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Momentum:
A Deeper Look
into Motion
Which of the following has the
most Momentum?
Question 1
a. A hockey puck at rest
b. A bowling ball at rest
c. Both have the same momentum
Which of the following has the
most Momentum?
Question 2
a. A VW beetle moving at a high
velocity
b. A big truck moving at the same
speed
c. Both have the same momentum
Which of the following has the
most Momentum?
Question 3
a. A VW beetle moving at a slow speed
b. The same VW beetle moving at a
fast speed
c. Both have the same momentum
Which of the following has the
most Momentum?
Question 4
a. A tennis ball falling freely
b. A bowling ball falling freely for the
same amount of time
c. Both have the same momentum
Which of the following has the
most Momentum?
Question 5
a. A bullet fired from a rifle (which was
initially at rest)
b. The rifle from which it was fired
(immediately after firing)
c. Both have the same momentum
Which of the following has the
most Momentum?
Question 6
a. A car moving at 50 mi/hr
b. The passengers inside that car
c. Both have the same momentum
Which of the following has the
most Momentum?
Question 7
a. A golf ball hit with 200 N of force for
.01 seconds
b. The same ball hit with 20 N of force
for .1 seconds
c. Both have the same momentum
Which of the following has the
most Momentum?
Question 8
a. A 900 kg VW beetle moving at 10
m/s
b. A 9000 kg truck moving at 1 m/s
c. Both have the same momentum
Which of the following has the
most Momentum?
Question 9
a. A VW beetle going uphill at a
constant speed
b. The same beetle going downhill at
the same speed
c. Both have the same momentum
Which of the following has the
most Momentum?
Question 10
a. A tennis ball sitting motionless on a
shelf
b. A bowling ball sitting on the same
shelf
c. Both have the same momentum
#
Option A
Option B
A, B, or Same?
Why?
1
Hockey Puck
at rest
Bowling Ball at
rest
C
v = 0 for both,
so p = 0
2
VW moving
const. speed
Truck w/ same
speed
B
v is same, so larger m
has larger p
3
VW moving
slowly
VW moving
quickly
B
m is same, so larger v
has larger p
4
Tennis ball in
free fall
Bowling ball in
free fall
B
v is same, so larger m
has larger p
5
Bullet fired
from rifle
Rifle that fired
bullet
C
6
Car moving
50 mph
Passengers
inside
A
v is same, so larger m
has larger p
7
Ball 200 N for
0.01 s
Ball 20 N for
0.1 s
C
I=Δp=FΔt
8
900 kg VW @
10 m/s
9000 kg truck
@ 1m/s
C
p=mv
VW uphill
VW downhill @
same speed
C
v is same, m is same,
so p is same
Tennis ball on Bowling ball on
shelf
shelf
C
v = 0 for both,
so p = 0
9
10
Δp are equal and
opposite
What Is Momentum?
 What factors do you think determine
an object’s momentum?
 Momentum can be conceptually
defined as the “strength of motion”
 It is kind of like inertia, but relates to
the tendency of a moving object to
continue moving
𝒑=𝑚∙𝒗
Does This Look Familiar?
Newton’s 2nd Law
(The Original Version!)


 dp
 p
F
F 
dt
t


 (mv )
v
F
m
t
t


F  ma
What About Impulse?
 What does an applied force do to an object?
 Exactly! It causes an acceleration…which
changes its velocity…which changes its
momentum!
 The amount of change depends on the amount
of time it is applied
 An impulse is defined as a force applied for a
given length of time
𝑰 = 𝑭 ∙ Δ𝑡
Impulse with 2 Objects
 For an interaction between 2 objects,
where one object acts on another object…
Impulse is a change in momentum
 Since
2nd
Law tells us 𝑭 =
∆𝒑
:
∆𝑡
𝑰 = Δ𝒑 = 𝑚 ∙ ∆𝒗
Units!!
• 𝑭 · Δ𝑡 = 𝑚 · Δ𝒗
• N · sec = kg ·
•
•
kg∙m
kg∙m
𝑠
s2
m
s
· sec = kg ·
= kg ·
m
m
s
s
• So, impulse and momentum can be expressed in
 kg∙m 𝑠 or N · s
Nùmero Uno
1. Paul deTrigga fires a rifle. The rifle recoils
from firing the bullet. The acceleration of
the rifle’s recoil is small because the:
a. Force against the rifle is less than the
force against the bullet
b. Acceleration is mainly concentrated
in the bullet since it is being fired.
c. Rifle has more mass than the bullet.
d. Momentum of the rifle has changed
e. None of these
Nummer Zwei
2. Pat, a karate expert, executes a swift
blow and severs a cement block with her
bare hand. Which of the following are true
statements?
a. The impulse on both the block and
Pat’s hand have the same magnitude.
b. The force on both the block and Pat’s
hand have the same magnitude.
c. The time of impact on both the block
and Pat’s hand is the same.
d. All of the above
e. None of the above
Think-Pair-Share:
Impulse in Car Crashes
 In a car collision, the driver’s body must
change speed from a high value to zero.
This is true whether or not an airbag is
used, so why use an airbag? How does it
reduce injuries? Explain using momentum
and impulse.
 The air bag increases the time over which
the force is applied. Since the change in
momentum is the same, this means that the
impulse is the same. So increasing time
decreases force!
Think-Pair-Share:
Impulsive Actions
 You want to close an open door by throwing either a 400 gram lump of
clay or a 400 g rubber ball toward it. You can throw either object with
the same speed, but they are different in that the rubber ball bounces
off the door while the clay just sticks to the door. Which projectile will
apply the larger impulse to the door and be more likely to close it?
Explain.
 The ball! Since it bounces off the door, its
change in momentum is greater because in
addition to losing its initial momentum toward
the door, it now has momentum in the opposite
direction, hence a greater change. Since the
change in momentum is greater, so is the
impulse, and thus the force will be as well.
A New Version of Newton’s 3rd Law
 All IMPULSES are equal and opposite!
 Thus, we can say all changes in momentum
are equal and opposite!
 Another way to say this is that momentum is
conserved in all interactions as long as there
are no external forces involved
Total momentum before = Total momentum after
𝒑𝒃𝒆𝒇𝒐𝒓𝒆 = 𝒑′𝒂𝒇𝒕𝒆𝒓
Think – Pair – Share:
Earth Moving?
 Okay, let’s assume that an average person has
a mass of 65.0 kg. There are 7 billion people or
so on the Earth. If all 7 billion people somehow
managed to all start from rest and accelerate
to a velocity of 4.00 m/s in the same direction
at the same time…
a. How much change in momentum would they
have?
b. By how much would the Earth’s momentum
change?
c. If the Earth has a mass of 5.98 x 1024 kg, then by
how much would the Earth’s velocity change?
d. If all the people took 1.50 seconds to change
their velocity, how much force was exerted?
Think – Pair – Share: Earth Moving?
a. How much change in momentum would they have?
𝑚𝑝𝑒𝑜𝑝𝑙𝑒 = (7.00 × 109) ∙ (65.0 kg) = 4.55 × 1011 kg
∆𝑝𝑝𝑒𝑜𝑝𝑙𝑒 = 𝑝2 − 𝑝1 = 𝑚𝑝𝑒𝑜𝑝𝑙𝑒 ∙ 𝑣2 − 0
∆𝑝𝑝𝑒𝑜𝑝𝑙𝑒 = 4.55 × 1011 kg ∙ 4.00 m s − 0
∆𝒑𝒑𝒆𝒐𝒑𝒍𝒆 = 𝟏. 𝟖𝟐 ×
𝟏𝟎𝟏𝟐
𝐤𝐠 ∙ 𝐦
𝐬
b. By how much would the Earth’s momentum change?
∆𝒑𝑬𝒂𝒓𝒕𝒉 = −𝟏. 𝟖𝟐 ×
𝟏𝟎𝟏𝟐
𝐤𝐠 ∙ 𝐦
𝐬
Think – Pair – Share: Earth Moving?
c. If the Earth has a mass of 5.98 x 1024 kg, then by how much
would the Earth’s velocity change?
∆𝑝𝐸𝑎𝑟𝑡ℎ = 𝑚𝐸𝑎𝑟𝑡ℎ ∙ ∆𝑣𝐸𝑎𝑟𝑡ℎ
kg ∙ m
∆𝑝𝐸𝑎𝑟𝑡ℎ 1.82 × 1012
s
∆𝑣𝐸𝑎𝑟𝑡ℎ =
=
𝑚𝐸𝑎𝑟𝑡ℎ
5.98 × 1024 kg
∆𝒗𝑬𝒂𝒓𝒕𝒉 = 𝟑. 𝟎𝟒 × 𝟏𝟎−𝟏𝟑 𝒎 𝒔
d. If all the people took 1.50 seconds to change their velocity,
how much force was exerted?
𝐼𝑚𝑝𝑢𝑙𝑠𝑒 = ∆𝑝𝐸𝑎𝑟𝑡ℎ = 𝐹 ∙ ∆𝑡
kg ∙ m
𝐼𝑚𝑝𝑢𝑙𝑠𝑒 1.82 × 1012
s
𝐹=
=
∆𝑡
1.50 s
𝑭 = 𝟏. 𝟐𝟏 × 𝟏𝟎𝟏𝟐 𝐍
Conservation of Momentum
 If the quantity of the amount after an
interaction does not change, we say that it
is conserved
 Because the momentum in a defined system
is the same before a collision as it is
afterwards, we say that momentum is
conserved
Collisions!
 Elastic Collisions (Bouncy):
 Objects involved bounce off each other
𝑚1𝒗𝟏 + 𝑚2𝒗𝟐 = 𝑚1𝒗𝟏’ + 𝑚2𝒗𝟐’
 Inelastic Collisions (Sticky):
 Objects involved stick together
𝑚1𝒗𝟏 + 𝑚2𝒗𝟐 = (𝑚1 + 𝑚2 )𝒗’
Elastic (aka “bouncy”)
𝒑𝒃𝒆𝒇𝒐𝒓𝒆 = 𝒑′𝒂𝒇𝒕𝒆𝒓
𝑚1𝒗𝟏 + 𝑚2𝒗𝟐 = 𝑚1𝒗𝟏’ + 𝑚2𝒗𝟐’
A
B
Inelastic (aka “sticky”)
𝒑𝒃𝒆𝒇𝒐𝒓𝒆 = 𝒑′𝒂𝒇𝒕𝒆𝒓
𝑚1𝒗𝟏 + 𝑚2𝒗𝟐 = (𝑚1 + 𝑚2 )𝒗’
A
B
Let’s Recap!
 Momentum: inertia in motion
𝒑 = 𝑚∙𝒗
 Impulse:
𝑰 = 𝑭 ∙ Δ𝑡
𝑰 = Δ𝒑 = 𝑚 ∙ ∆𝒗
(you might also see impulse defined as 𝑱 )
𝒑𝒃𝒆𝒇𝒐𝒓𝒆 = 𝒑′𝒂𝒇𝒕𝒆𝒓