Newton’s Three Laws and
Momentum and Concepts
Newton’s
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st
1
Law
A body in motion (or at rest) tends to stay in
motion (or at rest) if no forces acts upon it
In momentum concepts this becomes: an
object has momentum
2 pts on test
Momentum
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The symbol for momentum: p
The units for momentum: [kg*m/s]
Momentum is a vector and therefore has
direction. An object that is traveling north has
a different momentum than a vector traveling
south
The formula for momentum: p = m x v,
RV versus Mini
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i. The RV would have a bigger momentum because
it has more mass
ii. The RV would be more likely to stay in motion
because it has a bigger momentum from its bigger
mass.
iii. The RV would have a harder time stopping
because it has a bigger momentum from its bigger
mass.
iv. The RV would do more damage if it hit anything,
with its large mass, because it has a bigger
momentum from its bigger mass.
The formula for momentum: p = m x v,
Volvo at 100mi/hr vs Volvo at 50 mi/hr
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i. The 100 mi/hr-Volvo would have a bigger
momentum because it has more speed
ii. The 100 mi/hr-Volvo would be more likely to stay
in motion because it has a bigger momentum from
its bigger speed.
iii. The 100 mi/hr-Volvo would have a harder time
stopping because it has a bigger momentum from its
bigger speed.
iv. The 100 mi/hr-Volvo would do more damage if it
hit anything, with its large mass, because it has a
bigger momentum from its bigger speed.
Newton’s
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nd
2
Law
F=ma
In momentum concepts this becomes:
J = Ft = ∆p 2 pts on test
(called the “impulse-momentum theory”)
(you do NOT need to know the derivation, but it comes from
a = v / t, and mv=∆p)
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The symbol for impulse is J, with the units
[N*sec]
Impulse is a vector, therefore it has direction
Impulse
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Example A) a mack truck would have a
greater impulse simply because it has more
momentum than a compact car
Example B) the volvo going 100 mi/hr would
have a greater impulse than the other volvo
going 30 mi/hr because it too has a greater
momentum
 Didn't talk about Concept Problems 4-6 about
pitched vs caught (same impulse since same v
for each, but caught = bigger force since t smaller in
Ft = mv), or bullets from pistols vs rifles (rifle
bigger v since bigger t in Ft=mv). 
Impact time—long vs. short
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The shorter the impact time the larger the force (WHY???)
needed to say “Use the equation J=F*t where J is constant”
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Example: Lets compare a karate chop from a bunt of
a baseball. A karate chop occurs during a small time
period and creates a strong force. Thinking oppositely,
when you want to bunt a baseball, you take a swing
for a period of time, making a small force so the ball
won’t go to the other team.
For bunting, should have said “move bat backwards to
increase impact time so force on ball is lessened”. MANY
other examples! ...… such as Concept problems 7 or 8
(landing when jumping, or catching a hardball bare-handed.)
Bouncing vs. Sticking in Collisions
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Lets compare two objects, one that bounces and one that sticks. An
object that bounces will have a bigger velocity when it hits the
ground and therefore a bigger momentum and a bigger force and
bigger impact time than an object that would stick to the floor. This is
because when an object bounces off the floor the final velocity is
negative, meaning that it has a large change in momentum
Object that bounces has a bigger: ∆v, ∆p, F, and J
 The part in purple is WRONG. There is a difference between “velocity” and
“change in velocity”; they are NOT the same thing! (Note – if we weren’t so lazy
it would be called the “impulse-change in momentum formula”, because it is
CHANGE that is in that formula!
On the test, make up numbers of a specific example:
Bounce: v0 = 100 m/s, vF = -100 m/s, so v = (-) 200 m/s
Stick: v0 = 100 m/s, vF = 0 m/s, so v = (-)100 m/s
Its the CHANGE in VELOCITY that is greater, so the 2nd bullet above is correct:
bounces has a bigger ∆v, ∆p, F, and J
BUT, didn’t talk about any specific examples in Concept Problems 9-12 (bullets, cars, etc)
Impulse Momentum Problems
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When finding the change in momentum we
use this formula:
J=Ft=∆p=pf-pi=mvf=m(Vf-Vi)=m∆v
a b c
d
e
f
g
Only J and F should be capitals; all
others are lower case. The f and i for final
and initial should be subscripted!
Memorize at least first 3 parts for test!
Impulse Momentum Problems
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Example Rocio strikes a 0.058-kg golf ball with a
force of 272 N and gives it a velocity of 62.0 m/s.
How long was Rocio’s club in contact with the club?
M=0.058-kg
F=272N
This is wrong. If you look
V=62.0 m/s
at the last slide, that
formula has “CHANGE IN
Use F x t = m x v
(272N)(t)=(0.058kg)((62.0m/s) velocity”, not velocity.
How could/should this
t=0.013 sec
problem be fixed? Hint v0=?
Impulse Momentum Problems
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Example A Force of 186 N acts on a 7.3-kg bowling ball for 4.0 s.
What is the bowling ball’s change in momentum? What is the
bowling ball’s change in velocity?
F = 186N
m = 7.3 kg
t = 4.0 sec
∆p=?
For finding momentum use F x t = ∆ p
So (186N)(4.0sec) = ∆ p
∆p = 744 kg*m/s
For finding velocity use F x t = m x v How could/should this
(186N)(4.0sec) = (7.3-kg)(v)
problem be fixed? (There
v =102. m/s
are 3 of the 4 purple things
that are wrong.)
Newton’s Third Law
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When one object exerts a force on another, the
second exerts a force of equal magnitude on the first,
but in the opposite direction
In momentum concepts this becomes: momentum is
conserved in a closed and isolated system 2 pts on test
When a system is closed or isolated, Fon the system = 0,
and thus Jon the system = 0, so ∆pof the system = 0 too.
(Recall: J = Ft = ∆p)
In other words: P initial total = P final total
P should be a lower case p. Remember
to write ppinitial total = pfinal total for EACH
cons. of momentum problem on the test!
Conserved vs Constant
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Conserved: total amount
before and after is the same,
but the forces can transfer
Constant: there is no change
While constant and conserved
may seem the same, there are
some differences: a constant
system has objects that never
change at all; a conserved
force overall does not change
over a time period, but the
internal forces transfer
Closed: nothing enters or
leaves a system
Isolated: no external forces (no
friction)
Excellent defn. BUT, “forces” do
not “transfer”. MOMENTUM
TRANSFERS.
 Better to say: there is no change
in any object’s momentum at all,
ever.
 Constant is done OK, but once
again forces are being confused
with conserved momentum
 4 points on the test to know “the
2 conditions required for the
conservation of momentum” and
to “define each of them
separately.”
 PS – know that in science,
energy and mass are also
conserved quantities
 Didn't talk about Concept
Problems 26-27, or 16-21.
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The Recoil Effect
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Recoil effect can be explained in two different
ways:
(A) equal but opposite forces
or (B) the conservation or momentum....
pit=0
then if pFa=20 kgm/s, pFb= 20 kgm/s
therefore pFt=0
Didn’t give any specific examples from
And finally, pit=pFt Concept Problems 22-25 (or lab or cat or
hose, etc) and didn’t explain with method A
well enough. They would get full credit for
method B. 8 points on unit test!!!!!!
Conservation of Momentum Problems
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Example: Two lab carts are pushed together with a
spring mechanism compressed between them.
Upon release, the 5.0-kg cart repels one way with a
velocity of 0.12 m/s, while the 2.0-kg cart goes in the
opposite direction. What is the velocity of the 2.0-kg
cart?
Pit=PFt
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(5-kg)(0) + (2.0-kg)(0) = (5-kg)(0.12m/s) + (2.0-kg)(VF)
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Vf = -0.30 m/s
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P and V should be a lower case p and v.
BE VERY CAREFUL OF DIRECTION IN THESE
and J=Ft problems; “bounces”, “head-on”, “hit
back” are all words to mean one of the velocities
will be negative!
Take this self-QUIZ:
1.
2.
3.
Write EACH of Newton’s 3 laws (in order), and what
they become in our Momentum unit
If a thrust of 35 Newtons is used to change the
velocity of a 72000-kg craft by 0.63 m/s. How long
should the thrusters be applied?
A 0.115-kg hockey puck moving 35.0 m/s strikes an
octopus sitting on the ice. The octopus has a mass of
0.265 kg. Find their velocity as they slide off together.
Can you explain recoil effect with both N’s 3rd law and momentum
concepts??
Can you explain impact time??
What about bouncing vs sticking?
Do you know how to do a 2-dimensional problem??
Do you know at least 6 correct things about angular momentum??