Momentum
1) How do we measure the momentum of an
object?
2) How is momentum conserved in collisions?
3) Describe an example of angular momentum?
Chapter 6
Linear Momentum
 Momentum is defined as mass times
velocity.
 Momentum is represented by the symbol p,
and is a vector quantity.
p = mv
momentum = mass  velocity

As mass increase momentum increases
 As velocity increase momentum increases.
Day 1: Practice Problem
1.
When comparing the momentum of two moving
objects, which of the following is correct?
a)The object with the higher velocity will have less
momentum if the masses are equal.
b)The more massive object will have less momentum if
its velocity is greater.
c)The less massive object will have less momentum if the
velocities are the same.
d)The more massive object will have less momentum if
the velocities are the same.
2. What is the momentum of a 60 kg child
running at 3 m/s?
Day 2: Practice
Answers :
1. C
2.
p = mv
= (60.0 kg) (3.0 m/s)
•
= 180 kg * m/s
Chapter 6
Day 2: Momentum is Conserved,
 Newton’s third law
leads to conservation
of momentum
 During the collision,
the force exerted on
each bumper car
causes a change in
momentum for each
car.
 The total momentum
is the same before
and after the collision.
Chapter 6
Day 2: Momentum is Conserved
The Law of Conservation of Momentum:
The total momentum of all objects interacting
with one another remains constant regardless
of the nature of the forces between the
objects.
m1v1,i + m2v2,i = m1v1,f + m2v2,f
total initial momentum = total final momentum
Day 2: Conservation of Momentum
BOING! SPLAT! Holy Vectors Batman, its
Momentum.
 The conservation of momentum is very important in
the study of collisions (atoms, highway accidents,
sports science etc..)
 Go to this website and observe how the different
masses react in a collision. Don’t worry about the
math just yet. Just predict which mass will slow down
and which will speed up.
 http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Spcl.html#1
 http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Exmpl.html#5
Chapter 6
Sample Problem
Conservation of Momentum
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?
Chapter 6
Sample Problem, continued
Conservation of Momentum
1. Define
Given:
m1 = 76 kg m2 = 45 kg
v1,i = 0
v2,i = 0
v1,f = 2.5 m/s to the right
Unknown:
v2,f = ?
Chapter 6
Sample Problem, continued
Conservation of Momentum
2. Plan
Choose an equation or situation: Because
the total momentum of an isolated system
remains constant, the total initial momentum
of the boater and the boat will be equal to the
total final momentum of the boater and the
boat.
m1v1,i + m2v2,i = m1v1,f + m2v2,f
Chapter 6
Sample Problem, continued
Conservation of Momentum
2. Plan, continued
Because the boater and the boat are initially at
rest, the total initial momentum of the system is
equal to zero. Therefore, the final momentum of
the system must also be equal to zero.
m1v1,f + m2v2,f = 0
Rearrange the equation to solve for the final
velocity of the boat. m v  – m v
2
v 2,f
2,f
1 1,f
 m1 
 –
 v1,f
 m2 
Chapter 6
Section 2 Conservation of
Momentum
Sample Problem, continued
Conservation of Momentum
3. Calculate
Substitute the values into the equation and
solve:
v 2,f
v 2,f
 76 kg 
 –
 2.5 m/s to the right 

 45 kg 
 –4.2 m/s to the right
Chapter 6
Sample Problem, continued
Conservation of Momentum
4. Evaluate
The negative sign for v2,f indicates that the
boat is moving to the left, in the direction
opposite the motion of the boater. Therefore,
v2,f = 4.2 m/s to the left
Day 3: Practice Problems
 1) A roller coaster climbs up a hill at 4 m/s and then zips
down the hill at 30 m/s. The momentum of the roller
coaster




A) is greater up the hill than down the hill.
B) is greater down the hill than up the hill.
C) remains the same throughout the ride.
D) is zero throughout the ride.
 2) In a two-body collision,
 A) momentum is always conserved.
 B) kinetic energy is always conserved.
 C) neither momentum nor kinetic energy is conserved.
 D) both momentum and kinetic energy are always
conserved.
Day 3 : Practice continued
1. The law of conservation of momentum states that
 A) the total initial momentum of all objects interacting with one
another usually equals the total final momentum.
 B) the total initial momentum of all objects interacting with one
another does not equal the total final momentum.
 C) the total momentum of all objects interacting with one another
is zero.
 D) the total momentum of all objects interacting with one another
remains constant regardless of the nature of the forces between
the objects.
2. Which of the following statements about the conservation of
momentum is not correct?
 A) Momentum is conserved for a system of objects pushing away
from each other.
 B) Momentum is not conserved for a system of objects in a headon collision.
 C) Momentum is conserved when two or more interacting objects
push away from each other.
 D) The total momentum of a system of interacting objects remains
constant regardless of forces between the objects.
Day 4: Quiz (Let’s Go!!!)