Title: The Immaculate Reception
1The Immaculate Reception
2MOMENTUM
3What 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?
4What is Momentum?
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
5What is Momentum?
If object is moving in arbitrary direction
6What do we know about momentum?
7What 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.
8How 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.
9Pause 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!
10Pause 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
11Pause 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
12Impulse-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!
13A 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.
14Another question please
15To stop a speeding train Explain these videos
in physics terms.
16Quick 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.
19Examples
- 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???
20Observing changes in momentum
21Consider 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
22The particles must undergo the same changes in
momentum!
Lets look at this mathematically.
23What 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!
24The 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).
25Find 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.
26A 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
27How 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?
28Types 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.
29Inelastic Collisions
These collisions are considered PERFECT when the
objects collide and combine to move as one
object.
30Perfectly Inelastic Collisions
31Elastic Collisions (ideally)
32For elastic collisions, find an expression for
relative speed of the objects before and after
collision.
From momentum conservation
33For 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
34Combine our two results
The relative speed of the two objects before an
elastic collision equals the negative of their
relative speed after.
35Solve for final speeds in terms of initial speeds
and mass.
36Two-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
37The types of collisions are treated the same
mathematically.
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