First:
Impulse, Momentum, &
The Conservation of Momentum
Concept Summary
Sec. 9.1
Impulse and Momentum
 Objectives
 Compare the system before and after an event
in momentum problems
 Define the momentum of an object
 Determine the impulse given to an object
 Recognize that impulse equals the change in
momentum of an object
Momentum
 Momentum is what Newton called the
“quantity of motion” of an object.
 Momentum can be thought of as “how
hard it is to stop an object”.
Momentum
 The momentum of an object:
 Depends on the object’s mass.
Momentum is directly proportional to mass.
 Depends on the object’s velocity.
Momentum
 In symbols:
p = mv
p
m v
Momentum is directly proportional to velocity.
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Momentum
Impulse
 Momentum is a vector quantity.
 Common units of momentum: kg m/s
 The impulse exerted on an object
depends on:
 The force acting on the object.
Impulse is directly proportional to force.
 The time that the force acts.
Impulse is directly proportional to time.
Impulse
Impulse
 In symbols:
Impulse is a vector quantity.
Common units of impulse: N s
J = Ft
J
F t
Impulse & Momentum
 The impulse exerted on an object equals
the object’s change in momentum.
 In symbols:
J = p
Why are there two equations for J?


J  p
Well, …


F  ma
or
J= Ft
multiply both sides by t...
and
 
J  Ft

 v
a
t
so


 v 
F m

 t 
Ft  mv 
m(v2  v1 )  mv2  mv1  p2  p1  p
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Why are there two equations for J?


J  p
 
J  Ft
Both equations are useful, in
different circumstances….
…you will often need to set them
equal to each other.
Conservation of Momentum
 Since impulse = change in momentum,
…if no impulse is exerted on an object, the
momentum of the object will not
change.
…and remember p = p2 - p1
Conservation of Momentum
 If no external forces act on a system,
the total momentum of the system will
not change.
Such a system is called an “isolated system”.
Conservation of Momentum
 Another way to think about it is:
Internal forces can never change the
total momentum of a system.
 Momentum is conserved in every
isolated system.
Impulse Problems
Impulse
 Impulse = (force) x (time of contact)
 Impulse = F·t
What is the impulse of a bat on a ball that is
hit for .050s with a force of 25N?
measured in N·s
Impulse = ?
t = .050s
F = 25N
Impulse = Ft
Impulse = 25N (.050s)
Impulse = 1.25N·s
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Impulse
Impulse
A boy falls and hits his head with an impulse of
20N·s. On cement, the boy would hit for .010s.
What force did the floor exert on the boy?
A boy falls and hits his head with an impulse of
20N·s. On sand, the boy would hit for .20s. What
force did the sand exert on the boy?
Impulse = Ft
Impulse = 20N·s
t = .010s
F=?
20N·s = F
(.010s)
Impulse = 20N·s
t = .20s
F=?
2000N = F
Impulse = Ft
20N·s = F
(.20s)
100N = F
Momentum
Impulse and Momentum
A 5.0kg bowling ball is rolling down the lane
with a velocity of 12.0m/s. What is the
momentum of the bowling ball?
Impulse creates a change in momentum
p = mv
m = 5.0kg
v = 12.0m/s
p=?
If a 10N·s impulse hits a stationary object
The object gets a momentum of 10kg·m/s
10N·s
p = (5.0kg)(12.0m/s)
10kg·m/s
p = 60
kg·m/
s
Impulse and Momentum
Impulse and Momentum
Units for Momentum:
 Impulse can also cause objects to speed
up or slow down because of a change in
momentum.
p  mv so...
Units for Impulse:
J  Ft
so...
kg  m / s
N s
m
Vi
Vf
m
Impulse
Is there a difference?
 kg  m 
 kg  m 
N s   2 s  
  kg  m / s
 s 
 s 
No difference!
They are the
same units!
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Impulse and Momentum
Impulse
 Impulse can also cause objects to speed
up or slow down because of a change in
momentum.
m
Vi
Impulse
Vf
m
Impulse (J) =
= Ft
= p
= mv
= m(vf – vi)
Units: N·s
or kg·m/s
Impulse and Momentum
Real Life Applications..
A .125kg baseball at rest is hit off of a tee
with a force of 10.0N for .020s. How fast did
the ball leave the tee?
m= .125kg Ft = m(vf – vi)
(10.0N)(.020s) =(.125kg)(Vf – 0)
Vi = 0m/s
.20N·s = (.125kg)Vf
F = 10.0N
t = .020s
Vf = ?
1.6m/s = Vf
Warm up
5min
4min
3min
2min
 Sports…
 Follow-through!
 Gymnastics Mats
 Cars…
 Airbags!
 Before airbags….
 Bumpers
 Jumping…
 Knees
 Shoes
1min
1. What impulse would cause a 1.0kg block
to speed up from 10.0m/s to 12.0m/s?
2. If the impulse in #1 took 2.0s then what
force was used over that time?
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