honors physics - impulse and momentum
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Honors Physics
Impulse and Momentum
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Impulse = Momentum
Consider Newton’s 2nd Law and the definition of
acceleration
Units of Impulse:Units of Momentum:
Momentum is defined as “Inertia in
Motion”
Ns
Kg x m/s
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Impulse – Momentum Theorem
vm Ft
IMPULSE CHANGE IN MOMENTUM
This theorem reveals some
interesting relationships such
as the INVERSE relationship
between FORCE and TIME
t
vm F
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Impulse – Momentum Relationships
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Impulse – Momentum Relationships
V m fT
Constant
Since TIME is directly related to theVELOCITY 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.
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How about a collision?
Consider 2 objects speedingtoward each other. Whenthey collide......
Due to Newton’s 3rd Law the
FORCE they exert on eachother are EQUAL andOPPOSITE.
The TIMES of impact are alsoequal.
Therefore, the IMPULSES of the 2 objects colliding are
also EQUAL21
21
2121
)()(
J J
Ft Ft
t t F F
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How about a collision?
If the Impulses areequal then the
MOMENTUMS are
also equal!
22221111
222111
2211
21
21
)()(oo
oo
vmvmvmvmvvmvvm
vmvm
p p
J J
22112211 vmvmvmvm
p p
oo
after before
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Momentum is conserved!
The Law of Conservation of Momentum: “In theabsence of an external fo rce (gravity, fr ict io n),
the total momentum before the col l is ion is
equal to the total momentum after the
collision.”
smkg p
smkg p
smkg p
smkg p
smkg p
smkg mv p
total
car
truck
total o
car o
otruck o
/*3300
/*18005.4*400
/*15003*500
/*3300
/*800)2)(400(
/*2500)5)(500(
)(
)(
)(
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Types of Collisions
A situation where the objects DO NOT STICK isone type of collision
Notice that in EACH case, you have TWO objects BEFORE and AFTER
the collision.
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A “no stick” type collision
Spbefore = Spafter
1
1
1
22112211
100010000
)10)(3000())(1000(0)20)(1000(
v
v
v
vmvmvmvm oo
-10 m/s
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Types of Collisions
Another type of collision is one where the objects“STICK” together. Notice you have TWO objects
before the collision and ONE object after the
collision.
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A “stick” type of collision
Spbefore = Spafter
T
T
T
T T oo
v
v
v
vmvmvm
400020000
)4000(0)20)(1000(
2211
5 m/s
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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.
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Backwards Inelastic - Explosions
Suppose we have a 4-kg rifleloaded 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 gunRECOIL backwards?
Spbefore = Spafter
2
2
2
2211
430
))(4()300)(010.0()0)(010.4(
v
v
v
vmvmvm T T
-0.75 m/s
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Collision Summary
Sometimes objects stick together or blow apart. Inthis case, momentum is ALWAYS conserved.
2211)(
022011
2211022011
vmvmvm
vmvmvm
vmvmvmvm
p p
total ototal
total total
after before
When 2 objects collide and DON’T sti
When 2 objects collide and stick toget
When 1 object breaks into 2 objects
Elastic Collision = Kinetic Energy is Conserved
Inelastic Collision = Kinetic Energy is NOT Conser
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Elastic Collision
J Af ter KE
J Af ter KE
J mv Before KE
car
truck
car
000,50)10)(1000(5.0)(
000,150)10)(3000(5.0)(
000,200)20)(1000(5.02
1)(
2
2
22
Since KINETIC ENERGY is conserved during the collision we call this an
ELASTIC COLLISION.
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Inelastic Collision
J After KE
J mv Before KE
car truck
car
000,50)5)(4000(5.0)(
000,200)20)(1000(5.02
1)(
2
/
22
Since KINETIC ENERGY was NOT conserved during the collision we call
this an INELASTIC COLLISION.
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Example Granny (m=80 kg) whizzesaround the rink with a
velocity of 6 m/s. Shesuddenly collides with Ambrose (m=40 kg) whois at rest directly in her path. Rather than knock
him over, she picks himup and continues inmotion without "braking."Determine the velocity of Granny and Ambrose.
How many objects do I have before the collision?
How many objects do I have after the collision?
2
1
T
T
T T oo
ab
v
vvmvmvm
p p
120)0)(40()6)(80(
2211
4 m/s
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Collisions in 2 Dimensions
The figure to the left showsa collision between twopucks on an air hockeytable. Puck A has amass of 0.025-kg and ismoving along the x-axis
with a velocity of +5.5m/s. It makes a collisionwith puck B, which has amass of 0.050-kg and isinitially at rest. Thecollision is NOT head on.
After the collision, thetwo pucks fly apart withangles shown in thedrawing. Calculate thespeeds of the pucksafter the collision.
vA
vB
vAcosq
vAsinq
vBcosqvBsinq
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Collisions in 2 dimensions
A B vv 757.0
smv
v
vv
vv
A
A
A A
A A
/84.2
04845.01375.0
03785.00106.01375.0
)757.0)(050.0(0106.01375.0
B A vv 040.00106.01375.0
smv B /15.2)84.2(757.0