Download Ch 6 - Momentum

Ch 6 - Momentum
What is momentum?
Momentum = a vector quantity defined as
the product of an object’s mass and
velocity
 p = mv
(momentum = mass x velocity)
SI Unit = kgm/s (kilogram meter per second)
A 2250 gram toy truck has a velocity of 4 m/s to the east. What is
the momentum of the toy?
M = 2250 g = 2.25 kg
V = 4 m/s
p = mv = 2.25 x 4 = 9 kgm/s east
Momentum Continued…
A change in momentum takes force and
time
When a soccer ball is moving very fast, the
player must exert a large force over a short time
to change the ball’s momentum and quickly
bring the ball to a stop
Impulse – Momentum Theorem
Impulse = for a constant external force, the
product of the force and the time over
which it acts on an object; OR, the change
in momentum of an object
FΔt = Δp = mvf – mvi
Impulse = change in momentum =
final momentum – initial momentum
A 1400kg car moving westward with a velocity of 15 m/s collides with a utility pole
and is brought to rest in 0.30s. Find the magnitude of the force exerted on the car
during the collision.
 M = 1400kg
 Δt = 0.30s
 Vi = 15 m/s west =
-15 m/s
 Vf = 0 m/s
mv f  mvi
F
F=?
t
(1400kg )(0m / s )  (1400kg )( 15m / s )
F
0.30 s
21000
F
 70, 000 N to the East
0.30
6.2 – Conservation of
Momentum
Law of Conservation of Momentum
 The total momentum is conserved
That is, the total momentum at the beginning of the
situation has to equal the total momentum at the end
m1v1i  m2v2i  m1v1 f  m2v2 f
 This formula can be used in lots of different
examples, like collisions, explosions, or when
objects push away from each other.
A 76kg boater, initially at rest in a stationary 45kg boat, steps out of the boat and
onto the dock. If the boater moves out of the boat with a velocity of 2.5 m/s to the
right, what is the final velocity of the boat?
m1  76kg
m1v1i  m2v2i  m1v1 f  m2v2 f
m2  45kg
0  m1v1 f  m2 v2 f
v1i  0
v2i  0
v1 f  2.5m / s
v2 f  ?
0  (76kg )(2.5m / s)  (45kg )v2 f
0  190  45v2 f
190  45v2 f
190
 v2 f
45
v2 f  4.2m / s
Momentum Continued…
The conservation of momentum fits with
Newton’s Third Law
Every action has an equal but opposite reaction
Real World vs. Physics World
In real life, forces during collisions are not
constant
In physics world, we will work as if we are
using the “average force” in our
calculations
6.3 – Elastic and Inelastic
Collisions
Types of Collisions
 Perfectly Inelastic Collisions
Two objects collide and stick together, moving together
as one mass
Momentum is Conserved
m1v1i  m2v2i  (m1  m2 )v f
NOTE: You will get the same results using the equation we already learned for conservation of
momentum. This just reminds you that the masses stuck together!
Perfectly Inelastic Collisions, Cont.
 Kinetic Energy is NOT constant (conserved) in
inelastic collisions
When the two objects stick together, some energy is lost
 Deformation of objects (crunching of cars)
 Sound
 Heat
1
1
2
KEi  m1v1i  m2v22i
2
2
1
1
2
KE f  m1v1 f  m2v22 f
2
2
Then compare the initial
KE to the final KE to see
how much energy was
“lost”
Type of Collisions
 Elastic Collisions
Two objects collide and then move separately
Both Momentum and Kinetic Energy are Conserved
m1v1i  m2v2i  m1v1 f  m2v2 f
KEi  KE f
1
1
1
1
2
2
2
2
m1v1i  m2v2i  m1v1 f  m2v2 f
2
2
2
2
Real World vs. Physics World
In the real world, most collisions are
neither elastic nor perfectly inelastic
In physics world, we act as if they fall into
one of the two categories
Review
 Perfectly Inelastic
Collision
Stick together
Momentum Conserved
Kinetic Energy NOT
Conserved
 Elastic Collision
Bounce off
Momentum Conserved
Kinetic Energy
Conserved