Transcript Impulse and Momentum

Impulse and Momentum
Honors Physics
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 – Momentum Theorem
Ft  mv
IMPULSE
CHANGE IN MOMENTUM
This theorem reveals some
interesting relationships such
as the INVERSE relationship
between 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.
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
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
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
Spbefore
=
Spafter
m1vo1  m2 vo 2  m1v1  m2 v2
(1000)( 20)  0  (1000)(v1 )  (3000)(10)
 10000
v1 
-10 m/s
 1000v1
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.
A “stick” type of collision
Spbefore
=
Spafter
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?
Spbefore
mT vT
=
Spafter
 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
m1v1i  m2v2i  m1v f  m2v f
When 2 objects collide and DON’T stick
m1v1i  m2v2i  mtotalvtotal
When 2 objects collide and stick together
mtotalv( total)i  m1v1  m2v2
When 1 object breaks into 2 objects
Elastic Collision = Kinetic Energy is Conserved
Inelastic Collision = Kinetic Energy is NOT Conserved
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 and Impulse
 Momentum (mv) is Inertia in motion
 Impulse (Ft) is the change in momentum
 Objects exert equal and opposite forces,
therefore, equal and opposite impulses in
collisions
 The total momentum does not change in
collisions. (Pi=Pf)
Which vehicle will experience the
greater Force? A car that crashes
into a wall at or one that coasts to
a stop with the same initial speed?
 The car that crashes into a wall will experience the greater
force because it experiences its change in momentum over a
smaller time period
 Impulse (Ft) is the change in momentum with smaller t, F
must be greater
Which vehicle will experience the greater
Impulse? A car that crashes into a wall at or
one that coasts to a stop with the same
initial speed?
 If the change in momentum is equal, the impulse must be
equal.
Which object experiences the greater impulse?
An egg that splatters against the floor, or a ball
with the same mass and speed that bounces off?
 A bouncing ball will have the greater change in its
momentum as it changes direction.
 The egg only experiences enough impulse to stop its
momentum.
 The ball experiences enough impulse to stop and reverse its
momentum
A man pushes a 500kg car from
rest with a force of 100N for 5
seconds
 Impulse:
 Change in Momentum:
 Change in velocity:
A 100g ball travelling at 5m/s
bounces off a wall and heads in
the opposite direction at 5m/s
 Initial Momentum:
 Final Momentum:
 Change in Momentum:
 Impulse:
A boy (m = 60kg) standing on his
skateboard (m = 5kg) at rest jumps
forward at 0.5m/s
 Total Initial Momentum:
 Total Final Momentum:
 Momentum of the boy:
 Momentum of the skateboard:
 Velocity of the skateboard:
A basketball(m=0.5kg) moving upwards at 1m/s collides
with a tennis ball (m = 0.06kg) moving down at 1m/s.
Afterwards, the basketball is moving upwards at 0.9m/s.
What is the velocity of the tennis ball?
Pi  Pf
mb vbi  mt vti  mb vbf  mt vtf
o.5kg  1m / s  0.06kg * ( 1m / s )  0.5kg * 0.9m / s  0.06kg * vtf
0.5kgm / s  .06kgm / s  4.5kgm / s  0.06kg * vtf
4.94kgm / s  4.5kgm / s  0.06kg * vtf
0.44kgm / s  0.6kg * vtf
7.3m / s  vtf
A 500kg train car travelling at 6m/s
collides and sticks to a 1000kg train car
initially at rest. How fast do they move after
the collision.
 Total initial Momentum:
 Total Final Momentum:
 Total mass of two cars:
 Final velocity of two cars:
 Impulse delivered to 10,000kg car
 Impulse delivered to 5,000kg car