Download Momentum - Physics

Momentum:
Conservation of Momentum:
Vocabulary:
.Momentum
Vocabulary:
.Law of conservation of momentum
.Impulse
.Impulse-Momentum Theorem
.Elastic collision
.Inelastic collision
.Perfectly inelastic collision
I can:
give examples and compare the momentum of
different moving objects.
calculate impulse and compare to its change in
momentum.
discuss how force and time vary in a collision
using the impulse-momentum theorem.
I can:
explain the law of conservation of momentum.
recognize when to solve a problem using the law of
conservation of momentum.
calculate velocities and other variables within a
given collision using the law of conservation of
momentum.
differentiate between elastic, inelastic and
perfectly inelastic collisions.
Equations:
p  mv
J  Ft
J  p
pi  p f
m1v1i  m2v2 i  m1v1 f  m2v2 f
Is it harder to stop the Titanic or a
rubber ducky if they are traveling
at the same speed?
 We
say that Titanic has more
MOMENTUM than the rubber
ducky.
 Momentum
is inertia in motion.
the product of an object’s
mass and velocity.
p = mv
Vector
Formula
 Units


Abbreviations
p =m x v
kg·m/s = kg x m/s
p = momentum
m = mass (kg)
v = velocity (m/s)

The result of force acting on an object
for a specific time.

Impulse (J):
J = FΔt

Units: Newton Seconds (N·s)
Vector
Impulse Example Problems
A 500 kg car moving at 10 m/s hits a
brick wall and comes to a stop.
What is the impulse imparted on the
car?
It is found that it took the car
0.21 seconds to stop. What is
the magnitude of the force
exerted on the car?
A 1.5 kg superball is moving to the right
with a velocity of 20 m/s when it strikes
a wall and bounces back to the left
with a speed of 15 m/s.
What is the impulse on the ball?
How much force is exerted on the ball
if it is in contact with the wall for a time
of 0.02 seconds?
A 1000 kg car moving at 30 m/s
(p = 30,000 kg*m/s)
can be stopped by
30,000 N of force acting for 1.0 s (a crash!)
or
by 3000 N of force acting for 10.0 s
(normal stop)
Impulse is the area under a Force
vs. Time Graph
 Impulse
= change in momentum
 Can be written as:
J = Δp
OR
F Δ t = mΔv
 The
units must be the same also!
N·s= kg·m/s
MOMENTUM
Decreasing Momentum:
Which would it be more safe to hit in a car ?
Ft
mv
mv
Ft

In each case, the momentum is decreased by the same
amount or impulse (force x time)

Hitting the haystack extends the impact time (the time in
which the momentum is brought to zero).

The longer impact time reduces the force of impact and
decreases the deceleration.

Whenever it is desired to decrease the force of impact,
extend the time of impact !
Example 1
What is the momentum of a 2.9 kg seagull which is
flying at a velocity of 19.1 m/s to the west?
p  mv
p  (2.9kg)(19.1 m )
s
p  55.4kg  m
s
Example 2
A 2.7 kg soccer ball approaches a player with a velocity of 3.8
m/s to the North. The player strikes the ball and causes it to
move toward the south with a speed of 20 m/s. What impulse
was delivered to the ball by the player? Assume North is
Positive and South is Negative.
J  p
v  v f  vi
J  mv
p  (2.7kg)( 20 m  3.8 m )
s
s
p  64.3kg  m
s
Example 3
A 620 kg car driven by Toonces the cat predictably flies off a
cliff and collides with the ground at a speed of 33 m/s. If the
car crumples during the collision for 0.7 s before coming to a
complete stop, what is the magnitude of the average force
experienced during the impact?
J  p
Ft  mv
v  v f  vi
F (0.7 s)  (620kg)(33 m  0 m )
s
s
F (0.7 s)  20460kg  m
s
F  29228.6N