Download Jason Kidd high in the air drops a 0.60-kg

Physics/D'Amato/2010/Momentum
1
Period:
Name:
1. "Constant" and "conserved"
1.1.
System, environment, process
From time to time, we will find it useful to focus our attention on a certain part of the universe and
consider it separately from everything else. We select a number of physical objects and call them the
system. Everything else in the universe is called the environment.
As time goes by, the system may change. We can pick two clock readings, and call what happens in
between a process. Before the process, the system is in its initial state and at the end of the process
the system is in its final state.
In a sketch, we outline the system objects carefully. If the earth is in the system we show this clearly.
Consider the following sketches of a system which includes two carts on a track:
Initial state
v0
Final state
v0
v
v
a)
In the sketch above, what objects are in the system?
b)
What objects are NOT in the system?
c)
Describe the process that occurred
d)
External interactions are between a system object and an object in the environment.
Describe at least two external interactions in this process
e)
Internal interactions are between two system objects. Describe one above.
f)
Describe a "process" that might occur in a playground. Select system objects and sketch
initial and final states.
The concept of "system" is similar to "object of interest" except that a system can contain many objects.
The choice of system objects is up to the investigator and depends on the problem being addressed.
Learning to choose useful systems is part of the skill that makes you a good scientist. Like any other
skill, it is developed by trial and error at first, then improved by practice.
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Physics/D'Amato/2010/Momentum
1.2.
2
Period:
Name:
Constant and conserved
Constant describes a quantity that does not change over a time interval.
For example, the amount of money in my pocket is constant from 6am when I get up to 11am when I go
to lunch. The amount does not change.
Conserved describes a quantity that may change during a period of time, but does NOT appear from
nowhere or disappear without trace. You can always find a system within which a conserved quantity
is constant.
For example: At 11am I spend $2.75 on lunch in the cafeteria. The amount of money in my pocket
changes, but my money does not disappear. The cafeteria lady has it now.
1.3.
a)
In the "buying lunch" situation, within what choice of system is the quantity of money
NOT constant?
b)
Within what choice of system is the quantity of money constant?
Quantities and Symbols
Before we apply the concepts of constancy and conservation to physical situations, let's practice using
these concepts to describe transformations of a quantity that is familiar to us.
a)
Use $ to represent a quantity of money. Use the subscripts i and f to indicate initial and
final quantities. Use the subscripts P, A, and G to indicate money in your pocket, ATM card,
and gift card. Complete the table below
Initial value
Money in pocket
Final value
$Pi
Money in ATM card
Money in gift cart
b)
Use the symbols above to make a mathematical representation of the quantity "initial net
wealth"
c)
Invent a symbol to represent the quantity "amount I earn or spend"
d)
Use these symbols to make a mathematical representation of the statement "my total net
wealth changes by the amount of money I earn or spend".
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Physics/D'Amato/2010/Momentum
1.4.
3
Period:
Name:
Conservation bar charts
Use the symbols we made up to practice the concept of conservation using a familiar quantity.
The total amount of money you have remains the same before and after unless you earn some or spend
some -- right? Fill in the bar charts. Show that the two sides balance by writing a arithmetic statement
equation using the given values (i.e. 30 + 10 - 20 = 10 + 10)
Situation and process
Conservation bar chart
(a) You have no money in your pocket, $60 in your ATM account, and
a gift card with $20 on it. You withdraw $20 cash from the ATM.
a. Complete the bar chart to match this process. Did you earn
or spend any money?
before
$Pi + $Ai + $Gi +
Earn or
spend
Δ$
after
=$Pf + $Af + $Gf
+50
0
0
b. Represent this process with an arithmetic statement
-50
(b) Next, you buy a snow shovel for $10 cash at Jones Hardware. (The
initial state for this process is the same as the final state of the
previous process.)
a. Represent this process on the bar chart. Did you earn or
spend any money?
before
$Pi + $Ai + $Gi +
Earn or
spend
Δ$
after
=$Pf + $Af + $Gf
+50
0
b. Represent this process with an arithmetic statement
-50
(c) After returning from the hardware store, you spend two hours
shoveling snow for an old lady who pays you 10 $/hr.
a. Represent this process on the bar chart. Did you earn or
spend any money?
before
$Pi + $Ai + $Gi +
Earn or
spend
Δ$
after
=$Pf + $Af + $Gf
+50
0
b. Represent this process with an arithmetic statement
-50
(d) When you are finished shoveling, you spend $20 cash to put gas
in your car so you can drive to the Best Buy.
a. Represent this process on the bar chart. Did you earn or
spend any money?
before
$Pi + $Ai + $Gi +
+50
0
b. Represent this process with an arithmetic statement
-50
Activity continues …
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Earn or
spend
Δ$
after
=$Pf + $Af + $Gf
Physics/D'Amato/2010/Momentum
4
Period:
Situation and process
Name:
Conservation bar chart
(e) At Best Buy, you purchase a "Cher's Greatest Hits" DVD Box Set
for $40. You empty out your gift card and use your ATM card to pay
for the rest.
a. Represent this process on the bar chart. Did you earn or
spend any money?
before
$Pi + $Ai + $Gi +
Earn or
spend
Δ$
after
=$Pf + $Af + $Gf
+50
0
b. Represent this process with an arithmetic statement
-50
(f) What happens next? What do you do with the Cher DVDs?
Continue the story.
before
$Pi + $Ai + $Gi +
Earn or
spend
Δ$
after
=$Pf + $Af + $Gf
+50
a. Represent this story on the bar chart. Did you earn or
spend any money?
0
b. Represent this process with a mathematical statement
-50
(g) You can forget about the Cher DVD's now, if you want. Does this
bar chart represent a process that could really happen? If not, explain
why not. If so, describe a situation it could match.
before
$Pi + $Ai + $Gi +
Earn or
spend
Δ$
after
=$Pf + $Af + $Gf
+50
0
0
-50
(h) Draw the missing bar.
before
$Pi + $Ai + $Gi +
Write a mathematical statement to match the chart.
Earn or
spend
Δ$
after
=$Pf + $Af + $Gf
+50
Describe a story that could match.
0
-50
(i) Make a chart to match this mathematical statement:
before
$Pi + $Ai + $Gi +
$20 + $0 + $0 + $40 = $20 + $40 + $0
+50
Describe a story that could match.
0
-50
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Earn or
spend
Δ$
after
=$Pf + $Af + $Gf
Physics/D'Amato/2010/Momentum
5
Period:
Name:
1.5.
Represent conservation with different choices of system
1.6.
This time let's consider a married couple, Chris and Grey, and their pocket money.
a)
Create symbols and bar charts to represent the same processes for two different choices
of system. Complete the table below
Chris is the system
Process
Chris and Grey are the system
On his way out
the door in the
morning, Chris
takes $20 from
Grey's wallet.
(Did net wealth
change?)
During the day,
Chris spends $5
on bagels and $5
on lunch.
In the afternoon,
Chris is given
$10 by Charles
who owes him
for springs.
In the evening,
Chris returns
$10 to Grey's
wallet
b)
Choose one process and one choice of system in which money is constant. Explain how
you know, and what this means.
c)
Choose one process and one choice of system in which money is conserved but NOT
constant. Explain how you know, and what this means.
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Physics/D'Amato/2010/Momentum
6
Period:
Name:
2. "Throws" and "catches"
2.1.
Warm up
Fill in the blanks to make sure you remember how to use the concept of Δv
Initial motion
v
(a)
Not moving
–x direction
(b)
Moving in –y
direction
Moving faster in –y
direction
(c)
Moving in –x
direction
Not moving in x
direction
(d)
–x direction
Final motion
Motion diagram to match
Not moving in x
direction
(e)
(f)
(g)
x
(h) Which has a larger v , a tennis ball that falls into mud and stops, or a tennis ball that falls onto
pavement and bounces?
(i) Which has a larger v , a tank that accelerates from 0 to 1m/s or a softball pitched underhand?
(j) Which has a larger v , a tank that accelerates from 12m/s to 13m/s or a bike that accelerates from
2 to 3 m/s?
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Physics/D'Amato/2010/Momentum
2.2.
7
Period:
Name:
Look for a pattern
Watch and describe a series of experiments. Fill in the table and think of an explanation that might
account for all of the experiment outcomes.
Experiment
Sketch the initial state. Draw velocity
arrows for both objects.
Sketch the final state. Draw velocity
arrows for both objects.
(a) Jon, on a skateboard,
is holding a medicine ball.
He throws the ball
forward and rolls
backwards. The initial
speed of the ball is much
larger than Chris’s speed.
Before throw
After throw
vci  0
vbi  0
vcf 
vbf 
Describe the direction and
magnitude of the
velocities of both
interacting objects
Compare the Δv of both
objects
(b) Jon is standing still
and catches a medicine
ball thown at him. He rolls
backwards holding the
ball. His speed (and the
speed of the ball after he
catches it) is much
smaller than the speed of
the ball before it hit him
Δvb=
Δvj=
Before throw
After throw
Describe the direction and
magnitude of the
velocities of both
interacting objects
Δvb=
Compare the Δv of both
objects
(c) Jon is moving to the
right and catches the ball
thrown at him (moving
left). He slows down after
he catches the ball. Jon
and the ball continue to
move to the right slower
than Jon was moving
before he caught the ball.
Δvj=
Before catch
After catch
Describe the direction and
magnitude of the
velocities of both
interacting objects
Δvb=
Compare the Δv of both
objects
Δvj=
(d) Consider the observations above, and find a pattern that describes what happens to the velocity of
the two objects involved in a throw or catch
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Physics/D'Amato/2010/Momentum
2.3.
8
Period:
Name:
Predict and test
Use the pattern that you devised in 2.2(d) to predict the results of the following experiments. Then
compare your prediction with the outcome of the real experiment or with your previous experiences.
(b) Cart A is loaded with a block of metal
and has a velcro pad on the front. It moves
slowly to the right on a low-friction track,
and hits the empty and stationary cart B,
which has a velcro patch on the side facing
cart A.
(a) Chris is standing on a skateboard and
then he jumps off of it toward the back.
Describe your
prediction in
words and
sketch
Explain how
you made the
prediction
using the
pattern in
2.2(d)
Compare to
observations
(c) Discuss whether the pattern you described in 2.2(d) was successful in predicting the results of
these new experiments.
2.4.
Explain
Suppose you place a rifle on gliders and pull the trigger. A bullet (mass 0.020-kg) shoots at high speed
(300 m/s) out of the barrel and the rifle (mass 2.0-kg) recoils back in the opposite direction at speed
3.0 m/s. Does this match the pattern you detected in the experiments above? Explain.
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Physics/D'Amato/2010/Momentum
2.5.
9
Period:
Name:
Physics in the movies
What do you see when somebody fires a handgun in the movies? What happens to the handgun and the
hand holding it? Can you explain this in terms of the pattern we have discovered?
What happens in the movies when somebody (hopefully a bad guy) is shot? Can you explain this in
terms of the pattern we have discovered?
2.6.
Stopped dead
At the National Transportation Safety test facility, they video the collision of two identical cars initially
moving at 80 km/h (45 mph) toward each other. Immediately after the collision, the cars are at rest
stuck to each other. The velocities before the collision were the same magnitude but in opposite
directions. Explain.
2.7.
A creative solution
You wear ice skates and a backpack on a frozen pond. How might you start moving without pushing off
on the ice? Explain.
2.8.
Homework
Describe what will happen and explain in terms of our new principle: (1) a moving train car is rolled
gently toward another train car that is not moving. The two cars touch and lock together. What
happens next and why? (2) a small pirate ship fires a large cannon from its rear deck. What happens
next and why?
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Physics/D'Amato/2010/Momentum
10
Period:
Name:
3. Conservation in throws and catches
3.1.
Look for a quantity that is conserved
Imagine observing the following experiments with two frictionless gliders moving on an air track.
Complete the table that follows for each experiment.
Try to find a physical quantity that is conserved if the choice of system includes both carts.
Experiment
Sketch the process before the
collision and after the collision.
Label known quantities
Determine if anything is the same before and after the
collision (i.e., is any quantity conserved). Hint: think of
mass, speed, velocity, acceleration or some
combination of these quantities
(a) Cart A (200 g)
moving left at a
constant 0.70 m/s
speed hits identical
cart B (200 g) that is
stationary. Cart A
stops and cart B
starts moving at
speed 0.70 m/s to the
left.
(b) Cart A loaded
with blocks (total
mass of the cart with
blocks is 400 g)
moving left at 0.70
m/s hits stationary
cart B (mass 200 g).
After the collision,
both carts move left,
cart B at speed 0.86
m/s and cart A at
speed 0.27 m/s.
(c) Cart A (200 g)
with a piece of
modeling clay
attached to the front
moves left at 0.70
m/s. Identical cart B
(200 g) moves right
at constant speed
0.70 m/s. The carts
collide, stick together
thanks to the clay,
and stop.
(d) Repeat
experiment (c) but
this time cart A is
loaded (total mass of
the cart with blocks is
400 g). After the
collision both carts
stick together and
travel left at speed
0.23 m/s.
(e) After you come up with a physical quantity that is conserved in each experiment, decide if a single
quantity is conserved in all of the experiments.
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Physics/D'Amato/2010/Momentum
3.2.
11
Period:
Name:
Represent with conservation bar charts
Create a conservation bar chart to represent the new quantity in each of the previous experiments
Experiment
(a) Cart A (200 g) moving left at a constant
0.70 m/s speed hits identical cart B (200 g)
that is stationary. Cart A stops and cart B
starts moving at speed 0.70 m/s to the left.
before
Δ
after
before
Δ
after
before
Δ
after
before
Δ
after
+
0
(b) Cart A loaded with blocks (total mass of
the cart with blocks is 400 g) moving left at
0.70 m/s hits stationary cart B (mass 200 g).
After the collision, both carts move left, cart
B at speed 0.86 m/s and cart A at speed 0.27
m/s.
+
0
(c) Cart A (200 g) with a piece of modeling
clay attached to the front moves left at 0.70
m/s. Identical cart B (200 g) moves right at
constant speed 0.70 m/s. The carts collide,
stick together thanks to the clay, and stop.
+
0
(d) Repeat experiment (c) but this time cart
A is loaded (total mass of the cart with
blocks is 400 g). After the collision both
carts stick together and travel left at speed
0.23 m/s.
+
0
(e) Do your bar charts show conservation of the same quantity for all experiments? State this new
principle of conservation in your own words.
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Physics/D'Amato/2010/Momentum
3.3.
12
Period:
Name:
Look for the same pattern in other observations
The following table provides more data about the collisions of two dynamics carts, including the
masses of the carts, initial velocities of the carts before the collision (vi), and the final velocities after
the collision (vf).
Sketch before and after
Make a conservation bar chart
Cart 1: mass = m, vi =+2.0 m/s, vf =+1.0 m/s
Cart 2: mass = m, vi = 0 m/s, vf =+1 m/s
(a)
Cart 1: mass = m, vi =+2.0 m/s, vf =+1.0 m/s
Cart 2: mass = m, vi = –2.0 m/s, vf =+1 m/s
(b)
Cart 1: mass = 2m, vi =+2.0 m/s, vf =+0.5 m/s
Cart 2: mass = m, vi = –1.5 m/s, vf =+1.5 m/s
(c)
Cart 1: mass = 2m, vi =+2.0 m/s, vf = 0 m/s
Cart 2: mass = m, vi = –2.0 m/s, vf = +2.0 m/s
(d)
(e) Determine whether the same quantity is conserved in each of these experiments as was conserved
in 3.1(e)
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Physics/D'Amato/2010/Momentum
3.4.
13
Period:
Name:
Real world connections
When considering weapons for defense against attacking zombies, the most important consideration is
stopping power. If the motion of the undead can be reduced or stopped there may be enough time for a
survivor to escape.
Two survivors are discussing the merits of the weapons they have looted from the ruins of the sporting
goods store. Matt has a high-powered hunting rifle that fires a 0.05kg bullet at 1000m/s. He observes
that his bullets often pass right through attacking zombies. Kerry has a shotgun that fires 0.1kg of
birdshot at 500m/s. The small particles of ammunition from her weapon penetrate a short distance
into the flesh of the zombies but never go all the way through.
(a) Matt insists that his high-powered weapon would be much better at stopping a zombie shambling
toward them. Use your new principle of conservation to determine whether or not he is correct. What
assumptions did you make in your analysis?
Matt and his weapon
Kerry and her weapon
Choice of system
objects
ammo, zombie
ammo, zombie
Initial moment
Just before ammo strikes zombie
Just before ammo strikes zombie
Final moment
After ammo strikes zombie
After ammo strikes zombie
Sketch and label
initial and final
states
Calculate initial
momentum of
ammo
Calculate final
momentum of
ammo. Make
reasonable
assumptions
about its
velocity.
Calculate initial
momentum of
zomie. Make
reasonable
assumptions
about its mass
and velocity
Construct a
momentum bar
chart for the
system and
process
Which weapon
will be more
effective in
slowing the
zombie?
Explain.
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Period:
Name:
(b) Jimmy has a shotgun just like Kerry's. He find himself cornered by a 90kg zombie that is shambling
toward him at 2m/s. He has four shells left in his repeating shotgun, and no time to reload before he
will be torn apart. Can he stop the zombie? Describe the assumptions you made in your analysis.
(c) Josh has a 4kg axe which he can swing at 12m/s. When he uses it on a zombie, it thunks into
mouldering flesh and stops dead. Katelyn has a big 6kg mallet which she can swing at 8m/s. When she
uses it on a zombie, it bounces off the zombie in the opposite direction at almost the same speed.
If they are facing identical zombies, shambling at the same speed toward each of them, which has a
better chance of stopping the zombie long enough to escape? Explain your answer with conservation
bar charts. What assumptions did you make?
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Physics/D'Amato/2010/Momentum
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Period:
Name:
4. Solving momentum problems in isolated systems
4.1. Summary and definitions
Momentum
Momentum is a fundamental physical quantity that is possessed by all objects
The momentum p of an object is equal to the object's mass m times the object's velocity v
p  mv
Momentum is a vector quantity in the same direction as velocity. (It has the same sign as velocity on a
number line coordinate axis.)
System
A choice of objects that are considered separately from all other objects for the purpose of analysis
Environment
All other objects that are not in the system
External
interaction
A force (push or pull) between an object in the environment and an object in the system
Internal
interaction
A force (push or pull) between two objects both in the system
Initial state
The properties of the system objects at a moment in time
Final state
The properties of the system objects at a later moment in time
Process
The properties of the objects in the system change from one state to a different state over a period of time
Constant
When the total amount of quantity within a system remains the same as time changes, the quantity is said to
be constant.
Conserved
A conserved quantity does not appear from nowhere or disappear without trace. You can always choose a
system within which the quantity is constant. The classic example of a conserved quantity is mass.
Momentum conservation bar chart
This is a tool that allows us to visualize the transfer of momentum within system objects. Sometimes
we will draw the bars with precise values, or sometimes we will just show the relative sizes.
A properly drawn bar chart will show the same total momentum on the "before" side and the "after"
side
Each side of the chart shows a bar for each object in the system. The size of the bar is determined by
calculating the momentum p of the object in the initial or final state.
before
p1i
Δ
p2i
after
p1f
p2f
+
0
0
-
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Period:
Name:
4.2. Warm up
When no unbalanced forces are exerted on the objects in a system, the total amount of momentum in a
system remains constant. Let's practice using this principle to reason about
The initial and final states for four processes are shown below. The system includes both blocks and
the spring, if present.
Which process are possible and which are not according to your knowledge of momentum
conservation? Explain your reasons. The numbers indicate the relative mass and the relative speeds of
the blocks.
(a)
(b)
(c)
(d)
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4.3. Bar chart jeopardy
before
p1i
Δ
p2i
after
p1f
p2f
+
0
0
(a) If the initial momentum of object 1 is equal to 40 kg m /s and its mass is 5kg, convert the bar chart
above into a mathematical description constant momentum for two objects.
(b) Describe in words and sketch a process consistent with the bar chart and mathematical statement
you have formulated.
4.4. Equation jeopardy
Come up with a problem that is consistent with each of the two mathematical descriptions of processes
provided in the table below.
Mathematical description of a process
(a)
Pose a problem consistent with the process.
(24 kg)(–2.0 m/s) + (30 kg)(+3.0 m/s) = (24 kg + 30 kg) v
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Period:
Name:
4.5. Introduction to problem solving
Apply the constant-momentum problem solving strategy to these situations
Problem solving
strategy for
momentum in an
isolated system.
Order of steps is a
guide only
(a) A 1000-kg rocket traveling west at 40
m/s ejects its booster segment. Immediately
after the ejection, the larger 800-kg segment
continues west at 60 m/s. Determine the
velocity (magnitude and direction) of the
ejected booster immediately after the
ejection.
A. Sketch and list
1. Identify the
unknown quantity
and select system
objects, initial
moment, and final
moment
2. Sketch the initial
and final states
3. Circle the system
objects
4. Draw an axis and
choose a + direction
5. List all the known
quantities using
familiar symbols
B. Momentum
4. Construct a
constant momentum
bar chart
5. Complete the bar
chart to show
constant momentum
in the system
If you can't find
constant
momentum,
consider changing
your selection of
system objects and
moments.
C. Math & Physics
8. Use the
conservation bar
chart to compose a
math statement of
constant momentum
10. Substitute
known quantities
and solve for
unknown quantities
11. Evaluate your
answer for
reasonableness
(magnitude, sign,
units)
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(b) A 1000-kg car, traveling west at 20 m/s,
collides with an 800-kg car traveling north at 16
m/s. The cars stick together. Determine the
velocity of the cars (magnitude and direction)
immediately after the collision.
Physics/D'Amato/2010/Momentum
19
Period:
Name:
5. Change in the momentum of the system
5.1. Warm up: Calculate the change in momentum
(a) A 1998 910-kg Toyota Tercel travels at a speed of 32 m/s. (a) At what speed must a 2002 1950-kg
Toyota 4Runner travel to have the same momentum? (b) At what speed must a 7.3-kg bowling ball
travel to have the same momentum?
(b) Your 0.0567-kg tennis ball traveling at 25 m/s hits a practice wall and rebounds in the opposite
direction with the same speed. Determine the ball’s change in momentum (magnitude and direction).
(c) A 145-g baseball traveling at 35 m/s is hit by Barry Bonds’ bat so that it rebounds in the opposite
direction at 40 m/s. Determine the ball’s change in momentum (magnitude and direction).
(d) Tiger Woods’ golf club hits a 0.055-kg golf ball so that it leaves the grass at a speed of 50 m/s.
Determine the magnitude of its change in momentum.
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Name:
5.2. Derive a new expression
Cart A of mass m is at moving at velocity vA1 on a horizontal, frictionless track.
At clock reading t1 your hand begins to push on the cart with force Fh on A
At clock reading t2 the cart is moving at faster velocity vA2 and your hand stops pushing
(a) Use the cart as your choice of system and before and after the push as the initial and final states.
Sketch the system in the initial and final state, and label all given quantities.
(b) Has the total momentum in the system change from before the push to after? If so, identify the
external object that caused the change. Sketch a conservation bar chart.
(c) Let's try to calculate the quantity of change. Use Newton’s second law and the definition of
acceleration to show Fh on A (t2  t1 )  mvA2  mvA1
The term on the left Fh on c (t2  t1 ) is called the impulse due to the external force Fh on c during that time
interval. The term on the right mvc2  mvc1 is called the change in the momentum of the cart.
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(d) Suppose that friction is not negligible. How would you modify the expression for the impulse on the
cart to include both the effect of the hand and of friction?
(e) Suppose the cart’s forward velocity decreased due to the force of a hand pushing lightly back on it.
How would you write the expression for the impulse due to that force?
5.3. Problems including a change in total momentum
(a) Junior’s bat contacts a 0.145-kg baseball for 1.3 x 10-3 s. The average force of the bat on the ball is
8900 N. If the ball has an initial velocity of 36 m/s toward the bat, what is the ball's final velocity
(magnitude and direction)?
(b) John Glenn’s 65-kg body pushes against the inside back wall of a 2000-kg spaceship, causing his
speed toward the front to increase from zero to 1.6 m/s. (a) If the push lasts 0.30 s, what is Glenn’s
average force on the spaceship? (b) With what speed does the spaceship recoil if initially at rest?
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6. Problems with conserved momentum
6.1. Warm up
Chris and Grey are married.
(a) On Saturday, Chris stays home reading while Grey teaches yoga for 2 hours at $50/hour. When
Grey comes home she gives Chris $20 for lunch money. How much does their net worth change during
this time?
(b) On Sunday afternoon, Grey teaches yoga while Chris goes to the go-kart track with his friends. If the
go-kart track charges $40 an hour to race, what is the total change in their net wealth if they are both
out for 2.5 hours?
6.2. Warm up
Practice reasoning with the change in momentum or "impulse": 𝐼 = ∆𝑝 = 𝐹net external ∆𝑡
(a) The rails of the Washington D.C. Metro train track exert a 2.0 x 10 5 N friction force on the train
causing it to stop in 50 s. Choose system objects so that the tracks exert an impulse on the system
objects. Calculate the impulse.
(b) Peter is on ice skates, initially at rest. His father pushes him from behind with an average force of
12N. If Peter's momentum increases by 46 kg m/s how long did his father push?
(c) A 400g cart on a frictionless track is rolling at 3 m/s. A hand pushes lightly on the front of the cart
until it stops. If the cart takes 1.2 seconds to stop, what was the average force of the hand on the cart?
(d) Your heart pumps about 80g of blood with each beat. Each beat lasts about 0.17s. The blood starts
at rest and reaches a speed of about 1 m/s. What is the impulse exerted by the heart on this amount of
blood? What is the average force exerted on the blood by the heart?
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6.3. Real problems
Address these real college-level momentum problems using the problem solving strategy
Order of steps is a
guide only
Junior’s bat contacts a 0.145-kg baseball for 1.3
x 10-3 s. The average force of the bat on the
ball is 8900 N. If the ball has an initial velocity
of 36 m/s toward the bat, what is the ball's
final velocity (magnitude and direction)?
1. Choose system
objects
read
imagine
2. Sketch initial
moment and label
known quantities
(include +/- axis)
sketch
At least twice
3. Sketch final
moment and label
known quantities
4. Identify external
object(s) exerting
unbalanced forces
on system
object(s)
5. Write an
expression for
𝐹net ext
6. Write an
expression for the
net impulse
exerted on system
objects by external
objects
∆𝑝 = 𝐹net ext ∆𝑡
7. Construct a
conservation bar
chart for
momentum in the
system
8. Use the
conservation bar
chart to construct a
mathematical
statement of
conservation of
momentum:
𝑝Ai + 𝑝Bi + ∆𝑝
= 𝑝Af + 𝑝Bf
9. Substitute
known quantities
and solve for
unknown
quantities
10. Evaluate your
answer for
reasonableness
(magnitude, sign,
units)
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Jason Kidd high in the air drops a 0.60-kg
basketball so that it reaches the floor falling
vertically at 6.0 m/s. The ball rebounds upward
at a speed of 5.2 m/s. Determine the ball's
change in momentum (magnitude and
direction). Determine the average net force of
the floor on the ball if the collision lasts 0.12 s.
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6.4. Real problems
Address these real college-level momentum problems using the problem solving strategy
Order of steps is a
guide only
(a) John Glenn’s 65-kg body pushes against the
inside back wall of a 2000-kg spaceship,
causing his speed toward the front to increase
from zero to 1.6 m/s. If the push lasts 0.30 s,
what is Glenn’s average force on the spaceship?
With what speed does the spaceship recoil if
initially at rest?
1. Choose system
objects
2. Sketch initial
moment and label
known quantities
(include +/- axis)
3. Sketch final
moment and label
known quantities
4. Identify external
object(s) exerting
unbalanced forces
on system
object(s)
5. Write an
expression for
𝐹net ext
6. Write an
expression for the
net impulse
exerted on system
objects by external
objects
∆𝑝 = 𝐹net ext ∆𝑡
7. Construct a
conservation bar
chart for
momentum in the
system
8. Use the
conservation bar
chart to construct a
mathematical
statement of
conservation of
momentum:
𝑝Ai + 𝑝Bi + ∆𝑝
= 𝑝Af + 𝑝Bf
9. Substitute
known quantities
and solve for
unknown
quantities
10. Evaluate your
answer for
reasonableness
(magnitude, sign,
units)
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(b) The bone in the upper part of the cheek
(the zygomatic bone) can be fractured by a
900-N force lasting 6.0 ms or longer. A hockey
puck can easily provide such a force when
hitting an unprotected face. (a) What change in
velocity of a 0.11-kg hockey puck is needed to
provide that impulsive force?
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