Chapter 7
Momentum
Chapter Warm Up
1. What is a non physics definition of
momentum? Give an example.
2. What is the physics definition of momentum?
Give an example.
3. How can the momentum of an object be
changed?
4. What is impulse?
5. What does it mean when a quantity is
conserved?
6. How are elastic and inelastic collisions the
same?
7. How are elastic and inelastic collisions
different?
Section 1: Linear Momentum
Definition:
Inertia in motion
Example:
Symbol:p
Equation:
Momentum = mass x velocity
p=mv
Units:
p= kg m = kgm
s
s
Vector quantity
Examples:
1. A 2250 kg pickup truck has a velocity of
25m/s to the east. What is the momentum of
the pickup truck?
5.6 x 104 kgm/s east
2. A car has a mass of 1210 kg. How fast must
it be traveling if its momentum is 2.5 x 103
kgm/s?
2.1 m/s in the direction of travel
3. A child is riding a bike, and is traveling at a
velocity of 4.5 m/s to the northwest. If the
momentum of the bike and the child is 1.2 x
102 kg m/s to the northwest, what is the
combined mass of the bike and the child?
27 kg
How can an object’s momentum be changed?
change mass or velocity
if change velocity – object accelerates– a force is
needed
larger force – larger change in momentum
BUT: TIME FORCE IS APPLIED IS ALSO
IMPORTANT
How about the time the force is applied?
apply force briefly to an object – change in
momentum
apply same amount of force for a longer time–
larger change in momentum
Why????
p = mv, but velocity has a time component– so
the larger the Δt, the larger the Δv, and the
larger the momentum change
So….
A large force over a small time can equal the
same momentum change as a smaller force
over a longer time
FORCE AND TIME ARE BOTH IMPORTANT
This leads to a new quantity: Impulse
Impulse
Definition:
Product of force and time interval during
which the force acts
Causes momentum to change
Equation:
Impulse = FΔt
But, from NII:
F = ma
and from Chapter 2
a = Δv/Δt
substituting
F = mΔv/Δt
rearranging
FΔt = Δ(mv)
So impulse = Δ momentum
This is the Impulse – Momentum Theory
Section 2: Impulse – Momentum
Theory
Definition:
Any impulse acting on a system changes the system's
momentum.
(http://faculty.wwu.edu/vawter/PhysicsNet/Topics/Momentum/ImpulseMomTheorem.html)
Equation:
FΔt = Δ(mv)
usually written as
FΔt = mΔv
Examples:
1. A 1400 kg car moving westward with a
velocity of 15 m/s collides with a utility pole
and is brought to rest in 0.30 s. What force is
exerted on the car during the collision?
7.0 x 104 N east
2. A 0.50 kg football is thrown with a velocity
of 15 m/s to the right. If a stationary receiver
exerts a force of 3.8 x 102 N to the left when
catching the ball, how long did it take the
receiver to catch the ball and bring it to a
halt?
0.020s
3. A man drops from rest off a diving board that
is 3.0 m above the surface of the water and
comes to rest 0.55 s after reaching the water.
If the force on the diver is 1.1 x 103 N
upward, what is the diver’s mass?
79kg
So… How do we change the momentum of an
object?
change any or all
force of impact
time of impact
mass of object
velocity of object
Impulse – Momentum in the Real
World
Hitting a ball
Barrels on the Interstate at bridges
Catching a ball
Your own examples
The bottom line:
Impact time and impact force are inversely
proportional for the same change in
momentum
A moving object has a certain amount of
momentum, so if you increase the impact time,
you will decrease the impact force ( which is
what you usually want)
or
If you decrease the impact time, you will
increase the impact force
DON’T CONFUSE IMPULSE, IMPACT, AND
MOMENTUM!!!!
Impact is a force
Impulse is what is applied to an object to
change it’s momentum
To bring an object to a stop,
impulse applied = change in momentum ( as
momentum goes to zero.)
Check your concepts:
1. Which involves less impulse, a dish falling to
a tile floor, or a dish falling the same distance
to a carpet?
Neither– the change in momentum is the same, so the
impulse required is the same. Mass doesn’t change, and
Δv is a free fall issue, depending on the height.
2. Why is basketball played on a wood or
composite floor rather than concrete?
The wooden or composite floor has more “give”,
which increases the impact time, therefore decreasing
the impact force, which means the player feels less
force on the body.
3. Why do athletes get injured on artificial grass
more often than on real grass?
Same as the basketball floor – the grass increases impact
time, so decreases impact force.
Section 3: Conservation of Momentum
What does conserved mean?
The amount of a quantity in a system is not
changed during an interaction
The amount you end with must be the same as
the amount you started with.
Conservation Laws
Energy
Energy cannot be created nor destroyed, it
merely changes form
Matter
Matter cannot be created nor destroyed, it
merely changes form
Momentum
Conservation of Momentum
In a closed system, the total amount of
momentum is conserved(constant)
Momentum can be transferred from one object
to another within the system
To change the amount of momentum of a system,
an outside force or impulse must be applied to
the system
Internal ones are action-reaction pairs and don’t
affect the momentum of the system
sitting in a car and pushing on the
dashboard is internal
pushing on the bumper is external
If there is no net force, there is no net impulse,
so no net change in momentum of the system
This leads to the Law of Conservation of
Momentum
In the absence of an
external force, the
momentum of a
system remains
unchanged
Equation:
m1v1i + m2v2i = m1v1f + m2v2f
m1 = mass of object 1
v1i = initial velocity of object 1
m2 = mass of object 2
v2i = initial velocity of object 2
v1f = final velocity of object 1
v2f = final velocity of object 2
Examples:
1. A 76 kg boater, initially at rest in a stationary
45 kg 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?
4.2m/s to the left
2. An astronaut is at rest on a space walk when
the tether line to the shuttle breaks. The
astronaut is able to throw a spare 10.0 kg
oxygen tank in a direction away from the
shuttle with a speed of 12.0 m/s, propelling
the astronaut back to the shuttle with a speed
of 1.90 m/s. What is the astronaut’s mass?
63.2kg
Section 4: Collisions
What is a collision?
A collision occurs when 2 objects try to
occupy the same space at the same time
IN COLLISIONS, MOMENTUM IS
CONSERVED
Net momentum before collision = net momentum after collision
2 Types of collisions:
Elastic collisions
Inelastic collisions
Elastic collisions
2 objects collide and fly apart
momentum is transferred from one object to the
other
Example
Billiard balls
one moving towards the other
when collide and bounce apart
momentum is transferred from the one
with more initial momentum to the one
with less initial momentum
Equation:
m1v1i + m2v2i = m1v1f + m2v2f (look familiar?)
Examples:
1. A 16.0 kg canoe moving to the left at 12.5
m/s makes an elastic head-on collision with a
14.0 kg raft moving to the right at 16.0 m/s.
After the collision, the raft moves to the left
at 14.4 m/s. Find the velocity of the canoe
after the collision. Disregard any effects of
the water.
14.1 m/s to the right
2. A 25.0 kg bumper car moving to the right at
5.00 m/s overtakes and collides elastically with
a 35.0 kg bumper car moving to the right.
After the collision, the 25.0 kg bumper car
slows to 1.50 m/s to the right, and the 35.0 kg
car moves at 4.50 m/s to the right. What is the
velocity of the 35 kg bumper car before the
collision?
2.0m/s to the right
Inelastic collisions
2 objects collide and stick together ( 2 objects
become 1 object)
Example
A person catching a ball
When the person catches the ball, two objects,
a ball and a person, become 1 object a ball-person
Equation:
m1v1i + m2v2i = (m1 + m2)vf
Examples:
1. An 1850 kg luxury sedan stopped at a traffic
light is struck from the rear by a compact car
with a mass of 975 kg. The two cars become
entangled as a result of the collision. If the
compact car was moving at a velocity of 22.0
m/s to the north before the collision, what is
the velocity of the entangled mass after the
collision?
7.58 m/s north
2. A dry cleaner throws a 22 kg bag of laundry
onto a stationary 9.0 kg cart. The cart and the
laundry bag begin moving at 3.0 m/s to the
right. What was the velocity of the laundry bag
before the collision?
4.2 m/s to the right
3. A 47.4 kg student runs down the sidewalk
and jumps with a horizontal speed of 4.20 m/s
onto a stationary skateboard. The student and
the skateboard move down the sidewalk with a
speed of 3.95 m/s. What was the mass of the
skateboard?
3.0 kg