Momentum and Its Conservation

1. Momentum and Its Conservation
Chapter 9

2. If you were to step in front of a fast moving train,
would you be afraid of its momentum?
A near miss!!!

3. Introduction
 Well…. You should be afraid of the force it
would apply to you! Momentum and force
are directly related, but strictly speaking it’s
the force that will hurt you.

4. Momentum and Impulse
 Momentum itself cannot be felt. It is a
calculated (vector) quantity representing the
“strength” or perhaps the “inertia” of an
object’s motion
 The quantity of momentum is represented in
an equation by a letter “p”. The simplest
formula for momentum is: p = mv
(CES) (Units?)

5. Momentum and Impulse
 Can a freight train and a feather have the
same momentum? (In the absence of air)
(In the presence of air?) Explain
 Recall that (net) forces change the velocity
of objects.
F = ma
F = mDv
Dt
FDt = mDV (CES) Explanation of variables on next page.

6. Momentum and Impulse
 “FDt” (combined) is known as an impulse
which causes an equivalent change in
momentum “mDv”
 Let’s look at the units on both sides of this
equation. Let’s also not get “hung up” on
which symbols are bold and which aren’t in
the book. As in the past, it is only bolding
vector quantities.

7. Momentum and Impulse
 What’s the formula for DV?
 DV = Vf – Vi
 FDt = mvf – mvi = pf – pi (CES)
 Example on overhead
 Assign. P.233 #1-4 Don’t get hung up on
the sketches. I always recommend them,
but they don’t have to be in the detail they
suggest.

8. Newton’s 3rd Law and
Momentum
Recall that forces occur only as interactions
between 2 or more objects. Newton’s 3rd
Law states that forces occur in pairs (or
multiples of 2), never alone. Any force is
always accompanied by an equal and
opposite (in direction) force.

9. (Continued)
 Remember this question? If in kicking a
football there are equal and opposite forces,
why does the ball move? Are there net
forces? (Let’s refresh our memories.)
 Do these forces cause equal and opposite
accelerations? What about the change of
momenta of the objects involved?

10. The Law of Conservation of
Momentum
 Recall that (net) forces applied over time
(impulses) change momentum. Newton’s
3rd law and the Law of Conservation of
Momentum are closely related to each
other.
 Football example: You kick the ball, the
ball kicks you - Newton’s 3rd law.
 Your foot slows down a little (loses “p”),
the ball accelerates (gains “p”)

11. Conservation of Momentum
 How is the momentum lost by your foot
compared to the momentum gained by the
ball?
 The Law of Conservation of Momentum
states that the total momentum within a
defined system remains constant unless
acted upon by an external force. (We’ll talk
about what an external force is - later.)

12. Conservation of Angular Momentum
 Tough question: Why is it that an ice skater
spins faster when he/she pulls their arms
in? Video Demo/volunteers for spinning on
lab stool?
 To comply with the law of conservation of
momentum, of course. To explain this in a
simple way recall that p = mv. The
skater’s mass does not change at any time in
this example -so let’s look at the velocity.

13. Conservation of Momentum
 Recall V = d/t If the distance is decreased
(circumference) then the time of the spin
must decrease to keep “v” the same! This
means they have to spin in less time
(keeping the velocity the same). Here the
skater is said to be conserving angular
momentum. Bicycle wheel demo. Video
 Let’s look at something a bit simpler - how
this law applies to collisions in a straight
line.

14. Conservation of Momentum
plost = pgained
mDvlost = mDvgained
If two objects are involved in a collision, then
the sum of their momenta before and after
are the same! (Does this make sense?)
Mathematically:
m1v1 + m2v2 = m1v1` + m2v2`
(before) (after)

15. Cons of Momentum Example
 A glider of mass 0.355 Kg moves along a
friction-free air track with a velocity of
0.095
𝑚
𝑠
. It collides with a second glider of
mass 0.710 Kg moving in the same
direction at a speed of 0.045
𝑚
𝑠
. After the
collision, the first glider continues in the
same direction with a velocity of 0.035
𝑚
𝑠
.
What is the velocity of the second glider
after the collision?
 Answer: 0.075
𝑚
𝑠
.

16. Conservation of Momentum
 Assign p. 238 # 13-18 Plus this problem:
 A billiard ball of unknown mass travels at
40
𝑐𝑚
𝑠𝑒𝑐
. This ball overtakes a second billiard
ball of mass 150 g which is traveling along the
same line at 15
𝑐𝑚
𝑠𝑒𝑐
. After the collision, the first
ball moves along the same line at 20
𝑐𝑚
𝑠𝑒𝑐
. The
second ball is moving at 42
𝑐𝑚
𝑠𝑒𝑐
. What is the
mass of the first ball?

17. Cons. of Momentum (cont)
 http://jersey.uoregon.edu/vlab/Momentum/i
ndex.html(works only on site!)
 Demo - collision balls/”Java Applets On
Physics”
 Video disk 3E Ch 31(1),32(2) 61(N)
63(N)64,66(N)67(2)68(1)
 Sponge? Phys SimElastic Collisons 1 Dim.

18. Internal and External Forces
 Recall that how a “system” or “frame of
reference” (basically synonymous) is
defined changes our interpretation. Let’s
look at how this affects the game of pool.
 Case 1 If we define our system to contain
the cue ball and nothing else, what type of
force does the cue stick represent?
 An external force. The momentum of the
cue ball changes as the law says it can.

19. Internal and External Forces
 Case 2 If we define our system to contain the
cue ball and the cue stick (and the person
holding it), then what type of force does the
cue stick represent now? Does the total
momentum change?
 The cue stick is an internal force. The total “p”
does not change. The objects do accelerate in
opposite directions, the amount of which is
dictated by Newton’s 2nd law and their
masses. Example p.157 old book (overhead
and our formula)
 Video disk 1a77 Frame 49247

20. Internal Vs. External Force Example
 A cannon at rest with a mass of 1.20 x 103
Kg fires a 53 Kg mass in a horizontal
direction of 67
𝑚
𝑠
. The cannon can roll
without friction. What is the velocity of the
cannon after firing the shot?
 Answer: -3.0
𝑚
𝑠
.
 Assign p.240 #19-21 plus problem on next
slide and Challenge!

21. Additional Practice Problem
 A 50.0 g projectile is launched with a
horizontal velocity of 647
𝑚
𝑠
from a 4.65
Kg launcher moving at 2.00
𝑚
𝑠
. What is the
velocity of the launcher after the projectile
is launched?

22. Conservation of Momentum
In 2 or 3 Dimensions
 The LOCOM does not apply only to interactions
in a straight line, but to all interactions! When
two objects collide, they may go off in different
directions, but the vector sum (Oh no!) of their
resulting momenta will equal the sum of the
momenta of the objects before the collision!
Confused? How many of you play pool?
 p.159 (old book) overhead
 http://fys.kuleuven.be/pradem/applets/suren/Collis
ions/Collisions.html
 Video - Mechanical Universe - Con. of “P

23. Chapter 9 Review
 Pp. 250-253
 MC 33-36, 38-43 AC 46-50, 53-55
 MP 56,57, 60, 65, 67, 69, 70, 72, 80
 MR 83, 86,