The Law of the Conservation of Momentum
Conservation of Momentum
• The law of conservation of momentum states
when a system of interacting objects is not
influenced by outside forces (like friction), the
total momentum of the system cannot
change.
• If you throw a rock forward from a
skateboard, you will move backward
in response.
How did my sister get this huge bump
and black eye?
The Law of the Conservation of Momentum
states…
The total momentum of all objects interacting
with one another remains constant regardless
of the nature of the forces between the
objects.
The total momentum of a system will stay the
same before and after a collision.
Can you try to explain my sister’s
black eye using the “Law of the
Conservation of Momentum”?
The Law of the Conservation of Momentum
states…
The total momentum of all objects interacting
with one another remains constant regardless
of the nature of the forces between the
objects.
The total momentum of a system will stay the
same before and after a collision.
Why does Mr Stickfigure on the ice
move
backwards?
Before Collision
After Collision
+p
-p
p = -5 kgm/s
Momentum = zero (not moving)
ptotal = 0kgm/s
p = 5 kgm/s
Momentum = zero
ptotal = 5kgm/s + (-5kgm/s)
ptotal = 0kgm/s
Why does Mr Stickfigure move backwards?
•Answer the Question
–Mr Stickfigure moves backwards because he threw
the ball forward.
•Explain the Relationship
–The Law of the Conservation of Momentum states
that the total momentum of a system must stay the
same before and after. Before the ball and Mr
Stickfigure had a total momentum of zero, so after the
total momentum needed to stay zero.
•Support with Data/Observations
–When the ball moved forward it had a positive
momentum, so Mr Stickfigure needed a negative
momentum to cancel it out. This is why he moved
backwards.
Why do both skaters move after?
Before
ptotal = 0 kgm/s
(not moving)
After
ptotal = 0 kgm/s
Why do both skaters move after?
•Answer the Question
–Both skaters move after in order
to conserve momentum.
•Explain the Relationship
–The Law of the Conservation of Momentum states
that the total momentum of a system must stay the
same before and after. Before the two skaters had a
total momentum of zero, so after the total momentum
needed to stay zero.
•Support with Data/Observations
–When they push against each other one moved
forward and had a positive momentum, so the other
needed to move backwards to have a negative
momentum, so the total momentum stayed zero.
“recoil”
Recoil is a term that refers to moment when a gun
moves backwards after it is shot.
Recoil happens because everything must follow “The
Law of the Conservation of Momentum”!!!
Why a gun “recoils”.
The total momentum before was zero
So the total momentum after has to be zero
The gun moves with a negative momentum because the bullet
moves with a positive momentum and they cancel out, the total
momentum stays zero.
This explains my sister’s face!!!
She shot her gun without
positioning herself correctly
and when the gun recoiled it
hit her!!!!
3 Types of Collisions
• Elastic
• Inelastic
• Perfectly Inelastic
Elastic or Inelastic?
An elastic collision loses
no energy. The deformation on collision is fully
restored.
In an inelastic collision,
energy is lost and the
deformation may be
permanent. (Click it.)
Elastic
• A collision in which two
objects move separately with
different velocities, but not
permanent deformation
Inelastic
• A collision in which two objects
deforms so that the objects move in
the same direction but with different
final velocities after colliding.
Perfectly Inelastic
• A collision in which two
objects stick together and
move with the same velocity
after colliding.
For each of the
following examples,
identify the type of
collision…
Perfectly Inelastic
Perfectly Inelastic
Elastic
Perfectly Inelastic
Inelastic
Perfectly Inelastic
Elastic
Explain why the final velocity of the moving object
“makes sense” in order to conserve total momentum.
After the collision the 1st ball transferred its momentum
to the 2nd ball. Since the balls have the same mass, the
velocity of the second ball should be the same as the
first in order to conserve momentum.
Explain why the final velocity of the moving object
“makes sense” in order to conserve total momentum.
After the collision, the 1st block transferred its
momentum to the 2nd block. Since the 2nd block has
more mass, the velocity should be less, in order to
conserve momentum.
The block is 2x bigger, it is ½ as fast.
Explain why the final velocity of the moving object
“makes sense” in order to conserve total momentum.
After the collision the cart
and McDonald are
moving.
Since there is more mass,
there should be less
velocity to conserve
momentum.
Easy Problem Solving
• A 50.0kg girl jumps into a 100kg raft at rest on the water. If the
velocity of the girl is 4.00m/s as she jumps, what is the final
velocity of the girl and the raft?
1st Draw a Picture
Before
After
G
G
R
mG = 50.0kg
VG = 4.00m/s
R
mR = 100kg
VR = 0m/s
mG = 50.0kg
mR = 100kg
Vf = ?
mGVG + mRVR = (mG + mR)Vf
(50.0kg)(4.00m/s)+(100.0kg)(0m/s) = (50.0kg +100kg)(Vf)
200kgm/s = (150kg)Vf
1.33m/s = Vf
Easy Problem Solving
• A 63.0kg astronaut throws a 5.0kg hammer in a direction away
from the shuttle with a speed of 18.0m/s, pushing the astronaut
back to the shuttle. Assuming that the astronaut and hammer
start from rest, find the final speed of the astronaut after throwing
+90kgm/s
-90kgm/s
the hammer.
Before
After
1st Draw a Picture
A
A H
H
mA = 63.0kg
VA = 0m/s
mH = 5.0kg
VH = 0m/s
mA = 63.0kg
VA = ?
mH = 5.0kg
VH = 18m/s
mAVA + mHVH = mAVA + mHVH
(63.0kg)(0m/s)+(5.0kg)(0m/s) = (63.0kg)VA + (5.0kg)(18.0m/s)
0kgm/s = (63.0kg)VA + 90.0kgm/s
-90.0kgm/s = (63.0kg)VA
-1.43m/s = VA
Easy Problem Solving
• A 15.0kg cart moving to the right with a speed of 4.0m/s collides
with a 6.5kg cart moving to the left with a speed of 2.0m/s. If the
carts stick together, find the final speed of the two carts.
1st Draw a Picture
Before
After
1
2
m1 = 15.0kg
V1 = 4.0m/s
A
m2 = 6.5kg
V2 = -2.0m/s
H
m1 = 15.0kg
Vf = ?
m1V1 + m2V2 = (m1 + m2)Vf
(15.0kg)(4.0m/s)+(6.5kg)(-2.0m/s) = (15.0kg + 6.5kg)(Vf)
60kgm/s + (-13.0kgm/s) = (21.5kg)Vf
60kgm/s -13.0kgm/s = (21.5kg)Vf
47.0kgm/s = (21.5kg)VA
2.19m/s = VA
m2 = 6.5kg
Key Concepts
Elastic
m1v1i + m2v2i = m1v1f + m2v2f
“Starts from rest” Vi = 0m/s
“Stops” Vf = 0m/s
Perfectly Inelastic
Inelastic
m1v1i + m2v2i = (m1+ m2)vf
m1v1i + m2v2i = m1v1f + m2v2f