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Ch. 9 Momentum
Momentum & Impulse
A
moving object has momentum
 Inertia in motion = momentum!
 Linear momentum = p = (mass) X
(velocity)
 p = m·v
 Where p and v are both vector
quantities and are in same direction.
 Units: kg·m/s or N·s
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A massive truck & small car both traveling at
same velocity…
Which will be more difficult to stop?
Which can do more damage upon impact?
If they both travel toward each other…
Which will experience greater impact force upon
colliding?
Which experiences more acceleration?
The force upon impact will be...
The same for both the truck and the car.
 Ftruck = Fcar (Newton’s 3rd Law)
 mt·at = mc·ac (Newton’s 2nd Law)

mt·a

t
=
ac
mc·
Force is the same, but because mass is
different, the accelerations experienced by each
vehicle will be different.
 Force
is required to change the
momentum of an object.
 The rate of change of momentum of
a body is proportional to the net force
applied to it…
 ΣF = Δp/Δt = m Δv /Δt = ma
 Going back to our example… During
impact, which vehicle had a greater
change in momentum?
 It’s the same!
What’s required to change the
momentum of an object?
What’s required to change the momentum of anobject?
Impulse!
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In order to change the
momentum of an object, an
impulse is required…
A net force acting for some
time will cause an object to
change its momentum.
ΣF = Δp/Δt
ΣF Δt = Δp = mΔv
Impulse=change in momentum
We assume that the net force is
constant throughout the
duration of changing
momentum. (Usually use
average net force.)
Impulse
The force of the
foot on the ball is
an impulsive force.
Graphical Interpretation of Impulse
J = Impulse = area under the force curve  Favg t
The Impulse-Momentum Theorem:
Impulse causes a change in momentum:
Example Problem: Two 1-kg stationary cue balls
are struck by cue sticks. The cues exert the forces
shown. Which ball has the greater final speed?
A.
B.
C.
Ball 1
Ball 2
Both balls have the same final speed
Answer
Two 1-kg stationary cue balls are struck by cue
sticks. The cues exert the forces shown. Which
ball has the greater final speed?
A. Ball 1
B. Ball 2
C. Both balls have the same final
speed
Example Problem
A 0.5 kg hockey puck slides to the right at 10
m/s. It is hit with a hockey stick that exerts the
force shown. What is its approximate final speed?
Answer…
 ΣF avg
 ΣF avg
Δt = m Δv
Δt = m (vf – vi)
 (25N)(0.020s) = (0.5kg) (vf – 10m/s)
 0.50 Ns = (0.5kg) (vf – 10m/s)
 1 m/s = vf – 10m/s
 vf = 1 m/s + 10 m/s
vf
= 11 m/s
1.
Impulse is
A. a force that is applied at a
random time.
B. a force that is applied very
suddenly.
C. the area under the force
curve in a
force-versus-time graph.
D. the interval of time that a
force lasts.
Slide 9-5
Answer
1.
Impulse is
A. a force that is applied at a random
time.
B. a force that is applied very
suddenly.
C. the area under the force curve
in a force-versus-time graph.
D. the interval of time that a force
lasts.
Law of Conservation of
Momentum

The sum of the momentums
before a collision equal the
sum of the momentums after
the collision in an isolated
system.
Law of Conservation of Momentum:
The total momentum of an isolated system of
bodies remains constant.
 (Isolated system: meaning that all forces
acting on the bodies are included… and the
sum of the external forces applied to the
system is zero. External forces like Ff or Fg.)
 Momentum before = Momentum after
 m1v1 + m2v2 = m1v'1 + m2v'2 (Elastic Collision)
 m1v1 + m2v2 = (m1 + m2)v‘ (Inelastic Collision)
 v = velocity before collision
 v' = velocity after collision

Elastic Collisions!
Elastic Collision
Elastic Collisions: Two or more objects
collide, bounce (don’t stick together), and
kinetic energy is conserved.
 An ideal situation that is often never quite
reached… billiard ball collisions are often
used as an example of elastic collisions.

 Kinetic
energy is conserved:
 KE1 + KE2 = KE'1 + KE'2
 ½m1v12+½m2v22=½m1v'12+½m2v'22
 Momentum is conserved:
 m1v1 + m2v2 = m1v'1 + m2v'2
Inelastic Collision
Inelastic Collision: two or more objects collide
and do not bounce off each other, but stick
together. Or, an explosion where one object
starts w/one momentum and then separates
into two or more objects w/separate final
momentums.
 Kinetic energy is not conserved.
 KEbefore = KEafter + heat + sound + etc.
 The kinetic energy “lost” is transformed into
other types of energy, but…
 Total energy is always conserved!
 m1v1 + m2v2 = (m1 + m2)v'

Elastic vs. Inelastic Collisions
(a) A hard steel ball
would rebound to its
original height after
striking a hard marble
surface if the collision
were elastic.
 (b) A partially deflated
basketball has little
bounce on a soft asphalt
surface.
 (c) A deflated basketball
has no bounce at all.

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Show “happy balls”

A ball of mass 0.250 kg and velocity +5.00 m/s
collides head on with a second ball of mass 0.800 kg
that is initially at rest. No external forces act on the
balls. If the balls collide and bounce off one another,
and the second ball moves with a velocity of +2.38
m/s, determine the velocity of the first ball after the
collision, including direction.
Did you get…?
 vf1
= -2.62 m/s (ball 1 rebounds)
Lets prove if energy is
conserved…..
Remember from a previous slide that
for Elastic Collisions: Two or more
objects collide, bounce (don’t stick
together), and kinetic energy is
conserved.
 KE1 + KE2 = KE'1 + KE'2
 ½m1v12+½m2v22=½m1v'12+½m2v'22
 Apply this equation to the last
problem and see if it is true.

Energy is conserved!
2. The total momentum of a
system is conserved
A. always.
B. if no external forces act on
the system.
C. if no internal forces act on
the system.
D. never; momentum is only
approximately conserved.
Answer
2. The total momentum of a system is
conserved
A. always.
B. if no external forces act on
the system.
C. if no internal forces act on the
system.
D. never; momentum is only
approximately conserved.
3.In an inelastic collision,
A. impulse is conserved.
B. momentum is conserved.
C. force is conserved.
D. Kinetic energy is conserved.
E. elasticity is conserved.
Slide 9-9
Answer
3.In an inelastic collision,
A. impulse is conserved.
B. momentum is conserved.
C. force is conserved.
D. Kinetic energy is conserved.
E. elasticity is conserved.
Slide 9-10
Slide 9-19
Forces During a Collision
Slide 9-20
The Law of Conservation of Momentum
In terms of the initial and final total momenta:
In terms of components:
Example Problem
A curling stone, with a mass of 20.0
kg, slides across the ice at 1.50 m/s.
It collides head on with a stationary
0.160-kg hockey puck. After the
collision, the puck’s speed is 2.50
m/s. What is the stone’s final
velocity?
Slide 9-23

Answer: 1.48 m/s
Rocket propulsion is an example of conservation of momentum:
The rocket doesn’t push on the environment. The rocket pushes the exhaust
gas in one direction (backward), and the exhaust gas pushes the rocket in the
opposite direction (forward).
Newton’s third law, the force and time acting on the rocket and the gas (as a
whole) are equal and opposite. The momentum is conserved. The momentum
before is zero and the momentum after is a total of zero. Positive momentum of
Slide 9-24
the rocket = Negative momentum of the gas.
Inelastic Collisions: For now, we’ll consider perfectly
inelastic collisions:
A perfectly inelastic collision results whenever the two
objects move off at a common final velocity.
Slide 9-25
Example Problem
Jack stands at rest on a skateboard.
The mass of Jack and the skateboard
together is 75 kg. Ryan throws a 3.0
kg ball horizontally to the right at 4.0
m/s to Jack, who catches it. What is
the final speed of Jack and the
skateboard?
Answer:
0.154 m/s
Recall from a previous slide…
Inelastic Collision: two or more objects collide
and do not bounce off each other, but stick
together. Or, an explosion where one object
starts w/one momentum and then separates
into two or more objects w/separate final
momentums.
 Kinetic energy is not conserved.
 KEbefore = KEafter + heat + sound + etc.
 The kinetic energy “lost” is transformed into
other types of energy, but…
 Total energy is always conserved!
 m1v1 + m2v2 = (m1 + m2)v'

Prove if the last problem
conserved energy….
KE1 + KE2 = KE1+2
 ½m1v12+½m2v22=½m1+2v'2
 Apply this equation to the last
problem and see if it is true.

Energy is not conserved!

A 20.0 g ball of clay traveling east at 2.00 m/s
collides with a 30.0 g ball of clay traveling 30.0o
south of west at 1.00 m/s. The two pieces
stick together and become one. What are the
speed and direction of the final piece of clay?
Momentum is a vector… including direction.
Hint: Draw your vectors tip to tail and draw the
resultant momentum vector (p final).
Resolve all vectors into x and y-components.
Determine the sum of the x-components and the sum
of the y-components and draw your final resultant
vectors making a right triangle.
Solve for p final and angle.
Solve for v final.