Transcript document

Law of Conservation of
Momentum and Collisions
Chapter 8.4-8.5
Momentum is conserved for all
collisions as long as external
forces don’t interfere.
LAW OF CONSERVATION OF
MOMENTUM
• In the absence of outside
influences, the total
amount of momentum in a
system is conserved.
• The momentum of the cue
ball is transferred to other
pool balls.
• The momentum of the pool
ball (or balls) after the
collision must be equal to
the momentum of the cue
ball before the collision
• p before = p after
8.5 Law of Conservation and
Collisions
Motion of the cue ball
Motion of the other balls
Whenever objects collide in the absence of
external forces, the net momentum of the
objects before the collision equals the net
momentum of the objects after the collision.
Figure 8.10
Momentum of cannon and cannonball
Read Page 131
• Read 1st paragraph
• What does Newton’s 3rd law have to say about the net
force of the cannon-cannonball system?
• Why is the momentum of the cannon-cannonball system
equal to zero before and after the firing?
Read Page 131
• Read 1st paragraph
• What does Newton’s 3rd law have to say about the net force of the
cannon-cannonball system?
• The net force of this system equals zero because the
action and reaction forces cancel each other out
• Why is the momentum of the cannon-cannonball system equal to
zero before and after the firing?
• The momentum in the system must be conserved; so if
the system starts with zero momentum, it must end
with zero momentum.
Read Page 131
• Read 2nd paragraph
• Why is momentum a vector quantity?
• Explain the difference between the momentum of the
cannon and the momentum of the cannonball, and the
momentum of the cannon-cannonball system.
Read Page 131
• Read 2nd paragraph
• Why is momentum a vector quantity?
• Momentum is a quantity that expresses both
magnitude and direction.
• Explain the difference between the momentum of the cannon and
the momentum of the cannonball, and the momentum of the
cannon-cannonball system.
• After the firing occurs, both the cannon and
cannonball have the same momentum (big mass, small
velocity vs. small mass, big velocity). But since the
momentum for each is moving in the opposite
direction, the momentums cancel out, causing the
cannon-cannonball system’s momentum to equal
zero.
Read Page 131
• Read 3rd paragraph
• Why do physicists use the word conserved for
momentum?
• State the law of conservation of momentum.
Read Page 131
• Read 3rd paragraph
• Why do physicists use the word conserved for
momentum?
• The word conserved refers to quantities
that do not change.
• State the law of conservation of momentum.
• In the absence of an external force, the
momentum of a system remains the same.
Read Page 131
• What does system mean?
• In terms of momentum conservation, why
does a cannon recoil when fired?
Final Thoughts about Page 131
• What does system mean?
• The word system refers to a group of interacting
elements that comprises a complex whole.
• In terms of momentum conservation, why
does a cannon recoil when fired?
• The cannon must recoil in order for
momentum to be conserved. (The
momentum of the cannon-cannonball system
was zero before the firing, and must remain
zero after the firing.)
Read Page 131
• What does conservation of momentum
mean?
• Conservation of momentum means that the amount
of momentum in a system does not change.
• Why is the momentum cannon-cannonball
system equal to zero?
• The momentum of the cannonball cancels
out the recoil of the cannon (both move in
opposite directions with an equal amount of
momentum.
8.4 Conservation of Momentum
The momentum before firing is zero. After firing, the net
momentum is still zero because the momentum of the
cannon is equal and opposite to the momentum of the
cannonball.
Velocity cannon to left is negative
Velocity of cannonball to right is
positive
(momentums cancel each other out!)
8.5 Two Types of Collisions
• Elastic Collision: When objects collide without sticking together
--Kinetic energy is conserved
--No heat generated
• Inelastic Collision: When objects collide and deform or stick
together.
--Heat is generated
--Kinetic energy is not conserved
Changes in Velocity Conserve
Momentum
A. Elastic collisions with equal massed objects show no
change in speed to conserve momentum
• http://www.walter-fendt.de/ph14e/ncradle.htm
• http://www.walter-fendt.de/ph14e/collision.htm
B. Elastic collisions with inequally massed objects show
changes in speed to conserve momentum
– Larger mass collides with smaller mass—smaller mass object’s
speed is greater than the larger mass object
– Smaller mass object collides with larger mass object—larger
mass object’s speed is much less than the smaller mass object
– http://www.walter-fendt.de/ph14e/collision.htm
C. Addition of mass in inelastic collisions causes the speed
of the combined masses to decrease in order for
momentum to be conserved
8.5 Examples of Elastic Collisions when the
objects have identical masses
a. A moving ball strikes a ball at rest.
Note: purple vector arrow represents velocity:
speed and direction
8.5 Examples of Elastic Collisions when the
objects have identical masses
a. A moving ball strikes a ball at rest.
Momentum of the first ball
was transferred to the
second; velocity is
identical
8.5 Examples of Elastic Collisions when the
objects have identical masses
b. Two moving balls collide head-on.
8.5 Examples of Elastic Collisions when the
objects have identical masses
b. Two moving balls collide head-on.
The momentum of each ball
was transferred to the other;
each kept same speed in
opposite direction
8.5 Examples of Elastic Collisions when the
objects have identical masses
c. Two balls moving in the same direction at different
speeds collide.
8.5 Examples of Elastic Collisions when the
objects have identical masses
c. Two balls moving in the same direction at different
speeds collide.
The momentum of the first was transferred to the second
and the momentum of the second was transferred to the
first. Speeds to conserve momentum.
Example of an elastic collision with
objects same speed but different
masses
What happens to the speed of the smaller car after the elastic collision with
the more massive truck?
Notice that the car has a positive velocity and the truck a negative velocity.
What is the total momentum in this system?
Example of an elastic collision with
objects same speed but different
masses
What happens to the speed of the smaller car after the elastic collision with
the more massive truck?
(the car’s speed increases to conserve
momentum)
Notice that the car has a positive velocity and the truck a negative velocity.
What is the total momentum in this system? (40,000 kg x m/s)
8.5 Inelastic Collisions
Start with less mass, end up with
more mass
Notice how speed changes to
conserve momentum (more mass,
less speed—inverse relationship!)
Calculating conservation of
momentum
• Equation for elastic collisions
m1v1 + m2v2 = m1v1 + m2v2
Before
collision
After
collision
• Equation for inelastic collision
m1v1 + m2v2 = (m1 + m2)v2
Before
collision
After
collision
Conservation of Momentum in an
elastic collision
A
B
Before elastic collision
Cart A mass = 1 kg
Cart B mass = 1 kg
Cart A speed = 5 m/s
Cart B speed = 0 m/s
After elastic collision
Cart A mass = 1 kg
Cart B mass = 1 kg
Cart A speed = 0 m/s
Cart B speed = 5 m/s
Conservation of Momentum in an
elastic collision
A
B
Before elastic collision
Cart A mass = 1 kg
Cart B mass = 1 kg
Cart A speed = 5 m/s
Cart B speed = -5 m/s
After elastic collision
Cart A mass = 1 kg
Cart B mass = 1 kg
Cart A speed = -5 m/s
Cart B speed = 5 m/s
Conservation of Momentum in an
elastic collision
A
B
Before elastic collision
Cart A mass = 1 kg
Cart B mass = 5 kg
Cart A speed = 5 m/s
Cart B speed = 0 m/s
After elastic collision
Cart A mass = 1 kg
Cart B mass = 5 kg
Cart A speed = 0 m/s
Cart B speed = 1 m/s
Conservation of Momentum in an
elastic collision
A
B
Before elastic collision
Cart A mass = 6 kg
Cart B mass = 1 kg
Cart A speed = 10 m/s
Cart B speed = 0 m/s
After elastic collision
Cart A mass = 6 kg
Cart B mass = 1 kg
Cart A speed = 2 m/s
Cart B speed = 48 m/s
Conservation of Momentum in an
inelastic collision
Before inelastic collision
After inelastic collision
Big fish mass = 4 kg
Big fish mass + Small fish mass = 5 kg
Small fish mass = 1 kg
Small fish + Large fish speed = 1 m/s
Small fish speed = 5 m/s
Large fish speed = 0 m/s
m1v1
=
m1 + m2
v2
8.5 Collisions
think!
One glider is loaded so it has three times the mass of another
glider. The loaded glider is initially at rest. The unloaded glider
collides with the loaded glider and the two gliders stick
together. Describe the motion of the gliders after the collision.
8.5 Collisions
think!
One glider is loaded so it has three times the mass of another
glider. The loaded glider is initially at rest. The unloaded glider
collides with the loaded glider and the two gliders stick
together. Describe the motion of the gliders after the collision.
Answer: The mass of the stuck-together gliders is four times
that of the unloaded glider. The velocity of the stuck-together
gliders is one fourth of the unloaded glider’s velocity before
collision. This velocity is in the same direction as before, since
the direction as well as the amount of momentum is
conserved.
1. Conservation of Momentum in
an elastic collision
m1v1 = v2
m2
A
B
Before elastic
collision
Cart A mass = 1 kg
Cart B mass = 5 kg
Cart A speed = 5 m/s
Cart B speed = 0 m/s
After elastic
collision
Cart A mass = 1 kg
Cart B mass = 5 kg
Cart A speed = 0 m/s
Find Cart B speed
2. Conservation of Momentum in
an elastic collision
m1v1 = v2
m2
A
B
Before elastic
collision
Cart A mass = 5 kg
Cart B mass = 2 kg
Cart A speed = 10 m/s
Cart B speed = 0 m/s
After elastic
collision
Cart A mass = 5 kg
Cart B mass = 2 kg
Cart A speed = 0 m/s
Find Cart B speed
8.5 Conservation of momentum for inelastice
collisions
Consider a 6-kg fish that swims toward and swallows a
2-kg fish that is at rest. If the larger fish swims at 1 m/s,
what is its velocity immediately after lunch?
m1v1
=
m1 + m2
v2
Find the speed of the
two fish after the
inelastic collision