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Today’s Topics:
 Impulse-Momentum
 Conservation of Momentum
 1D Collisions
Conservation of Momentum:
System of Particles
 Elastic
 Perfectly Plastic
•
Impulse and Momentum
Newton’s Second Law
tf
tf
t0
t0
•
F  ma
 Fdt  m  a dt  mv  mv
•
Multiply by dt and integrate
f
 mv0  p f  p0
•
tf
 F dt  F
avg
Can consider each particle _____________
t
t0
Impulse = _________ which is ____________________
Impulse – momentum for each particle
System of particles
•
Add individual ___________and
momentums
•
__________ addition
Special case for system of particles:
•
Sum of external forces is _______
•
Initial momentum = final momentum
•
________________________________
tf
 p f   p0    F dt
t0
p
f
  p0
Momentum = ____________
EF 151 Spring, 2017 Lecture 3-5
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Impulse-Momentum: Dimensional Analysis and Units
EF 151 Spring, 2017 Lecture 3-5
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Example: Tennis
A regulation tennis ball weighs between 2 and 2-1/16
ounces. During a serve, the tennis ball leaves a racket with
a speed of 110 mph. The racket is in contact with tennis
ball for about 4 ms. Estimate the average force on the ball.
 L  mL  T  mL 
T   F T 
mv  m  

T  T  T 2
T 
SI:
USC:
EF 151 Spring, 2017 Lecture 3-5
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EF 151 Spring, 2017 Lecture 3-5
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Collisions
Perfectly Inelastic Collisions (no external forces)
 Two masses stick together
 Perfectly _________ collision
 Mechanical energy is ___________
 Example: ______________
One-dimensional
v1
v2
v’ = v1’ = v2’
 Two masses do not stick together
 Perfectly Elastic
 Mechanical energy is ______________
 Example: ____________
m1v1  m2 v2  m1v1  m2 v2  m1  m2 v
initial velocity of mass 1
initial velocity of mass 2
final velocity of combined masses
v 
 Inelastic
 Mechanical energy is _________
 Example: __________________________
 Explosions
 Opposite of perfectly ________________ collision
EF 151 Spring, 2017 Lecture 3-5
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m1v1  m2 v2
m1  m2 
m1
v1
m2
v2
Car
Fast
Bug
0
Baseball
Fast
Catcher
0
‫ݒ‬ᇱ ൌ
݉ଵ
‫ݒ‬
݉ଵ ൅ ݉ଶ ଵ
EF 151 Spring, 2017 Lecture 3-5
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Example: Bullet
Example: Explosion
A 10 gram bullet is fired horizontally into a 5.0 kg stationary block of
wood resting on a table. The speed of the bullet before entry is 500 m/s.
A 5.0 kg rifle shoots a 0.020 kg bullet at 620 m/s.
Determine the recoil speed of the rifle and the force on the rifle if it is
brought to rest over a distance of 0.20m.
What is the velocity
of block after collision if
bullet embeds itself in
the block?
A.
B.
C.
0.1 m/s
1.0 m/s
10 m/s
EF 151 Spring, 2017 Lecture 3-5
What is the velocity of
block if bullet is rubber
and bounces back with a
speed of 400 m/s?
A.
B.
C.
0.0 m/s
0.2 m/s
1.8 m/s
What is the velocity of
block if bullet goes
through block and exits
with a speed of 200 m/s?
A.
B.
C.
Concept to find recoil speed?
Concept to find distance?
0.4m/s
0.6 m/s
1.0 m/s
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EF 151 Spring, 2017 Lecture 3-5
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