impulse (F ?t) change in momentum (m ?v)
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CONSERVATION OF LINEAR MOMENTUM   According to
the law of conservation of linear momentum, when
the vector sum of the external forces that act on
a system of bodies equals zero, the total linear
momentum of the system remains constant no matter
what momentum changes occur within the system.
Although interactions within the system may
change the distribution of the total momentum
among the various bodies in the system, the total
momentum does not change. Such interactions can
give rise to two general classes of events
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a. explosions, in which an original single body
flies apart into separate bodies
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b. collisions, in which two or more bodies
collide and either stick together or move apart,
in each case with a redistribution of the
original linear momentum.
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For two objects interacting with one another, the
conservation of momentum can be expressed
as  v1 and v2 are initial velocities,
and are final velocities
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7.4 Assume two objects have masses of 8 and 6 kg
respectively. The 8 kg mass moves initially to
the right with a velocity of 4 m/s and collides
with the 6 kg mass moving to the left at 5 m/s.
What is the total momentum before and after the
collision?
m1 8 kg m2 6 kg v1 4 m/s v2 -5 m/s
Initial momentum m1 v1 m2 v2 8(4) 6(-5)
- 2 kg m/s
initial momentum final momentum Final momentum
- 2 kg m/s
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ELASTIC AND INELASTIC COLLISIONS   If the Kinetic
energy remains constant in a collision, the
collision is said to be completely elastic. If
the colliding bodies stick together and move off
as a unit afterward, the collision is said to be
completely inelastic. In inelastic collisions
only the momentum is conserved.
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7.5 A 2 kg ball traveling to the left with a
speed of 24 m/s collides head-on with a 4 kg ball
traveling to the right at 16 m/s. Find the
resulting velocity if the two balls stick
together after impact.
m1 2 kg m2 4 kg v1 -24 m/s v2 16 m/s
m1 v1 m2 v2 ( m1 m2)V
2.67 m/s to the right
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7.6 The nucleus of an oxygen atom has a mass of
3.8x10-25 kg and is at rest. The nucleus is
radioactive and suddenly ejects a particle of
mass 6.6x10-27 kg and speed 1.5x107 m/s. Find the
recoil speed of the nucleus that is left behind.
m1 3.8x10-25 kg m2 6.6x10-27 kg
1.5x107 m/s
-2.6x105 m/s
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7.7 A 7500-kg truck traveling at 5 m/s east
collides with a 1500-kg car moving at 20 m/s in a
direction 210?. After the collision, the two
vehicles remain tangled together. With what speed
and in what direction does the wreckage begin to
move?
m1 7500 kg v1 5 m/s, 0º m2 1500 kg
v2 20 m/s, 210º
m1 v1 m2 v2 ( m1 m2)V
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m1 v1 m2 v2 ( m1 m2)V
x-comp y-comp 7500 (5) 0 1500 (20 cos
210º) 1500 (20 sin 210º)
Sx 11,519 kg m/s Sy - 15,000 kg m/s
Initial Momentum
18,912.7 kg m/s
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initial momentum final momentum (m1
m2) V
2.1 m/s
52.5º
IV quadrant V (2.1 m/s, 307.5º)
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