Momentum

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Momentum, Impulse and Collisions
Momentum everyday connotations? physical
meaning the true measure of motion (what
changes in response to applied forces) Momentum
(specifically Linear Momentum) defined to be
generalized later so note momentum is a vector
px mvx , py mvy , pz mvz
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Impulse During a constant force
Integral is area under the curve!
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For a particle initially at rest the particles
momentum equals the impulse that accelerated the
particle from rest to its current state of
motion. (analogous to K work to accelerate
particle from rest) Kinetic energy can be
written in terms of momentum and mass
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Consider 2 particles of the same mass, the
second with twice the speed of the first. How do
their momenta compare? How do their Kinetic
Energies compare? Consider 2 particles with the
same speed, the second with twice the mass of the
first. How do their momenta compare? How do their
Kinetic Energies compare? Consider 2 particles
initially at rest with the same size force acting
for the same amount of time, the second with
twice the mass of the first. How do their momenta
compare? How do their Kinetic Energies
compare? Consider 2 particles initially at rest
with the same size force acting through the same
distance, the second with twice the mass of the
first. How do their momenta compare? How do their
Kinetic Energies compare?
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Ex A 0.40 kg ball impacts a wall horizontally
with a speed of 30 m/s and rebounds horizontally
with a speed of 20 m/s. The ball is in contact
with the wall for .01s. Determine the impulse and
average force on the ball.
Ex A 0.40 kg soccer ball traveling
horizontally to the left at 20 m/s is kicked up
and to the right at a 45 degree angle with a
speed of 30 m/s. The ball is in contact with the
foot of the kicker for .01s. Determine the
impulse and average force on the ball.
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Conservation of Momentum an application of
action-reaction 2 interacting objects, no
external forces
Generalize and consider external forces If the
vector sum of external forces on a system is
zero, the total momentum of the system is
constant.
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mAvA1 mBvB1 mAvA2 mBvB2 Using
conservation of momentum in problems determine
if momentum is conserved select a coordinate
system (momentum is a vector!) sketch before and
after diagrams relate total initial momentum to
total final momentum, component by
component! solve equations (use additional
equations as appropriate such as conservation of
energy)
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Example Rifle recoil A 3 kg rifle is used to
fire a 5 g bullet. The velocity of the bullet
relative to the ground is 300 m/s after being
fired. What is the momentum and energy of the
bullet? What is the momentum and energy of the
rifle? What is the recoil speed of the rifle?
Example 1-D collision 2 carts collide head-on
on a frictionless track. The first cart has a
mass of .5 kg and approaches the collision with a
speed of 2 m/s. The second cart has a mass of .3
kg and approaches the collision with a speed of 2
m/s. After the collision, the second cart
rebounds from the collision at a speed of 2 m/s.
Determine the initial kinetic energies and final
velocities and kinetic energies of both masses.
How much energy is lost in this collision?
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Example 2-D collision. A 5.00 kg mass
initially moves in the positive x-direction with
a speed of 2.00 m/s, and then collides with a
3.00 kg mass which is initially at rest. After
the collision, the first mass is found to be
moving at 1.00 m/s 30º from the positive x-axis.
What is the final velocity of the second
mass? What is the total initial and final kinetic
energy of the system?
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Elastic and Inelastic Collisions Elastic
Collisions interaction is conservative
force mechanical energy is conserved no
stickiness Inelastic Collisions interaction is
not conservative force some mechanical energy is
lost some stickiness Completely Inelastic
Collisions interaction is not conservative
force maximum loss of mechanical energy colliders
stick together after the collision In all
collisions, momentum is conserved in elastic
collisions, energy is conserved as well.
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Completely inelastic collisions vA2 vB2 v2
so mAvA1 mBvB1 (mA mB)v2 take object B
initially at rest (can consider as 1-d problem)
? energy is always lost in a completely inelastic
collision
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Example 1-D collision 2 carts collide head-on
on a frictionless track. The first cart has a
mass of .5 kg and approaches the collision with a
speed of 2 m/s. The second cart has a mass of .3
kg and approaches the collision with a speed of 2
m/s. After the collision, the the carts stick
together. Determine the initial kinetic energies
and final velocity and kinetic energy of both
masses. How much energy is lost in this
collision?
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Example Ballistic Pendulum. A bullet of mass m
is fired into a block of wood of mass M, where it
remains imbedded. The block is suspended like a
pendulum, and swings up to a maximum height y.
Relate M, m and y to the bullets initial velocity.
Example A 2000 kg car traveling east at 10 m/s
collides (completely inelastically) with a 1000
kg car traveling north at 15 m/s. Find the
velocity of the wreckage just after the
collision, and the energy lost in the collision.
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Elastic Collisions examine 1-d elastic collision,
with B at rest before collision
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Example 1-D collision 2 carts collide
elastically head-on on a frictionless track. The
first cart has a mass of .5 kg and approaches the
collision with a speed of 2 m/s. The second cart
has a mass of . 3 kg and approaches the collision
with a speed of 2 m/s. Determine the initial
kinetic energies and final velocities and kinetic
energies of both masses.
Example A neutron (mass 1 u 1.66E-27 kg)
traveling at 2.6E7 m/s strikes a carbon nucleus
(mass 12 u). What are the velocities after the
collision? by what factor is the neutrons
kinetic energy reduced by the collision?
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Example A spacecraft of mass 825 kg approaches
Saturn head on with an initial speed of 9.6
km/s while Saturn (mass 5.69E26 kg) moves along
its orbit at 10.4 km/s. The gravitational force
of Saturn on the spacecraft swings the spacecraft
back in the opposite direction. What is the
final speed of the spacecraft.
Example An elastic (2-d) collision of two pucks
on a frictionless air table occurs with the first
mass ( 0.500 kg) approaching at 4.00 m/s in the
positive x-direction and the second mass (0.300
kg) initially at rest. After the collision, the
first puck moves off at a speed of 2.00 m/s in an
unknown direction. What is the direction of the
first pucks velocity after the collision, and
what is the speed and direction of the second
puck after the collision/
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Center of Mass aka Center of Inertia average
location of mass on a system of particles
motion of center of mass
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External forces and the motion of center of mass
example A 50.0 kg woman walks from one end of
5m, 40.0 kg canoe to the other. Both the canoe
and the woman are initially at rest. If the
friction between the water and the canoe is
negligible, how far does the woman move relative
to shore? How far does the boat move relative to
shore?