Transcript Impulse and Momentum

Momentum & Impulse
Level 1 Physics
What you need to know
 Essential Questions
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How is impulse and momentum
related?
How does the law of conservation of
momentum apply to objects at rest?
In motion?
 Objectives
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Define and give examples of impulse
and momentum
Restate Newton’s Second Law in terms
of momentum
Calculate the change in momentum
from the area under the curve of a force
versus time graph
Derive a statement of the conservation
of momentum between two objects by
applying Newton’s Third Law
Define and recognize examples of
elastic and inelastic collisions
Explain which conservation laws apply
to each type of collision
Demonstrate proficiency in solving
problems involving conservation of
momentum in collisions
Impulse Equals Change in
Momentum
Remember the following; N.S.L &
definition of acceleration
Im pulse  Change in momentum
J  p
Ft  mv
F
v
 a, a 
m
t
F v

 Ft  mv
m t
Ft  Im pulse (J)
mv  Change in momentum(p)


Units of impulse:
N*s
Units of momentum: kg*m/s
Impulse and Momentum
Ft  mv
Impulse
Change in Momentum
Notice the relationship
with force and time

mv
F
t
Impulse – Momentum Relationships
Impulse – Momentum Relationships
fT  mV
Constant
Since TIME is directly related to the
VELOCITY when the force and mass
are constant, the LONGER the
cannonball is in the barrel the greater
the velocity.
Also, you could say that the force acts
over a larger displacement, thus there
is more WORK. The work done on the
cannonball turns into kinetic energy.
Impulse – Momentum Relationships
Which would be more damaging: driving
into a massive concrete wall, or driving at
the same speed into a head-on collision
with an identical car traveling toward you at
the same speed?
Both cases are equivalent, because either way, your car is rapidly decelerating
to a dead stop. The dead stop is easy to see when hitting the wall, and a little
thought will show the same is true when hitting the car. If the oncoming car
were traveling slower, with less momentum, you'd keep going after the collision
with more 'give,' and less damage (to you!). But if the oncoming car had more
momentum than you, it would keep going and you'd snap into a sudden reverse
with greater damage. Identical cars at equal speeds means equal momenta -zero before, zero after collision.
Collisions
Consider 2 objects heading towards
one another. Upon colliding…
N.T.L. says that the FORCE they
exert on each other is EQUAL but
in the OPPOSITE direction
The time of impact is the
SAME for both…
Therefore, the IMPULSES of
the 2 objects are also EQUAL
and OPPOSITE
F1  F2
t1  t 2
Ft1  Ft2
J1  J 2
Collisions
If IMPUSES are EQUAL, then
the MOMEMTUMS of each
object are EQUAL as well
J1  J2
p1  p2
mv 1  mv 2
m1v11  m1v1  m2v12  m2v 2
m1v1  m2v 2  m v  m v
1
1 1
1
2 2
The marks are called
primes and they
indicate the velocity
after the collision.
Momentum is CONSERVED
pBefore  pAfter
m1v1  m2v 2  m v  m v
1
1 1

1
2 2
In the absence of external forces, the total momentum before a collision
is equal to the total momentum after the collision – The Law of Conservation
of Momentum
Example
pbefore  m1v1  m2v 2
 500kg5 ms   400kg2 ms 
 2500kg ms  800kg ms  3300kg ms

pafter  m1v11  m2v12
 500kg3.0 ms   400kg4.5 ms 
 1500kg ms  1800kg ms  3300kg ms
Types of Collisions
A situation where the objects DO NOT STICK is one type
of collision
Notice that in EACH case, you have TWO objects BEFORE and AFTER
the collision.
A “no stick” type collision
pbefore
=
pafter
m1vo1  m2 vo 2  m1v1  m2 v2
(1000)(20)  0  (1000)(v1 )  (3000)(10)
 10000
v1 
-10 m/s
 1000v1
A “stick” type of collision
pbefore
=
pafter
m1vo1  m2 vo 2  mT vT
(1000)(20)  0  (4000)vT
 4000vT
20000
vT 
5 m/s
The “explosion” type
This type is often referred to as
“backwards inelastic”. Notice you
have ONE object ( we treat this as
a SYSTEM) before the explosion
and TWO objects after the
explosion.
Backwards Inelastic Explosions
Suppose we have a 4-kg rifle
loaded with a 0.010 kg bullet.
When the rifle is fired the
bullet exits the barrel with a
velocity of 300 m/s. How fast
does the gun RECOIL
backwards?
pbefore
mT vT
=
pafter
 m1v1  m2 v2
(4.010)(0)  (0.010)(300)  (4)(v2 )
0
 3  4v2
v2

-0.75 m/s
Collision Summary
Sometimes objects stick together or blow apart. In this
case, momentum is ALWAYS conserved.
p
before
  p after
m1v01  m2 v02  m1v1  m2 v2
When 2 objects collide and DON’T stick
m1v01  m2 v02  mtotal vtotal
When 2 objects collide and stick together
mtotal vo (total )  m1v1  m2 v2
When 1 object breaks into 2 objects
Elastic Collision = Kinetic Energy is Conserved
Inelastic Collision = Kinetic Energy is NOT Conserved
Elastic Collision
KE car ( Before)  1 mv 2  0.5(1000)(20) 2  200,000 J
2
KE truck ( After )  0.5(3000)(10) 2  150,000 J
KE car ( After )  0.5(1000)(10) 2  50,000 J
Since KINETIC ENERGY is conserved during the collision we call this an
ELASTIC COLLISION.
Inelastic Collision
KE car ( Before)  1 mv 2  0.5(1000)(20) 2  200,000 J
2
KE truck / car ( After )  0.5(4000)(5) 2  50,000 J
Since KINETIC ENERGY was NOT conserved during the collision we call
this an INELASTIC COLLISION.
Example
How many objects do I have before the collision?
2
How many objects do I have after the collision?
1
Granny (m=80 kg) whizzes
around the rink with a
velocity of 6 m/s. She
suddenly collides with
Ambrose (m=40 kg) who is
at rest directly in her path.
Rather than knock him
over, she picks him up and
continues in motion without
"braking." Determine the
velocity of Granny and
Ambrose.

pb   pa
m1vo1  m2 vo 2  mT vT
(80)(6)  (40)(0)  120vT
vT  4 m/s