Transcript Impulse and Momentum

UT Homework is due Thursday the 26th!!
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Defined as the product of a body’s mass and
its velocity.
Vector quantity that points in the direction of
the velocity.
SI unit is the kg•m/s
A fast moving car will have
more momentum than a slower
car with the same mass.
p  mv
mc  2.5kg, md  9.25kg, vd  6.25m / s
pc  pd
mc vc  md vd
md vd
vc 
mc
9.25kg  6.25m / s
vc 
2.5kg
vc  23m / s
 F  ma
v
 F  m t
p
 F  t
 F t  p
This means that we exert force to
Change an object’s momentum. (Duh!)
m  15kg, t  1.0s, vi  20.0m / s, v f  0
 Ft  p
F 
mv f  mvi
t
15kg  0  15kg  20.0m / s
F 
1.0s
 F  300 N
2
F

3
.
0

10
N
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In an isolated system of bodies, the
momentum remains constant.
Generally, momentum is NOT conserved:
 In the presence of friction (object loses KE
because it gains thermal energy)
 When the object is working against gravity (object
loses KE because it gains PE)
pi  p f
m1v1  m2 v2  m1v1  m2 v2
skater1  m1  45kg, v1  6.5m / s, v1  4.5m / s
skater2  m2  65kg, v2  0
m1v1  m2 v2  m1v1  m2 v2
m1v1  m2 v2  m1v1  m2 v2
m1v1  m2 v2  m1v1
 v2
m2
(45kg  6.5m / s)  (45kg  4.5m / s )
 v2
65kg
v2  3.6m / s
 F t  p
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Recall :
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This means that a force applied over time
results in a change in momentum.
This is called Impulse! (J)
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J   F t
J  p
F  35 N , t  0.05s
J   F t
J  35 N  0.05s
J  2kg  m / s
m  0.25kg, vi  17.5m / s, v f  25m / s
J  p
J  mv f  mvi
J  (.25kg  25m / s)  (.25kg  17.5m / s)
J  11kg  m / s
Impulse (J) = area under the curve
∆p = Impulse (J) = area under the curve
Area 1:
.5x.02secx60N=
.6kgxm/s
 Area 2:
.02secx60N=
1.2kgxm/s
 Area 3:
.5x.02secx60N=
.6kgxm/s
Total Impulse = 2.4kgxm/s
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Elastic: momentum and kinetic energy are
conserved
 The only true elastic collisions are atomic particles
and subatomic particles
 We use billiard balls to model elastic collisions
because they lose very little KE.
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Inelastic: momentum is conserved but KE is
lost due to deformations, sound, etc.
 Most collisions fall into this category
 If I lose ANY KE (due to friction, sound energy, etc)
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Perfectly Inelastic: momentum is conserved
but KE is lost due to deformations, sound,
etc, AND the objects stick together after
collision!
 Example: cars that collide and stick together
m1v1  m2 v2  (m1  m2 )v f
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The point about which a body moves as if all
forces were exerted there.
The point has an x and y component.
SI unit is the meter (m)
m1 x1  m2 x2  m3 x3  ...
xcm 
M
m1 y1  m2 y2  m3 y3  ...
ycm 
M
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xcm
xcm
ycm
ycm
Center of raft is (6m, 6m)
(700kg  6m)  (45kg  0)  (45kg  6m)  (45kg  2m)

835kg
 5m
(700kg  6m)  (45kg  6m)  (45kg  0)  (45kg  4m)

835kg
 6m