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Momentum & Impulse
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The Law of Momentum Conservation
Momentum Conservation Principle
One of the most powerful laws in physics is the law of momentum conservation. The
law of momentum conservation can be stated as follows.
For a collision occurring between object 1 and object 2 in an isolated system, the
total momentum of the two objects before the collision is equal to the total
momentum of the two objects after the collision. That is, the momentum lost by
object 1 is equal to the momentum gained by object 2.
The above statement tells us that the total momentum of a collection of objects (a
system) is conserved" - that is the total amount of momentum is a constant or
unchanging value. This law of momentum conservation will be the focus of the
remainder of this lesson. To understand the basis of momentum conservation, let's
begin with a short logical proof.
Consider a collision between two objects - object 1 and object 2. For such a collision,
the forces acting between the two objects are equal in magnitude and opposite in
direction (Newton's third law). This statement can be expressed in equation form as
follows.
The forces act between the two objects for a given amount of time. In some cases,
the time is long; in other cases the time is short. Regardless of how long the time is,
it can be said that the time that the force acts upon object 1 is equal to the time that
the force acts upon object 2. This is merely logical; forces result from interactions (or
touching) between two objects. If object 1 touches object 2 for 0.050 seconds, then
object 2 must be touching object 1 for the same amount of time (0.050 seconds). As
an equation, this can be stated as
Since the forces between the two objects are equal in magnitude and opposite in
direction, and since the times for which these forces act are equal in magnitude, it
follows that the impulses experienced by the two objects are also equal in magnitude
and opposite in direction. As an equation, this can be stated as
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But the impulse experienced by an object is equal to the change in momentum of
that object (the impusle-momentum change theorem). Thus, since each object
experiences equal and opposite impulses, it follows logically that they must also
experience equal and opposite momentum changes. As an equation, this can be
stated as
The above equation is one statement of the law of
momentum conservation. In a collision, the momentum
change of object 1 is equal and opposite to the momentum change of object 2. That
is, the momentum lost by object 1 is equal to the momentum gained by object 2. In
a collision between two objects, one object slows down and loses momentum while
the other object speeds up and gains momentum. If object 1 loses 75 units of
momentum, then object 2 gains 75 units of momentum. Yet, the total momentum of
the two objects (object 1 plus object 2) is the same before the collision as it is after
the collision; the total momentum of the system (the collection of two objects) is
conserved.
A useful analogy for understanding momentum conservation involves a money
transaction between two people. Let's refer to the two people as Jack and Jill.
Suppose that we were to check the pockets of Jack and Jill before and after the
money transaction in order to determine the amount of money which each
possessed. Prior to the transaction, Jack possesses $100 and Jill possesses $100.
The total amount of money of the two people before the transaction is $200. During
the transaction, Jack pays Jill $50 for the given item being bought. There is a
transfer of $50 from Jack's pocket to Jill's pocket. Jack has lost $50 and Jill has
gained $50. The money lost by Jack is equal to the money gained by Jill. After the
transaction, Jack now has $50 in his pocket and Jill has $150 in her pocket. Yet, the
total amount of money of the two people after the transaction is $200. The total
amount of money (Jack's money plus Jill's money) before the transaction is equal to
the total amount of money after the transaction. It could be said that the total
amount of money of the system (the collection of two people) is conserved; it is the
same before as it is after the transaction.
A useful means of depicting the transfer and the conservation of money between
Jack and Jill is by means of a table.
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The table shows the amount of money possessed by the two individuals before and
after the interaction. It also shows the total amount of money before and after the
interaction. Note that the total amount of money ($200) is the same before and after
the interaction - it is conserved. Finally, the table shows the change in the amount of
money possessed by the two individuals. Note that the change in Jack's money
account (-$50) is equal and opposite to the change in Jill's money account (+$50) .
For any collision occurring in an isolated system, momentum is conserved - the total
amount of momentum of the collection of objects in the system is the same before
the collision as after the collision. This is the very phenomenon which was observed
in "The Cart and The Brick" lab. In this lab, a brick at rest was dropped upon a
loaded cart which was in motion.
Before the collision, the dropped brick had 0 units of momentum (it was at rest). The
momentum of the loaded cart can be determined using the velocity (as determined
by the ticker tape analysis) and the mass. The total amount of momentum was the
sum of the dropped brick's momentum (0 units) and the loaded cart's momentum.
After the collision, the momenta of the two separate objects (dropped brick and
loaded cart) can be determined from their measured mass and their velocity (found
from the ticker tape analysis). If momentum is conserved during the collision, then
the sum of the dropped brick's and loaded cart's momentum after the collision
should be the same as before the collision. The momentum lost by the loaded cart
should equal (or approximately equal) the momentum gained by the dropped brick.
Momentum data for the interaction between the dropped brick and the loaded cart
could be depicted in a table similar to the money table above.
Before
Collision
Momentum
After
Collision
Momentum
Change in
Momentum
Dropped Brick
0 units
14 units
+14 units
Loaded Cart
45 units
31 units
-14 units
Total
45 units
45 units
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Note that the loaded cart lost 14 units of momentum and the dropped brick gained
14 units of momentum. Note also that the total momentum of the system (45 units)
was the same before the collision as it is after the collision.
Collisions commonly occur in contact sports (such as football) and racket and bat
sports (such as baseball, golf, tennis, etc.). Consider a collision in football between a
fullback and a linebacker during a goal-line stand. The fullback plunges across the
goal line and collides in midair with linebacker. The linebacker and fullback hold each
other and travel together after the collision. The fullback possesses a momentum of
100 kg*m/s, East before the collision and the linebacker possesses a momentum of
120 kg*m/s, West before the collision. The total momentum of the system before
the collision is 20 kg*m/s, West (review the section on adding vectors if necessary).
Therefore, the total momentum of the system after the collision must also be 20
kg*m/s, West. The fullback and the linebacker move together as a single unit after
the collision with a combined momentum of 20 kg*m/s. Momentum is conserved in
the collision. A vector diagram can be used to represent this principle of momentum
conservation; such a diagram uses an arrow to represent the magnitude and
direction of the momentum vector for the individual objects before the collision and
the combined momentum after the collision.
Now suppose that a medicine ball is thrown to a clown who is at rest upon the ice;
the clown catches the medicine ball and glides together with the ball across the ice.
The momentum of the medicine ball is 80 kg*m/s before the collision. The
momentum of the clown is 0 m/s before the collision. The total momentum of the
system before the collision is 80 kg*m/s. Therefore, the total momentum of the
system after the collision must also be 80 kg*m/s. The clown and the medicine ball
move together as a single unit after the collision with a combined momentum of 80
kg*m/s. Momentum is conserved in the collision.
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Momentum is conserved for any interaction between two objects occurring in an
isolated system. This conservation of momentum can be observed by a total system
momentum analysis and by a momentum change analysis. Useful means of
representing such analyses include a momentum table and a vector diagram. Later in
this lesson, we will use the momentum conservation principle to solve problems in
which the after-collision velocity of objects is predicted
Check Your Understanding (to be completed on a separate sheet of paper)
Express your understanding of the concept and mathematics of momentum by
answering the following questions.
1. Explain why it is difficult for a firefighter to hold a hose which ejects large
amounts of high-speed water.
2. A large truck and a Volkswagen have a head-on collision.
a. Which vehicle experiences the greatest force of impact?
b. Which vehicle experiences the greatest impulse?
c. Which vehicle experiences the greatest momentum change?
d. Which vehicle experiences the greatest acceleration?
3. Miles Tugo and Ben Travlun are riding in a bus at highway speed on a nice
summer day when an unlucky bug splatters onto the windshield. Miles and Ben begin
discussing the physics of the situation. Miles suggests that the momentum change of
the bug is much greater than that of the bus. After all, argues Miles, there was no
noticeable change in the speed of the bus compared to the obvious change in the
speed of the bug. Ben disagrees entirely, arguing that that both bug and bus
encounter the same force, momentum change, and impulse. Who do you agree with?
Support your answer.
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4. If a ball is projected upward from the ground with ten units of momentum, what is
the momentum of recoil of the Earth? ____________ Do we feel this? Explain.
5. If a 5-kg bowling ball is projected upward with a velocity of 2.0 m/s, then what is
the recoil velocity of the Earth (mass = 6.0 x 10^24 kg).
6. A 120 kg lineman moving west at 2 m/s tackles an 80 kg football fullback moving
east at 8 m/s. After the collision, both players move east at 2 m/s. Draw a vector
diagram in which the before- and after-collision momenta of each player is
represented by a momentum vector. Label the magnitude of each momentum
vector.
Before
After
7. Would you care to fire a rifle that has a bullet ten times as massive as the rifle?
Explain.
8. A baseball player holds a bat loosely and bunts a ball. Express your understanding
of momentum conservation by filling in the tables below.
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9. A Tomahawk cruise missile is launched from the barrel of a mobile missile
launcher. Neglect friction. Express your understanding of momentum conservation by
filling in the tables below.
Isolated System Notes
Total system momentum is conserved for collisions occurring
in isolated systems. But what makes a system of objects an
isolated system? And is momentum conserved if the system is
not isolated? This is the focus of this part of Lesson 2.
A system is a collection of two or more objects. An isolated
system is a system which is free from the influence of a net
external force. There are two criteria for the presence of a net
external force; it must be...
a force which originates from a source other than the two
objects of the system
a force that is not balanced by other forces.
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Check Your Understanding I
Concepts of Physics - Mr. Lawrence
Express your understanding of the concept and mathematics of momentum by answering
the following questions.
1. Determine the momentum of a ...
a. 60-kg halfback moving eastward at 9 m/s.
b. 1000-kg car moving northward at 20 m/s.
c. 40-kg freshman moving southward at 2 m/s.
2. A car possesses 20 000 units of momentum. What would be the car's new momentum
if ...
a.
its velocity were doubled.
b. its velocity were tripled.
c. its mass were doubled (by adding more passengers and a greater load)
d. both its velocity were doubled and its mass were doubled.
3. A halfback (m = 60 kg), a tight end (m = 90 kg), and a lineman (m = 120 kg) are
running down the football field. Consider their ticker tape patterns below.
Compare the velocities of these three players. How many times greater is the velocity of
the halfback and the velocity of the tight end than the velocity of the lineman?
Which player has the greatest momentum? Explain.
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Vector Diagram
Greatest velocity change?
Greatest acceleration?
Greatest momentum change?
Greatest Impulse?
________________________________________________________________________
Velocity-Time Graph
Greatest velocity change?
Greatest acceleration?
Greatest momentum change?
Greatest Impulse?
________________________________________________________________________
Ticker Tape Diagram
Greatest velocity change?
Greatest acceleration?
Greatest momentum change?
Greatest Impulse?
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Check Your Understanding Part II
Concepts of Physics - Mr. Lawrence
Express your understanding of the impulse-momentum change theorem by answering the
following questions.
1. A 0.50-kg cart (#1) is pulled with a 1.0-N force for 1 second; another 0.50 kg cart (#2)
is pulled with a 2.0 N-force for 0.50 seconds. Which cart (#1 or #2) has the greatest
acceleration? Explain.
Which cart (#1 or #2) has the greatest impulse? Explain.
Which cart (#1 or #2) has the greatest change in momentum? Explain.
2. In a phun physics demo, two identical balloons (A and B) are propelled across the
room on horizontal guide wires. The motion diagrams (depicting the relative position of
the balloons at time intervals of 0.05 seconds) for these two balloons are shown below.
Which balloon (A or B) has the greatest acceleration? Explain.
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Which balloon (A or B) has the greatest final velocity? Explain.
Which balloon (A or B) has the greatest momentum change? Explain.
Which balloon (A or B) experiences the greatest impulse? Explain.
3. Two cars of equal mass are traveling down Lake Avenue with equal velocities. They
both come to a stop over different lengths of time. The ticker tape patterns for each car
are shown on the diagram below.
At what approximate location on the diagram (in terms of dots) does each car begin to
experience the impulse.
Which car (A or B) experiences the greatest acceleration? Explain.
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Which car (A or B) experiences the greatest change in momentum? Explain.
Which car (A or B) experiences the greatest impulse? Explain.
4. The diagram to the right depicts the before- and after-collision speeds of a car which
undergoes a head-on-collision with a wall. In Case A, the car bounces off the wall. In
Case B, the car "sticks" to the wall.
In which case (A or B) is the change in velocity the greatest? Explain.
In which case (A or B) is the change in momentum the greatest? Explain.
In which case (A or B) is the impulse the greatest? Explain.
In which case (A or B) is the force which acts upon the car the greatest (assume contact
times are the same in both cases)? Explain.
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5. Rhonda, who has a mass of 60.0 kg, is riding at 25.0 m/s in her sports car when she
must suddenly slam on the brakes to avoid hitting a dog crossing the road. She strikes the
air bag, which brings her body to a stop in 0.400 s. What average force does the seat belt
exert on her?
If Rhonda had not been wearing her seat belt and not had an air bag, then the windshield
would have stopped her head in 0.001 s. What average force would the windshield have
exerted on her?
6. A hockey player applies an average force of 80.0 N to a 0.25 kg hockey puck for a
time of 0.10 seconds. Determine the impulse experienced by the hockey puck.
7. If a 5-kg object experiences a 10-N force for a duration of 0.1-second, then what is the
momentum change of the object?
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Check Your Understanding Part III
Concepts of Physics - Mr. Lawrence
Express your understanding of Newton's third law by answering the following questions.
1. While driving down the road, an unfortunate bug strikes the windshield of a bus. Quite
obviously, a case of Newton's third law of motion. The bug hit the bus and the bus hit the
bug. Which of the two forces is greater: the force on the bug or the force on the bus?
2. Rockets are unable to accelerate in space because ...
a. there is no air in space for the rockets to push off of.
b. there is no gravity is in space.
c. there is no air resistance in space.
d. ... nonsense! Rockets do accelerate in space.
3. A gun recoils when it is fired. The recoil is the result of action-reaction force pairs. As
the gases from the gunpowder explosion expand, the gun pushes
the bullet forwards and the bullet pushes the gun backwards. The
acceleration of the recoiling gun is ...
a. greater than the acceleration of the bullet.
b. smaller than the acceleration of the bullet.
c. the same size as the acceleration of the bullet.
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4. Would it be a good idea to jump from a rowboat to a dock that seems within jumping
distance? Explain.
5. If we throw a ball horizontally while standing on roller skates, we roll backward with a
momentum that matches that of the ball. Will we roll backward if we go through the
motion of throwing the ball without letting go of it? Explain.
6. Suppose there are three astronauts outside a spaceship and two of them decide to play
catch with the other woman. All three astronauts weigh the same on Earth and are equally
strong. The first astronaut throws the second astronaut towards the third astronaut and the
game begins. Describe the motion of these women as the game proceeds. Assume each
toss results from the same-sized "push." How long will the game last?
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Egg Drop Lab
Theory and Inquiry
I.
Explain the theory behind the egg drop lab
impulse = Ft = mv = 
 Explain where the equation above came from and how it helps
in constructing the egg drop apparatus.
II.
Choose an equation from your equation sheet that will allow you to
solve for the final velocity of your egg. Calculate the final velocity
of your egg.
 You have to measure a variable in order to solve for the final
velocity. What is the variable?
Scoring:
1. Complete all questions in lab notebook
2. Egg drop apparatus is constructed
3. Egg survives drop from 1st flight of bleachers
4. Egg survives drop from top of bleachers
Total:




10 pts
5 pts
5 pts
+5 pts
20 pts
must be able to easily place and remove egg in apparatus
may only use cardboard, drinking straws, paper, and non-padded tape
may not use any parachute apparatus
apparatus may not exceed and 8 inch cube or sphere in size

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Hewitt Post-Video
1. Why does a boxer move his/her head away from the blow? Explain.
2. Cart 1 approaches cart 2 with a momentum of 10 units. If cart 2 is initially at rest
what is the momentum before the collision?
a.
If the carts stick together, what is their momentum after the collision?
b. Compared to cart 1’s velocity before the collision, what must their
velocity be after the collision? (assume the carts are of equal mass)
c. Draw the before and after situation below.
before:
after:
d. What law of physics does this support?
e. Write the equation for this law.
Bonus:
_________ provides
more impulse than
hitting.
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Momentum Video quiz (ESPN)
Name_______________
Date_1/08_
Period____
1. What is “sick” about momentum? ___________________________
2. What common force effects momentum? ________________
3. What happens to the momentum of objects that stick together?
_______________________________________________
4. What happens to the velocity of objects that stick together?
_______________________________________________
5. If two objects have the same mass with velocities in opposite directions, what
happens when they collide? _______________________
6. Based on physical evidence, did the driver stop at the stop sign? ____
Impulse Video Quiz w/ Napolean Kauffman (ESPN)
Name:_______________
Date:__1/08__
1. Napolean Kauffman does what when he gets hit by other football
players? ______________________________
2. ______________ is what makes force an impulse.
3. One watermelon broke. One did not.
Why?________________________________________________
____________________________________________________
____________________________________________________
4. In sports, whether throwing, kicking, or hitting the ball, you are told
to “follow through”. Why is your “follow through” so important?
____________________________________________________
____________________________________________________
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Physics Lab
Conservation of Momentum
Names:
Period: __________
Conservation of Momentum
Relevant Theory
From class, you know that momentum is mass in motion. It is calculated by using the formula
,
p = mv
and it is a vector quantity.
A collision occurs when two objects paths cross. During a collision, momentum is transferred, as
is energy. You remember that there are two kinds of collisions, elastic and inelastic. In elastic
collisions, no kinetic energy is converted into other energy forms. Conversely, inelastic collisions
see kinetic energy being converted into heat, sound, or work (generally damage) done to the
colliding objects.
Most collisions can not be classified as simply elastic or inelastic. Rather, elastic and inelastic are
ends of a continuum, and most collisions fit somewhere in between, as shown below. The point
is, how much of its initial kinetic energy can one object retain after the collision. It is appropriate
to think of a collision’s elasticity, or what percentage elastic a collision is.
under-inflated
basketball
bouncing
billiard balls
colliding
100%
90%
Blob of mud
hitting the
ground
30%
ELASTIC
proton colliding with
another proton
0%
INELASTIC
inflated
basketball
bouncing
In this lab, we will collide two collision carts together to determine if momentum is conserved in
all types of collisions. To do this, we will obviously need to measure the velocity and mass of
each cart both before and after the collision.
Procedure
1. Set up apparatus as shown in figure A.
flag
cart 1
flag
cart 2
track
Figure A
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2. Determine the momentum before and after an inelastic collision. Be sure that the carts
have velcro ends pointing toward each other. This will make the carts stick together and
give us our inelastic collision (0% elastic). Send cart 1 towards a stationary
cart 2, at a medium speed. Set up a photogate to measure the velocity of cart 1 before the
collision, and another photogate to measure the velocity of the two carts together after the
collision.
M

M
?
Before
After
Flag Width
Before Inelastic Collision
Gate Time
Velocity
Mass
Momentum
Cart 1
0
Cart 2
Flag Width
After Inelastic Collision
Gate Time
Velocity
Mass
Momentum
Carts
1&2
3. Repeat the above procedure, but this time, instead of a stationary cart 2, we will also send
it in with a medium velocity, as shown below. Try to match the velocities of the two
carts as closely as possible.
4.

This time make cart 1 twice as massive as cart 2. You can easily do this by taking
the bar mass out of cart 2. Repeat steps 2 and 3.
?
M
m
Before
After
Flag Width
Before Inelastic Collision
Gate Time
Velocity
Mass
Momentum
Cart 1
0
Cart 2
Flag Width
After Inelastic Collision
Gate Time
Velocity
Mass
Momentum
Carts
1&2
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Conservation of Momentum Lab Results
Name:_________________
Pd. ________
For each pictured collision, predict what you think the outcome will be by drawing velocity vectors on the after
pictures.
M

M
Before

M


M
After
M
Before
After
m
Before
After
M
m
Before
M

After
M
Before

M

M

M
After
M
Before
After
m
Before
After
m
Before
After
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