Transcript Momentum and Impulse

Momentum &
Impulse
What is momentum and Impulse?






Consider an empty car rolling down a hill.
It reaches a flat road…The brakes have gone out.
You and a few friends have decided to stop the
car.
You all jump in front of it and push. The car
continues in the same direction…
and you find yourself having to run backward as
you push.
Over time, the car begins to slow, eventually it
comes to a stop.
The momentum in this situation…







The car already has momentum as this scene
begins.
Why? A) it has MASS B) this mass is moving and
has a VELOCITY.
Momentum is a property of a moving mass.
The formula?
p= mv (where p=momentum, m= mass, v=velocity)
Name two ways to increase the momentum of an object.
Increase the mass and/or velocity of the object!
The Impulse in this situation…








An object can only increase or decrease its
momentum if there is an impulse on it.
In this case the car decreases its momentum.
What exactly caused this decrease?
A) a FORCE put on the car
B) the force was not instantaneous- it was applied
over a certain amount of TIME.
An impulse is a force applied over an amount of
time.
The formula?
Impulse= F t (where F=force, and t=time of force)
How they are related







What does it take to get an object moving?
It takes a force over a certain amount of time to get
any mass to move and obtain a velocity.
Likewise, how do you get an object to slow down
or stop?
It takes a force over time.
In other words… It takes an impulse to cause or
change an object’s momentum.
Impulse = Δ momentum (Δ= change in/of)
Ft= Δ mv
Impulse= momentum






A 5.00 kg fat cat is on a skateboard
(Cat+skateboard = 5.00 kg). The cat is moving
3.00 m/s. There is 5.00 N of frictional force in this
situation.
15.0 units (TBA
How much p does the cat have currently?
15.0 units (TBA)
How much impulse will it take to bring it to a stop?
How long will it take for friction to bring this feline
to a stop? 3.00 sec
If the friction were, instead, 15 N how long would it
1.0 sec
take?
If the force is higher
the time will have to be
Why the difference?
Impulse= momentum






If an object is traveling 4 m/s north and it
changes direction and moves at 4 m/s south.
What is its change of velocity?
∆v= 8m/s
If the object has a mass of 2 kg. What would
its change of momentum be?
∆p= 16 kgm/s
If it took 8 seconds to change its velocity, what
average force was acting on the object?
F= 2 N
Try Another…




A .144 kg baseball is pitched horizontally at
38m/s. After it is hit by a bat, it happens to be
moving at -38 m/s (other direction).
A. 11 kgm/s
A. What impulse did the bat deliver to the ball?
B. If the bat and ball were in contact for 8.0 ms
(.0080 s) what was the average force the bat
That’s 1000 x more
1400 N
put on the ball? than a due to gravity!
C. Find the average acceleration of the ball
during its9700
contact
with the bat.
Follow through!
m/s2
Bellwork: Date:
Collisions!






Before we view several animations…
The big idea…
The conservation of momentum!
Basically it states that the momentum is conserved
(stays the same)
For example, the TOTAL momentum BEFORE and
AFTER collisions will be the same…
Let’s get into groups of 4 for discussion groups
Linear collisions
(Collisions that occur in a straight line)
1) Note any velocity changes. How can this
happen yet still show a conservation of
momentum?
Why does the big fish slow down
slightly?
How does the amount of momentum
change after the feeding?
Why is the big fish moving
more slowly than the smaller
fish was?
Who has all the momentum before
the collision?
Which vehicles have momentum after
the collision?
Was momentum conserved
overall? How can you tell?
How are they calculating 60,000 kgm/s for the
momentum of the truck before the collision?
Why can’t the car have momentum
(mathematically speaking) before the collision?
Discuss how momentum is conserved in this
situation.
Look closely at the numbers
here. Does this situation make
physical sense to your group?
Draw and try one for yourself!
Have the 1000 kg car hit the parked 3000
kg truck while moving at 20.0 m/s. How
fast should the truck end up moving if the
car is moving 5 m/s after the collision?
Explain the negative signs on the
truck’s momentum before and the
car’s velocity after.
What is the change of velocity of the car? (careful)
What is the change in momentum of the car?
What is the change of velocity of the truck?
What is the change of momentum of the truck?
Is momentum conserved here? Explain.
View and discuss this one until it makes
sense to everyone in the group.
Find the conservation of momentum.
Which has the greater change of
momentum?
Linear Collisions clips
Clip air glider a..\..\..\Mastek 5\02aEN.VOB
Clip air glider b..\..\..\Master movidisk 5\02bEN.VOB
Clip air glider c ..\..\..\Master movie video CLIPS\\02cEN.VOB
Let’s try a few…
Linear collision
(one object at rest)
Think in terms of TOTAL momentum for this type of problem
Which side can you determine the TOTAL momentum?
How fast will the green ball be moving afterward?
V
?
4 green
m/s!
4 Kg
2 m/s
2 Kg
0 m/s
0 kgm/s
8P=8
kgm/s
kgm/s TOTAL
4 Kg
2 Kg
0 m/s
?m/s
8P=?
kgm/s
0 kgm/s
P=8.0 kgm/s TOTAL
Conservation of momentum!
Linear collision
(both moving)
Think in terms of TOTAL momentum for this type of problem
Which side can you determine the TOTAL momentum?
How fast will the green ball be moving afterward?
V
?
5 green
m/s!
2 Kg
4 m/s
2 Kg
2 Kg
2 m/s
2 Kg
1 m/s
4 kgm/s
8P=12.0
kgm/s
2 kgm/s
kgm/s TOTAL
?m/s
10
kgm/s
P=?
P=12.0 kgm/s TOTAL
Conservation of momentum!
Linear collision
(one or more changing direction)
Think in terms of TOTAL momentum for this type of problem
Which side can you determine the TOTAL momentum?
How fast will the green ball be moving afterward?
7V
m/s!
green?
6 Kg
2 Kg
4 m/s
6 Kg
2 m/s
2 Kg
1 m/s
24 kgm/s -4 kgm/s (opp dir) 6 kgm/s
P=20.0 kgm/s TOTAL
?m/s
14
kgm/s
P=?
P=20.0 kgm/s TOTAL
Conservation of momentum!
It is equally important that you can understand it/do it this way
How fast will the green ball be moving afterward?
Note that it’s 18 because it changed from
-4 to 14 in the other direction…that’s a change of 18!
6 Kg
4 m/s
2 Kg
2 m/s
6 Kg
1 m/s
24 kgm/s -4 kgm/s (opp dir) 6 kgm/s
7
m/s!
Vgreen
?
2 Kg
?m/s
14 kgm/s
So how much p will it
How much has the red ball’s p changed by?= ?Δp 18 kgm/s have afterward?
How much must the green’s p change by?= ?Δp 18 kgm/s
Elastic vs. Inelastic Collisions
A perfectly elastic collision is defined as one in which
there is no loss of kinetic energy in the collision.
An inelastic collision is one in which part of the
kinetic energy is changed to some other form of
energy in the collision.
Clip elastic vs inelastic collisions a..\..\.isk 5\03aEN.VOB
clipelastic vs inelastic collisions b..\..mos\disk 5\03bEN.VOB
Clip elastic vs inelastic bouncing..\..\..\Masymos\disk 5\04EN.VOB
Lets revisit this one…
This is an inelastic collision.
Note the vehicles were deformed in the collision.
This means some of the kinetic energy was lost (becoming
heat energy).
The momentum was conserved but the kinetic energy (we
will cal. Next chapter) was not.
Non-linear collisions HONORS

(Collisions at angles)
Problem 1



A green 3.00 kg ball moving 12.0 m/s hits a nonmoving red 2.00 kg ball. After they hit, the red ball
is moving to the right at a 52.00 angle from the
green ball’s original direction. The green ball is
now moving at a 38.00 angle to the left of its
original direction.
What is the red ball’s momentum?
What is the green ball’s velocity?
Green ball’s velocity
Cosθ= adj/hyp
Cos 38.00= adj/36.0 kgm/s
Cal= 28.36838713
R= 28.4 kgm/s
p=mv
V=p/m
?
V= 28.4kgm/s/3.00kg
36.0 kgm/s
38.00 36.0 kgm/s!
Cal= 9.466666667
52.00 hyp
R= 9.47 m/s
3.00 kg
2.00 kg adj
Momentum is conserved in
?
12.0 m/s
magnitude AND DIRECTION
adj
Red ball’s momentum?
Cos 52.00= adj/36.0 kgm/s
Cal= 22.16381311
R= 22.2 kgm/s
“T-bone collision” (cp and honors)
Two objects collide, one is a 4.00 kg moving west
at 2.00 m/s. The other is a 5.00 kg object moving
at 3.00 m/s south. They stick together. What is
the resultant magnitude and direction of the
velocity?
head to _______!
tail
Add them ______
Warning: do not start this problem by adding
velocities tip to tail! Use momentums!
If a mac truck and a small car hit, their velocities AND
their masses affect what happens!
Using Momentum accounts for the objects’ velocity
and mass!
1800
(8.00 Kgm/s)
0O
(15.0 kgm/s)
270O
a basic 2 vector problem
magnitude
A2 + B2 = C2
C = A2 + B2
C = (8.00kgm/s)2 + (15.0 kgm/s)2
VELOCITY
p=mv V=p/m
V= 17.0 kgm/s/9.00 kg (2 masses added)
Cal= 17
R= 17.0 kgm/s
Cal=1.8888888
R= 1.89 m/s
As usual, choose the angle at
the base of the resultant to be
θ.
8.00 Kgm/s
1800
θ
direction
15.0 kgm/s
Function?
•Tan θ = opp/adj
•Tan θ = 15.0 kgm/s/8.00 kgm/s
270O
Cal= 61.92751306
R= 61.90
1800
0O
+61.90=
241.90
0
90

Collisions
A 1000.0 kg red on traveling north at 10.0
m/s, runs into a 1000.0 kg blue car traveling
20.0 m/s East. If they stick together, what
velocity will they have after the collisioninclude a magnitude and direction!
Momentum Clips
Newtons cradles to the extreme..\..\..\Master
Clip can you bounce higher than a drop height? ..\..\.er 5\05EN.VOB
Clip air puck collisions..\..\..\Masterdeo CLs\d
Clip air puck collisions with different masses..\..\.D\disk 5\07EN.VOB
Momentum Clips continued
Clips inelastic puck collisions 5\08EN.VOB
Clip egg a break post lab only ..\..\..\
Clip egg break b 5\09bEN.VOB
Try

0
another…(90
Collisions)
A 14.0 kg dog on ice skates traveling north at
12.0 m/s, runs into a 22.0 kg sloth on skates
traveling 4.00 m/s west. If they stick together,
what velocity will they have after the collisioninclude a direction!
Car collision Live!




















Trenton Shook
Physics Car Crashing Momentum Project
Problem 1: A red Corvette car runs a red light in the middle of a busy
intersection traveling due South at 24.5 m/s when
it is hit by a yellow Jeep. The SUV
is traveling due West at 12 m/s. The red car weighs
approximately 3,250 lbs. (1474 kg.) and the yellow
SUV weighs approximately 4,800 lbs. (2178 kg.).
What is the direction and velocity of the cars after
the collision if the cars stay together? It is an inelastic
accident.
Problem 2:
A white Dodge Viper is rubbernecking the turn at
4.25 m/s when it is hit from behind by an orange
sports utility vehicle traveling at 9.55 m/s. After the
impact the white car goes to the right at a 55.0 degree
angle from the origin of the incident and the orange
SUV goes the opposite direction at 35.0 degrees. The
white car weighs approximately 3,420 lbs. (1552 kg.),
while the Orange SUV weighs 4,250 lbs. (1928 kg.).
What is the momentum of both cars?