The Immaculate Reception

1
The Immaculate Reception
2
MOMENTUM

• AP Physics C Mechanics

3
What is Momentum?

• What is its definition?
• How do we calculate it?
• When do we use this term?
• Why was this word invented?
• What do we already know about it?
• What do we want to know about it?

4
What is Momentum?

• What is its definition?

Momentum quantity of motion -Newton
Momentum mass in motion
Momentum the product of an objects mass and its
velocity
Momentum It is a vector!
Momentum is sometimes called linear momentum
5
What is Momentum?

• How do we calculate it?

If object is moving in arbitrary direction

• What are its units?

6
What do we know about momentum?
7
What is Momentum?

• Why was this word invented?
• When do we use this term?

We are yet to make a distinction between a rhino
moving at 5m/s and a hummingbird moving at 5m/s.
Thus far, how have we handled forces that are
only briefly applied such as collisions?
(we pretended that doesnt happen)
Some believed that this quantity is conserved in
our universe.
8
How is momentum related to other physics concepts
that we have already studied?
The time rate of change of linear momentum of a
particle is equal to the net force acting on the
particle.
We will soon see that it has many things in
common with Energy, Newtons 3rd law, and The
Calculus.
9
Pause to think about calculus concepts

• Why is a derivative involved?
• What does this say about the slope of a
  momentum-time graph?
• The area under which graph might be meaningful?
• So, how might an integral be involved?

Momentum may be changing non-uniformly with time
The slope of a momentum-time graph is net force!
The area under a force-time graph is a change in
momentum!
The integral of force with respect to time is a
change in momentum!
10
Pause to think about calculus concepts
The integral of force with respect to time is a
change in momentum!
We call the left-hand side of this equation the
IMPULSE of the force
11
Pause to think about calculus concepts
The slope of a momentum-time graph is net force!
The area under a force-time graph is a change in
momentum or an impulse
12
Impulse-Momentum Theorem
The impulse of a force F equals the change in
momentum of the particle.
This is another way of saying that a net force
must be applied to change an objects state of
motion.
Why does this look different from the last
equation?
Because the force might be constant!
13
A few things about IMPULSE
It is a vector in the same direction as the
change in momentum.
It is not a property of an object! It is a
measure of the degree to which a force changes a
particles momentum. We say an impulse is given to
a particle.
What are its units?
From the equation we see that they must be the
same as momentums units (kgm/s).
Impulse approximation assume the force is
applied only for an instant and that it is much
greater than other forces present.
14
Another question please
15
To stop a speeding train Explain these videos
in physics terms.
16
Quick Conceptual Quiz

• Can a hummingbird have more momentum than a
  rhino?
• Why might an out of control truck hit a haystack
  or barrels and pile of sand as opposed to a wall
  as an emergency stop?
• How is a ninjas ability to break stacks of wood
  related to impulse and momentum?
• What good is it to know an objects momentum?

17

• Question 2 If a boxer is able to make his
  impact time 5x longer by riding with the punch,
  how much will the impact force be reduced?
• By 5x

18

• When a dish falls, will the impulse be less if it
  lands on a carpet than if it lands on a hard
  floor?
• No the same impulse the force exerted on the
  dish is less because the time of momentum change
  increases.

19
Examples

• Examples of Increasing Impact Time to decrease
  Impact Force

Bend knees when jumping Gymnasts and wrestlers
use mats Glass dish falling on carpet rather than
concrete Acrobat safety net Other examples???
20
Observing changes in momentum
21
Consider two particles that can interact, but are
otherwise isolated form their surroundings.
What do we know about a collision between these
two particles?
Newtons law says that they exert equal and
opposite forces on each other regardless of
comparative size (mass).
Is it possible for one particle to be in contact
with the second particle for a longer period of
time than the second on the first?
No, so the impulse imparted on each must be the
same. THEREFORE
22
The particles must undergo the same changes in
momentum!
Lets look at this mathematically.
23
What does it mean, conceptually, for a time
derivative of momentum to be zero
It means that the total momentum of the system is
constant over time.
aka Momentum is Conserved!
24
The Law of Conservation of Momentum
When two isolated, uncharged particles interact
with each other, their total momentum remains
constant.
OR
The total momentum of an isolated system at all
times equals its initial momentum (before and
after collisions).
25
Find the rebound speed of a 0.5 kg ball falling
straight down that hits the floor moving at 5m/s,
if the average normal force exerted by the floor
on the ball was 205N for 0.02s.
26
A mass m is moving east with speed v on a smooth
horizontal surface explodes into two pieces.
After the explosion, one piece of mass 3m/4
continues in the same direction with speed 4v/3.
Find the magnitude and direction for the velocity
of the other piece.

• A) v/3 to the left
• B) The piece is at rest.
• C) v/4 to the left
• D) 3v/4 to the left
• E) v/4 to the right

27
How good are bumpers?

• A car of mass 1500kg is crash-tested into a wall.
  It hits the wall with a velocity of -15m/s and
  bounces off with a velocity of 2.6m/s. If the
  collision lasts for 0.15s, what is the average
  force exerted on the car?

28
Types of Collisions
Energy is always conserved but may change types
(mv2/2, mgh, kx2/2 etc). There is only one type
of momentum (mv). We identify collisions based
upon their conservation of kinetic energy.
29
Inelastic Collisions
These collisions are considered PERFECT when the
objects collide and combine to move as one
object.
30
Perfectly Inelastic Collisions
31
Elastic Collisions (ideally)
32
For elastic collisions, find an expression for
relative speed of the objects before and after
collision.
From momentum conservation
33
For elastic collisions, find an expression for
final speed in terms of initial speeds and mass.
From kinetic energy conservation
Divide out ½ and move like mass terms to the same
side so mass can be factored out
Factor difference of squares
34
Combine our two results
The relative speed of the two objects before an
elastic collision equals the negative of their
relative speed after.
35
Solve for final speeds in terms of initial speeds
and mass.
36
Two-dimensional Collisions

• Set coordinate system up with x-direction the
  same as one of the initial velocities
• Label vectors in a sketch
• Write expressions for components of momentum
  before and after collision for each object

v1f
v1fsin?
v1fcos?
v1i
?
f
v2fcosf
-v2fsinf
v2f
37
The types of collisions are treated the same
mathematically.
38
(No Transcript)
39
(No Transcript)
40
(No Transcript)