### Chapter 6: Momentum and Collisions!

```Chapter 6:
Momentum and Collisions!
The Solar System
(not to scale!)
A Question for you to ponder…
Why do the Sun and all of the planets (except
Venus) rotate In the same direction?
The Answer lies in the Formation of
the Solar System
4 billion miles away…do you see
what I see?
That’s us 
So What?

What does this have to do with Chapter 6?

Planet formation is directly tied to the law of
conservation of momentum!

Yay for more laws 
Linear Momentum

Momentum describes how the motions of
objects are changed


Newton’s Laws explain why
The Linear Momentum equation
p=mv
 Momentum = mass x velocity

MOMENTUM IS A VECTOR!!
Sample Problem

A 3000kg elephant is chasing a 1 kg
squirrel across the road at a velocity of 5
m/s to the west. What is the momentum of
the elephant? If the squirrel is running at 7
m/s west what is its momentum?
Solve the Problem

Momentum of the elephant


p = mv = (3000 kg)(5m/s)= 15000 kgm/s West
Momentum of the squirrel

p=mv= (1kg)(7m/s)= 7 kgm/s West
Change in Momentum

A change in momentum takes force and
time

It takes a lot of force to stop an object that has
a lot of momentum
Impulse Momentum Theorem

A net external force, F, applied to an
object for a time interval, Δt, will cause a
change in the object’s momentum equal to
the product of the Force and the time
interval.

In other words…
Impulse Ft  p  mvf  mvi
What does that mean?

A small force acting for a long time can
produce the same change in momentum
as a large force acting for a short time.

In sports like baseball, this is why follow
through is important. The longer the bat is
in contact with the ball, the greater the
change in momentum will be.
Sample Problem p. 211 #3

A 0.40 kg soccer ball approaches a player
horizontally with a velocity of 18 m/s north.
The player strikes the ball and causes it to
move in the opposite direction with a
velocity of 22 m/s. What impulse was
delivered to the ball by the player?
What do we know?
M = 0.40 kg
 Vi= +18 m/s
 Vf= -22 m/s
 What does impulse mean?

Impulse is equal to FΔt
 Impulse is also equal to the object’s change in
momentum

Solve the problem
m
m
p  mv f  vi   0.40kg (22  18 ) 
s
s
kgm
kgm
 16
or 16
Sout h
s
s
Stopping Distance

The stopping distance is the distance it
requires an object to come to rest

The greater the momentum, the more
distance it takes to stop
Sample Problem p.213 #2

A 2500 kg car traveling to the north is
slowed down uniformly from an initial
velocity of 20.0 m/s by a 6250 N braking
force acting opposite the car’s motion. Use
the impulse momentum theorem to answer
the following questions:
 A.
What is the car’s velocity after 2.50 s?
 B. How far does the car move during 2.50 s?
 C. How long does it take the car to come to a
complete stop.
m= 2500 kg
 Vi= 20 m/s North
 F= -6250 N
 t= 2.50 s
 Vf= ?

Why is F negative?
Because it is acting
opposite the car’s
motion!
Use the impulse-momentum
theorem!!
p  mv f  vi   Ft
Ft
(6250 )( 2.50 s)
m
Vf 
 vi 
 20  13.75 North
m
2500
s
Solve Part B


How far does the car
move in 2.5 s?
Which kinematic
equation should we
use?
1
x  vi  v f t
2
1
1
x  V f  Vi t  (13.75  20)( 2.5s)  42.2m N
2
2
Solve Part c

How long does it take for the car to come to a
complete stop?

Use impulse momentum theorem!
m
0  (2500kg)(20 )
m
v

m
v
p
f
i
s  8s
t 


F
F
 6250N
Summary of 6.1

Momentum is a vector quantity that is equal to
the product of an object’s mass and its velocity
(p=mv)

Impulse = FΔt= Δp

A small force applied over a long period of time
produces the same change in momentum as a
large force applied over a short period of time
Section 6.2: Conservation of
Momentum

Remember...we talked
the solar system and
conservation of
momentum.
We are the only inner planet with a
large moon…why?

Our moon didn’t form with us in the nebula

We acquired it later through a collision
with another planetoid

http://vimeo.com/2015273
The Moon is trying to leave us

Every year, the moon moves about 4 cm away
from the Earth and thus it’s velocity increases

Conservation of Momentum says that velocity
has to come from somewhere. So…the moon
steals it from us

So every year, our rotation slows down… adding
about 0.0002 seconds to our day.
Momentum is Conserved

The Law of Conservation of Momentum
says:

The total momentum of all objects interacting
with one another remains constant regardless
of the nature of the forces between the
objects.
In mathematical form
m1v1,i  m2v2,i  m1v1, f  m2v2, f
Be very careful with your signs when using
this equation!!
Collisions

There are many different ways to describe
collisions between objects

In any collision, the total amount of
momentum is conserved but generally the
total kinetic energy is not conserved
Perfectly Inelastic Collisions

When two objects collide and move together as one
mass, the collision is perfectly inelastic

Since the two objects stick together and move as
one, they have the same final velocity.
m1v1,i  m2v2,i  (m1  m2 )v f

Kinetic Energy IS NOT CONSERVED in
PERFECTLY INELASTIC COLLISIONS
Sample Problem p. 219 #2

An 85.0 kg fisherman jumps from a dock
into a 135 kg rowboat at rest on the west
side of the dock. If the velocity of the
fisherman is 4.30 m/s to the west as he
leaves the dock, what is the final velocity
of the fisherman and the boat?
What do we know
M1= 85 kg
 M2= 135 kg
 V2,i=0
 V1,i= -4.30 m/s


What type of collision is this?

PERFECTLY INELASTIC because they stick
together and move as one mass
m1v1,i  m2v2,i  (m1  m2 )v f

vf 

Rearrange the equation and solve for
Vf
m1v1,i  m2 v2,i
m1  m2
m
(85kg )(4.3 )  0
s

 1.66
(135 85)
Vf= 1.66 m/s West
What is the change in Kinetic
Energy for this problem?

Initial Kinetic Energy of the boat= 0 J

Initial Kinetic Energy of the fisherman


KE= 0.5mv^2= 0.5(85kg)(4.3m/s)^2=785.3 J
Total Initial KE= 0+ 785.3 J= 785.3 J
Final KE= 0.5(85+135)(-1.66)^2=303.1 J
ΔKE=KEf – Kei = 482.2 J
Elastic Collisions

In an elastic collision, two objects collide
change in total energy.
After the collision, the two objects move
separately.
 Momentum is conserved
 Kinetic Energy is Conserved

Sample Problem p.229 #2

A 16.0 kg canoe moving to the left at 12
m/s makes an elastic head-on collision
with a 4.0 kg raft moving to the right at 6.0
m/s. After the collision, the raft moves to
the left at 22.7 m/s. Disregard any effects
of the water.

a. Find the velocity of the canoe after the
collision.
What do we know?
V1,i= -12 m/s
 V2,i = 6 m/s
 V1,f = ?
 V 2,f = -22.7 m/s
 M1= 16 kg
 M2= 4 kg

Conservation of Momentum says…

This is an elastic collision, so we should
use the following equation:
m1v1,i  m2v2,i  m1v1, f  m2v2, f
Rearrange and solve

We need to solve for V1,f
so we should rearrange
m1v1,i
the conservation of
momentum equation
v1, f
 m2v2,i  m2v2, f
m1
 v1, f
m
m
m
(16kg )(12 )  (4kg )(6 )  (4kg )(22.7 )
m
s
s
s

 4.8
16kg
s
So The final velocity of the
canoe is 4.8 m/s Left.
Impulse In Collisions
Think about Newton’s 3rd Law: Every action
force has an equal and opposite reaction force
Since Impulse = FΔt then in a collision
between objects, the impulse imparted to
each mass is the same!!!!
Comparison of Collisions
Perfectly Inelastic
Collisions
Inelastic
Collisions
Elastic Collisions
Objects stick
together and move as
one mass after the
collision

Objects are
deformed and move
separately after the
collision


Momentum
is
conserved
their original shapes
and move separately
after the collision
Momentum
Momentum
is
is
conserved
conserved
Kinetic
Energy is not
conserved because it
is converted to other
types of energy
Kinetic
KE
is not conserved
Energy is
conserved
Summary of Section 6.2 and 6.3

In all interactions between isolated
objects, momentum is conserved

Few collisions are elastic or perfectly
inelastic

Impulse imparted is the same for all
objects in a collision
```