Transcript Chapter 9: Momentum and Conservation

Chapter 9: Momentum
and Conservation
Newton’s Laws applied
Dynamics of Physics
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Dynamics are the CAUSES of CHANGE in
Physics.
Recall that position is changed by velocity.
Velocity is changed by acceleration.
Acceleration is caused by a net force.
Properties that remain constant are
described as CONSERVED.
Impulse and Momentum
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Momentum is described by Newton’s 3
laws of motion as the quantity of
motion.
If no net force acts on a body, its velocity
is constant.
If a net force acts on a body, velocity is
changed. (acceleration)
Forces on objects change over time.
Identify “before”, “during”, and “after” in
an interaction.
Developing Impulse
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F = ma can be rewritten to substitute a rate of
change in velocity for acceleration.
v
F m
t
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multiplying both sides by Δt, then
Ft  mv
Impulse is a force over a period of time. (N*s)
Since a FORCE causes a velocity to CHANGE, then
an IMPULSE causes MOMENTUM to change.
(kg*m/s)
Impulse-Momentum Theorem
v  v2  v1
Can also be stated as
mv2  mv1
The symbol for Momentum is ρ. Thus, ρ= mv.
Ft  2  1
Impulse = Change in Momentum
The force is not constant, and the impulse is
found using the AVERAGE FORCE times the
time interval, or finding the area under the curve
of a force-time graph.
Vectors
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Velocity is a vector, so momentum is a
vector.
Force is a vector, so impulse is a vector.
Vectors have positive and negative
directions associated with them.
Traditionally, positive direction is right and
left is negative.
Saving lives with Physics
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A large change in momentum comes from
a large impulse.
Since Impulse is FΔt, you can have a large
force OR a large time of contact to
produce a large impulse.
In a car crash, an air bag extends the
TIME of contact to reduce the FORCE of
impact. The Impulse is the same whether
you hit the air bag, or the steering wheel.
Thus the Δmv is the same.
Car crash video clip
Car crash with seatbelts
Angular Momentum
Just like linear momentum is mv, a
ROTATING object has momentum also.
The momentum of a rotating object is
called Angular Momentum and depends
on the object’s mass, distance from the
center axis of rotation, and tangential
velocity. If the radius gets smaller, the
velocity increases to maintain constant
angular momentum. Like water going
down the toilet, or a hurricane, or planets
around a star (sun).
Practice Problem
A 0.144kg baseball is pitched horizontally at
38.0m/s. After it is hit by the bat, it
moves at the same speed, but in an
opposite direction.
What was the change in momentum of
the ball?
What was the impulse delivered by the
bat?
Batter Up Solution
Given: mball =0.144kg, v=38.0 m/s,
+direction = direction after ball leaves bat
Unknown: FΔt = Δρ
Solve:
Δρ= mv2-mv1 =m(v2 – v1)
= (0.144kg)(38.0m/s-(-38.0m/s))
= (0.144kg)(76.0m/s) = 10.9 kg-m/s
Impulse = change in momentum
= 10.9 N-s
Your turn to practice
Do pg. 204-205 Practice Problems #
1,2,3,4,5,6
Do pg.217 #s 1,2,4,6,7
Do pg. 218 #s 22-27
Conservation of Momentum
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Forces are a result of an interaction between
objects moving in opposite directions.
During collisions, the force of one object on
another is = in strength but opposite in direction
to the force of the second object on the first.
FBonA   FAonB
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The time interval for the force is the same for
both objects, so the Impulse is = and opposite.
What about Momenta?
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According to the I-M theorem, the final
momentum = the impulse + the initial
momentum.
2  Ft  1
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In a collision, the final momenta must be equal to
the sum of the initial momenta in a system and
thus Momentum is Conserved.
 A2   B 2   A1   B1
Defining Closed Systems
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A system that doesn’t gain or lose mass is
said to be a closed system.
All forces within a closed system are called
internal forces.
All forces outside a closed system are
considered external forces.
In a system, objects that collide can either
stick together (inelastic collision), or come
apart (elastic collision). Momentum of the
collision in a closed system with no net
external force is still conserved.
Car collision problem
A 2275kg car going 28m/s rear-ends an 875kg
compact car going 16m/s on ice in the same
direction. The cars stick together. How fast does
the wreckage move after the collision?
Car crash solution
 A2   B 2   A1   B1
Because the cars stick together, their velocities after
the collision are equal. So, vA2 = vB2 = v2
mAvA1 + mBvB1 = (mA+mB)v2
m Av A1  mB vB1
v2 
m A  mB
(2275kg)( 28m / s)  (875kg)(16m / s)
v2 
(2275kg  875kg)
So v2 = 25 m/s, as we can see when mass increases,
velocity must decrease to conserve momentum.
Explosions
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As with the 2 skaters in Fig 9-8, if they both
start at rest and A gives B a push, both skaters
will move in opposite directions. The push is an
internal force. The total momentum of the
system must be zero after the push as it was
zero before the push. The momenta of the
skaters will be equal and opposite after the
push.
The chemicals in a rocket exploding to propel
the rocket are internal forces as they are
expelled into space propelling the rocket along.
mAvA2 = -mBvB2
Ch 9 Homework
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Please complete the following:
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Pg. 210 Prac. Probs. # 7,8,9, &12
Pg. 218 Rev #s 28,34,35, and 36.