Transcript Impulse and Momentum

Impulse and Momentum
AP Physics 1
Momentum
Momentum
 The product of a particle’s mass and velocity is called
the momentum of the particle:
 Momentum is a vector, with units of kg m/s.
 A particle’s momentum vector can be decomposed into
x- and y-components.
Slide 9-21
QuickCheck 9.1
The cart’s change of
momentum px is
A.
B.
C.
D.
E.
–20 kg m/s.
–10 kg m/s.
0 kg m/s.
10 kg m/s.
30 kg m/s.
Slide 9-22
QuickCheck 9.1
The cart’s change of
momentum px is
A.
B.
C.
D.
E.
–20 kg m/s.
–10 kg m/s.
0 kg m/s.
10 kg m/s.
30 kg m/s.
px = 10 kg m/s  (20 kg m/s) = 30 kg m/s
Negative initial momentum because motion
is to the left and vx < 0.
Slide 9-23
Impulse
Impulse = Momentum
Consider Newton’s 2nd Law and
the definition of acceleration
Units of Impulse: Ns
Units of Momentum: Kg x m/s
Momentum is defined as “Inertia in Motion”
Impulse is the Area
Since J=Ft, Impulse is the AREA of a Force vs. Time graph.
Impulse During a Collision
 A large force exerted
for a small interval of
time is called an
impulsive force.
 The figure shows
a particle with
initial velocity .
 The particle experiences
an impulsive force of
short duration t.
 The particle leaves
with final velocity .
Slide 9-26
Conservation of Momentum
Collisions
 A collision is a shortduration interaction
between two objects.
 The collision between
a tennis ball and a
racket is quick, but it
is not instantaneous.
 Notice that the right side of the ball is flattened.
 It takes time to compress the ball, and more time
for the ball to re-expand as it leaves the racket.
Slide 9-24
Atomic Model of a Collision
Slide 9-25
How about a collision?
Consider 2 objects speeding toward
each other. When they collide......
Due to Newton’s 3rd Law the FORCE
they exert on each other are
EQUAL and OPPOSITE.
The TIMES of impact are also equal.
F1   F2
t1  t 2
( Ft )1  ( Ft ) 2
J1   J 2
Therefore, the IMPULSES of the 2
objects colliding are also EQUAL
How about a collision?
If the Impulses are equal then
the MOMENTUMS are
also equal!
J1   J 2
p1   p2
m1v1  m2 v2
m1 (v1  vo1 )  m2 (v2  vo 2 )
m1v1  m1vo1  m2 v2  m2 vo 2
p
before
  p after
m1vo1  m2 vo 2  m1v1  m2 v2
QuickCheck 9.8
A mosquito and a truck have a head-on collision.
Splat! Which has a larger change of momentum?
A. The mosquito.
B. The truck.
C. They have the same change of momentum.
D. Can’t say without knowing their initial velocities.
Slide 9-60
QuickCheck 9.8
A mosquito and a truck have a head-on collision.
Splat! Which has a larger change of momentum?
A. The mosquito.
B. The truck.
C. They have the same change of momentum.
D. Can’t say without knowing their initial velocities.
Momentum is conserved, so pmosquito + ptruck = 0.
Equal magnitude (but opposite sign) changes in momentum.
Slide 9-61
Momentum is conserved!
The Law of Conservation of Momentum: “In the absence of
an external force (gravity, friction), the total momentum
before the collision is equal to the total momentum after
the collision.”
po ( truck)  mvo  (500)(5)  2500kg * m / s
po ( car )  (400)( 2)  800kg * m / s
po ( total)  3300kg * m / s
ptruck  500 * 3  1500kg * m / s
pcar  400 * 4.5  1800kg * m / s
ptotal  3300kg * m / s
Several Types of collisions
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  mtotalvtotal
When 2 objects collide and stick together
mtotalvo (total)  m1v1  m2 v2
When 1 object breaks into 2 objects
Elastic Collision = Kinetic Energy is Conserved
Inelastic Collision = Kinetic Energy is NOT Conserved
Collisions and Explosion
Example
A bird perched on an 8.00 cm tall swing has a mass of 52.0 g,
and the base of the swing has a mass of 153 g. Assume that
the swing and bird are originally at rest and that the bird
takes off horizontally at 2.00 m/s. If the base can swing
freely (without friction) around the pivot, how high will
the base of the swing rise above its original level?
How many objects due to have BEFORE the action?
1
How many objects do you have AFTER the action?
2
EB  E A
K o ( swing )  U swing
pB  p A
mT vo T  m1v1  m2 v2
(0.205)(0)  (0.153)v1( swing )  (0.052)( 2)
vswing 
-0.680 m/s
1 mvo2  mgh
2
vo2
(0.68) 2
h
 0.024 m
2g
19.6
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
Momentum in Two Dimensions
 The total momentum
is a vector sum of the
momenta
of the individual particles.
 Momentum is conserved only if each component of
is conserved:
Slide 9-86
Collisions in 2 Dimensions
The figure to the left shows a
collision between two pucks
on an air hockey table. Puck A
has a mass of 0.025-kg and is
vA
vAsinq
moving along the x-axis with a
velocity of +5.5 m/s. It makes
a collision with puck B, which
vAcosq
has a mass of 0.050-kg and is
initially at rest. The collision is
vBcosq
vBsinq
NOT head on. After the
vB
collision, the two pucks fly
apart with angles shown in the
drawing. Calculate the speeds
of the pucks after the collision.
Collisions in 2 dimensions
p
ox
  px
m AvoxA  mB voxB  m AvxA  mB vxB
(0.025)(5.5)  0  (.025)(v A cos 65)  (.050)(vB cos 37)
vA
vAsinq
vAcosq
vBcosq
vB
0.1375  0.0106vA  0.040vB
p
oy
  py
0  m Av yA  mB v yB
vBsinq
0  (0.025)(v A sin 65)  (0.050)( vB sin 37)
0.0300vB  0.0227v A
vB  0.757v A
Collisions in 2 dimensions
0.1375  0.0106vA  0.040vB
vB  0.757vA
0.1375  0.0106v A  (0.050)(0.757v A )
0.1375  0.0106v A  0.03785v A
0.1375  0.04845v A
v A  2.84m / s
vB  0.757(2.84)  2.15m / s