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MOMENTUM? CHAPTER 7
You might have heard people gaining momentum.
What is it and how do you get it???
Sure Thing
I’d like some
please
Momentum
Store
MOMENTUM?
You might have heard people gaining momentum.
What is it and how do you get it???
Here you go
Momentum
Store
Momentum is basically how hard it is to
stop something.
What would make a moving object hard to stop?
MORE MASS (INERTIA)
MORE SPEED
An object with a lot of mass moving
quickly has a lot of momentum
When playing red rover, why do you run instead of walk
when trying to break the chain
MOMENTUM
The faster you are moving the more momentum you have!!!!
Which person would you rather have on your team?
A
B
The more mass ( for a given speed) the more momentum!!
If they are all running the same speed who
has the most momentum?
Momentum = mass x velocity
p=mv
velocity of object
(m/s)
momentum of object
Kg m
s
mass of object
(Kg)
Which are vectors
both velocity and momentum are vectors
What would happen to the momentum of a cannonball if:
speed doubled
& mass is constant
a.) NO CHANGE
b.) x2
c.) 1/2
d.) x4
e.) 1/4
What would happen to the momentum of a cannonball if:
speed is constant
mass is cut in half
a.) NO CHANGE
b.) x2
c.) 1/2
d.) x4
e.) 1/4
What would happen to the momentum of a cannonball if:
speed is doubled
mass is doubled
a.) NO CHANGE
b.) x2
c.) 1/2
d.) x4
e.) 1/4
Can a bus and a bug have the same
momentum?
Momentum = mass x velocity
=mv
If the boulder and the boy
have the same momentum,
will the boulder crush the
boy?
Hint: Which would have the
larger speed?
What is the momentum of an 10 kg object
moving at 20 m/s?
How fast is a 40 kg object moving if it has
the same momentum?
p=mv
What is the momentum of a
1200 kg elephant at rest?
What does this vector thingee have to do with it?
What would direction mean????
r=mv
THE DIRECTION of momentum is just the
Direction of velocity!!!!
If a car (mass constant) had momentum vectors
changing as follows what does it mean?
Positive
Negative
What about signs?
If a car (mass constant) had momentum vectors
changing as follows what does it mean?
If a car (speed constant) had its momentum vector change
as below what does it mean?
What is the velocity of 750 kg rhinoceros, if its momentum
is -2800 kg m/s?
How do you change the momentum of an object?
(like a car at constant mass)
p=mv
Change the velocity --- Accelerate!
How do you accelerate an object?
Apply a Force!!
When you step on the gas and apply a force
to speed up your car, 2 things determine
how much your momentum (speed) changes
1.)
How far you push the pedal - Magnitude of force
2.)
How long you push the pedal - Duration of force (time)
A force applied for a time is called an:
IMPULSE
Impulse = F Dt
Time force is applied
Magnitude and direction of force
An impulse changes the momentum of an object.
More specifically Impulse = Change in Momentum
An object is accelerated from rest by an impulse.
How would the change in momentum of the object
compare if:
The Force was applied for half the time?
The Force is twice as strong over the same time
IMPULSE = CHANGE IN MOMENTUM
The equation relating Impulse and the change in
momentum it causes can be derived very easily:
First a force must be accelerating a mass:
F=ma
What is the definition of acceleration?
Dv
a=
Dt
plugging in for “a”
F = m Dv
Dt
Impulse
Cross multiplying
yields form 1 of the
equation
= change in momentum
FDt = mDv
Applied force
time force is applied &
time object accelerates
FDt = mDv
F Dt
Dv = v2 - v1
= m(v2 - v1)
F Dt = mv2 - mv1
F Dt = p 2 - p 1
F Dt = D p Form 2 of the equation
F Dt = D p
IMPULSE = change in momentum!!!!
All forces are applied over a time period
(An Impulse)
Even things that appear to be just
for an instant
Impact of a
racquetball with a
wall.
a balloon decelerating due
to an impulse
When trying to change the momentum
a ball two factors count:
1.) Magnitude of Force -
how hard you swing
2.) Duration of Force -
Follow through
F Dt
= Dp
IMPULSE = change in momentum
A speeding car (say 60 mph) can come to a stop two ways
Both will have the same Dr and the same impulse
Crashing into a wall
Gradually applying brakes
Dp =
F
Dp =
F
Dt
Dt
BOTH HAVE THE SAME CHANGE IN MOMENTUM
You can stop an object QUICKLY requires a LARGE
FORCE
F
Dt
Or you can stop an object gradually with a small force
F
Dt
BOTH HAVE THE SAME CHANGE IN MOMENTUM
Why is a falling glass more likely to break when it hits
concrete than carpet?
Objects that cushion,
spread the force out over
a longer time
What is the safest way to land from jumping off a roof?
What involves the greatest change in momentum
What involves the greatest IMPULSE?
What involves the greatest FORCE?
Slowing from 60 m/s to rest Quickly or Slowly
The puncher wants to deliver a large force over a
short time (reducing the momentum of his fist)
The puncher could
have gently pushed his
opponent for a minute
and changed his
momentum just as
much
Rolling with the punches
IfThe
time
of contact
with
the punch
is doubled,
puncher
wants
to deliver
a large
force,
what
the forcereduce
of thethe
punch?
How happens
could thetopunchee
force?
Other times you want a large force over a short period
Other examples:
Air bags
Bungee Jumping
Crumple Zones in Cars
Egg and bed sheet demo
What is the momentum of El Nino (6.0 kg) rolling along
at 2 m/s.
What is the change in momentum if El Nino comes to a stop?
What IMPULSE would be required to do this?
What force would be required to stop El Nino in 10 seconds?
A 25 N force accelerates a 1200 kg car
from rest to 20 m/s?
What is the change in momentum
Impulse?
How long did it take?
Which has the greater change in momentum
A ball that hits and stops?
or one that bounces back??
Let’s look at the ball that hits and stops,
Lets say it has a mass of 1 kg and is initially
traveling at 1 m/s (to the right)
After it stops what was the change in
momentum?
Now let’s look at the ball that bounces.
Again 1 kg and initially moving at 1 m/s (right) and
after it bounces it is moving 1 m/s (left)
Which will require a greater impulse ball
A ball which hits and stops
or
A ball that hits and bounces off
An object which bounces backwards at the same speed
requires twice the IMPULSE.
to bring it to a stop
accelerate it backwards
Which will hurt more a flower pot which hits your head
and breaks, or one which hits your head and bounces
off?
Force
ouch
Force
continued
Increasing Impulse
Curved blades
prolong contact
with water:
Impulse = F Dt
Greater impulse
means greater
change in
momentum of
the wheel.
(if needed)
A 2 kg ball moving to the right at 4 m/s hits a wall and
bounces to the left at 4 m/s. What is the change in
momentum.
Impulse momentum problems
Read Sections 7-1 to 7-4 in book
Answer Questions on pages 100 - 102
2, 4, 5, 7, 8, 9, 12, 19,
14, 15, 21, 24, 27, 35
CONSERVATION OF MOMENTUM.
Could you, like, save
some momentum for
the rest of us.
Which object changes momentum after firing?
Which
Which
feelsthe
force
greater
formomentum
force?
the
Whatfeels
does
itthe
mean
that
longest
time?
is conserved?
cannon
cannon ball
ball same
same
Think Newton’s 3rd law!!!
After the cannon fires both the
cannon and the ball experience the
same IMPULSE (Force x Time)
So they both experience the same
change in:_________
velocity speed momentum
After firing?
THEY BOTH HAVE THE
SAME MOMENTUM
Which has more momentum
Cannon
p=
m
V
ball
p=m
V
They both have the same amount of
momentum but something is
different….
THE DIRECTION
(consider signs)
- 5 kg m/s
Cannon
p=
m
V
+5 kgm/s
ball
p=m
V
What do you get if you add up the
momentum of the ball and cannon?
- 5 kg m/s
Cannon
+5 kgm/s
ball
What was the initial momentum of
the ball and cannon?
ZERO
The total momentum is the
same
AFTER Firing
BEFORE Firing
SUM = ZERO
0
-5
0
+5
SUM = ZERO
Conservation of momentum:
Without an EXTERNAL force the
momentum a system doesn’t change.
initial momentum = final momentum
A system:
Objects of interest
We looked at a cannon / ball “system”
No external forces
An external force would be from something other than
the ball or cannon
Here the cannon and ball had no initial momentum,
but the outside force gave them both positive momentum
No external forces
Would friction be considered an outside force?
Which will change the momentum of a car
Pushing a car from the inside
Pushing a car from the outside
both
ONLY pushing the car from the
outside changes the momentum
because it is an external force
Which will change the momentum of a car
Pushing a car from the inside
Pushing a car from the outside
both
Pushing from inside will not
change the momentum of the car
/person system
Initial momentum = Final Momentum
p1 = p2
Does this mean that the momentum of parts
of a system don’t change?
NO… When you add them up (taking into account +
and -) initial momentum = final momentum
Jack(80 kg) and Jill (40 kg) are at rest initially,
After pushing off Jack is moving at +10 m/s,
what is Jill’s velocity?
Initial Momentum = Final Momentum
pjack1 + pjill1 = pjack2 + pjill2
Car & Track Momentum Demos
Equal masses stationary
Unequal masses stationary
r=mv
Say the cannon has a mass of 650 kg and the ball has a
mass of 25 kg. After firing the ball flies out at 35 m/s to
the right, what is the velocity of the cannon?
Newton’s cradle applet
Astronaut Catch
What would happen if 2 astronauts played catch?
All of the scenarios we have looked, the
objects started from rest. So the
momentum always had to add up to ZERO.
Like Explosions
Conservation of momentum in collisions
In a collision the initial momentum may not be zero.
WHY?
2 Main Types of Collisions
ELASTIC- objects hit and bounce (no energy is lost)
INELASTIC- objects hit and stick together (energy IS lost)
BUT MOMENTUM IS ALWAYS CONSERVED
Car & Track Momentum Demos
Elastic Collisions
Equal masses 1 moving
Equal masses both moving opposite directions
Equal masses both moving same direction
UNEqual masses 1 moving
Car & Track Momentum Demos
INElastic Collisions
Equal masses 1 moving
UNEqual masses lighter moving
UNEqual masses heavier moving
Inelastic collision applet
A 4.0 kg car moving 15 m/s hits a 8.0 kg car at rest.
What is their velocity after they hit and stick together.
A large 210 kg hobo jumps into to the back of a 670 kg
truck moving at 14 m/s. Assuming the hobo has no initial
momentum, what is final the speed of the truck and hobo?
WS In Class
A 3 kg car traveling to the right at 5 m/s hit and sticks to a
6 kg car moving to the left at 2 m/s. What is the final
velocity of both after the collision?
Deep Space 1 was launched in 1998 and thrusted for
678 days straight. It reached a speed of 4,600 m/s.
Drawing of Deep Space 1
Test fire of ion
propulsion engine
Rocket Applet
Astronaut Catch
Conservation of Momentum Problems (1D)
Book Problems page 101-103
22, 28, 32, 35, 37 (2parts)
Conservation of Momentum Lab
Conservation of Momentum Lab
Recap Applet
http://www.walter-fendt.de/ph11e/collision.htm
Car Crash 2D momentum demo
Initial
It ruptures
After the can of gas ruptures how will it move?
a.) left
b.) right
c.) won’t
Conservation of Momentum in 2 Dimensions
A car and a bus collide and stick together.
What direction does the wreckage slide?
Car
Car
It moves off at an angle
Car
Car
But MOMENTUM is Still conserved
Conservation of Momentum in 2 Dimensions
Draw Vectors for the momentum
rx
Car
Car
rY
Momentum is conserved. So the outcome is just
the two momentums added together
rtotal
rx
Car
Car
rY
Before
After
rx
rtotal
Car
Car
rY
rx
Car
Car
DrX = 0
The X momentum is conserved
DrY = 0
The Y momentum is conserved
rY
Car Crash 2D momentum demo
Problems:
Honors Physics
Page 205 38,39
Physics
page 220
44, 45, 47 b only
Which has the greater change in
momentum a ball that:
Hits and sticks or
bounces backwards at the same speed ?
r = -mv
r=0
Initial Momentum
r = -mv
Final Momentum
r = mv
Dr = 0 –(-mv) Change Momentum Dr = mv –(-mv)
= mv
= 2mv
ELASTIC COLLIONS (things bounce)
& Conservation of momentum
ELASTIC COLLIONS (things bounce)
& Conservation of momentum
ELASTIC COLLIONS (things bounce)
& Conservation of momentum
ELASTIC COLLIONS (things bounce)
& Conservation of momentum