CHAPTER 6 Momentum and Collisions

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CHAPTER 6Momentum and Collisions
Momentum The linear momentum of an object of
mass m moving with velocity v is defined as the
product of its mass and its velocity
p mv
Momentum is a vector. It can be broken down into
components. px mvx py mvy
Newtons Second Law can be re-written in terms of
momentum
F ?t m?v F ?t ?p
Impulse change in Momentum
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Impulse Momentum Theorem
F ?t ?p mv mvo
Applications Objective Batter Striking a
Ball Maximize ?v of the ball Automobile Bumper
Design Maximize ?t so the F is minimized
Figure 6.1(a) could be an illustration of the
force involved when a tennis ball hits a
racket. Figure 6.1(b) illustrates how to estimate
the impulse involved in the collision.
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Example Problem (Baseball) A baseball thrown at
45m/s (100mph) is struck by a bat and moves
toward centerfield at 85m/s. The contact with the
bat last for only .0015 seconds. The ball has a
mass of .35kg. Calculate the average force caused
by the bat and the change in momentum of the ball.
Problem Solving Strategy Identify the
variables F ? ?t .0015sec m .35kg ?v
85m/s -45m/s (moving towards centerfield was
130m/s chosen as the positive
direction)
Solve the Problem ?p mv ?p .35kg 130m/s
?p 46kgm/s
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Conservation of Momentum
Any collision Momentum is conserved
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Linear Momentum Problem
A cue with a mass of . 25kg ball rolls along a
pool table with a velocity of .85m/s and strikes
the eight ball head-on which has a mass of .28kg
and is at rest. After the collision, the cue
ball continues to roll forward with a velocity of
.15m/s. What is the velocity of the eight ball
after the collision?
Problem Solving Strategy 1. Extract the data. m1
.25kg m2 .28kg v1 .85m/s v2 0m/s v1
.15m/s v2 ?
2. Plug data into Conservation of Momentum
equation and solve for the unknown variable.
m1v1 m2v2 m1v1 m2v2
v2 .63m/s
The total momentum before and after the collision
remains constant at .21kg m/s
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Example Problem (Railroad Car Coupling) A
91,000kg railroad car is moving at .35m/s toward
a 45,000kg railroad currently at rest. What will
be the velocity of the two cars after they
collide and couple up?
Identify the variables m1 91,000kg m2
45,000kg v1 .35m/s v2 0m/s v1 ? V2
? v1 v2 vT Total velocity
Solve the Problem m1v1 m2v2 m1v1 m2v2
m1VT m2vT (m1m2) vT All variables known
except vT
vT .23m/s
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Isolated Systems
Momentum is conserved regardless of the nature of
the forces between the objects.
Applications Objects Involved Rocketry Rocket
and Propellant Ice Skating Two Skaters pushing
away from each other Guns Gun and Bullet
Example Problem (Two Figure Skaters) An 80.kg
male skater pushed away from his 40.kg female
partner and achieves a velocity (relative to the
ice) of 2.5m/s. What will be the velocity of the
female partner?
Identify the variables m1 80.kg m2 40.kg v1
0m/s v2 0m/s v1 2.5m/s v2 ?
Solve the Problem m1v1 m2v2 m1v1
m2v2 Plug and solve for v2
v2 -5.0m/s
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Elastic Collisions
Momentum is always conserved. In elastic
collisions total kinetic energy is also
conserved. This allows us to write a second
equation (in addition to the conservation of
momentum equation) and solve two equations for
two unknowns. Thankfully, this is not required in
this class.
Second Equation (Conservation of Kinetic
Energy) m1v12 m2v22 m1v12 m2v22
Elastic Collisions occur between atoms,
molecules, and sub-atomic particles. Some larger
collisions may be approximated as elastic
collisions.
Inelastic Collisions Momentum is conserved.
Total kinetic energy is not conserved. Kinetic
energy is dissipated as heat.