Download Packet 8: Impulse Momentum

Name: ________________________________________________
Unit III-A: Impulse and Momentum
Equation
Variables/Units
Notes:
Period: ________
Unit III-A Objectives: Impulse and Momentum
By the time we finish this unit and all related activities you should be able to:
1. Define momentum; distinguish between momentum and velocity.
2. Calculate the momentum, impulse, or force exerted on an object.
3. Distinguish between elastic and inelastic collisions.
4. Use the law of conservation of momentum to solve problems involving elastic and inelastic
collisions for initial velocity, final velocity, or mass, given other values.
5. Define impulse; distinguish between impulse and force.
6. Determine the impulse acting on an object
a. given an F vs. t graph
b. given the change in momentum
7. Use the Impulse-Momentum theory to analyze the motion of rockets.
Momentum, Impulse and Momentum Change
Read from Lesson 1 of the Momentum and Collisions chapter at The Physics Classroom:
http://www.physicsclassroom.com/Class/momentum/u4l1a.html
http://www.physicsclassroom.com/Class/momentum/u4l1b.html
MOP Connection:
Unit
III-A: and
Impulse
and
Momentum
Momentum
Collisions:
sublevels
1 and 2
Worksheet 1
Momentum
1. The momentum of an object depends upon the object's ________. Pick two quantities.
a. mass - how much stuff it has
1. The momentum
of an object depends upon the object's ________. Pick two quantities.
b. acceleration - the rate at which the stuff changes its velocity
A) mass - how
much
stuffforce
it has
c. weight - the
by which gravity attracts the stuff to Earth
B) acceleration
the
rate
at
which
stuffdirection
changesit's
itsstuff
velocity
d. velocity - how fast
andthe
in what
is moving
C) weight -e.the
force by
whichthe
gravity
the stuff to Earth
position
- where
stuff isattracts
at
D) velocity - how fast and in what direction it's stuff is moving e. position - where the stuff is at
2.
Momentum is a ____________ quantity.
a. scalar
b. vector
2. Momentum
is a ____________
quantity.
A) scalar
B) vector
3. Which are complete
descriptions of the momentum of an object? Circle all that apply.
a. 2.0 kg/ s
b. 7.2 kg•m/ s, right
c. 6.1 kg•m/ s2 , down
3. Which are
complete
descriptionse.of1.9
thekg•m/
momentum
Circle
d. 4.2
m/ s, east
s, west of an object?
f. 2.3 kg•m/
s all that apply.
A) 2.0 kg/s
B) 7.2 kg•m/s, right
C) 6.1 kg•m/s2, down
two quantities
to calculate
an object's
momentum
D) 4.24.m/s,The
east
E) 1.9needed
kg•m/s,
west
F) 2.3
kg•m/s are __________ and ___________.
5.
Consider the mass and velocity values of Objects A and B below.
4. ConsiderCompared
the masstoand
velocity
values
of ____
Objects
A and B.
Object
B, Object
A has
momentum.
Compareda.to two
Object
B,
Object
A
has
____
momentum.
times the
b. four times the
A) two times
c. the
eight timesB)
thefour times the d. the same C) eight times the
D) the same
e. one-half theE) one-half the f. one-fourthF)
theone-fourth the
g. ... impossible
to tellknowledge
without knowledge
thea.F and a.
G) ... impossible
to tell without
of the F of
and
6. possesses
Calculate the
momentum
of ... . (Include
appropriate
units
onnew
yourmomentum
answers.) if ...
5. A car
20 000
units ofvalue
momentum.
What would
be the
car's
a.
...
a
2.0-kg
brick
moving
through
the
air
at
12
m/
s.
A) its velocity was doubled?
B) its velocity was tripled?
... a doubled
3.5-kg wagon
movingmore
alongpassengers
the sidewalkand
at 1.2
s.
C) its massb.was
(by adding
a m/
greater
load)?
D) both its velocity was doubled and its mass was doubled?
7.
With what velocity must a 0.53-kg softball be moving to equal the momentum of a 0.31-kg baseball
moving
at 21 m/ s? value of...
6. Calculate
the momentum
A) a 2.0-kg brick moving through the air at 12 m/s.
Impulse and Momentum Change
8. Insert these words into the four blanks of the sentence: mass, momentum,
B) a 3.5-kgacceleration,
wagon moving
along
the sidewalk
1.2 m/s.and force. (Not every
time,
impact,
weight, at
impulse,
word will be used.)
In a collision, an object experiences a(n) __________________ acting for a
certain amount of ____________________ and which is known as a(n)
7. With what velocity must a 0.53-kg softball be moving to equal the momentum of a 0.31-kg
; it serves to change the ________________ of the object.
baseball moving_______________
at 21 m/s?
© The Physics Classroom, 2009
Page 1
Momentum and Collisions
Name:
8. A 2-kg brick is placed gently upon
a 3-kg Analysis
Collision
Momentum
and Collisions
cart originally
moving with a speed of 0.25
Read
from
Lesson 2 of
thepost-collision
Momentum and
Collisions
chapter at The Physics Classroom:
m/s.
Determine
the
speed
of
http://www.physicsclassroom.com/Class/momentum/u4l2d.html
the combination
of brick and cart.
http://www.physicsclassroom.com/Class/momentum/u4l2e.html
3. A 0.150-kg baseball
moving at a speed of 45.0 m/ s crosses the
plate
and
strikes
the
0.250-kg catcher's
mitt (originally
at rest).
MOP Connection:
Momentum
and Collisions:
sublevels
7, 8 and 9
The catcher's mitt immediately recoils backwards (at the same
speed as the ball) before the
applies
an external
force toat a velocity of
1. catcher
A 10-kg
medicine
ball is thrown
stop its momentum. If the catcher's
hand
is
in
a
relaxed
15 km/ hr to a 50-kg skaterstate
whoat
is at rest on ice.
the time of the collision, it canThe
be assumed
that
no
net
external
skater catches the ball and subsequently
force exists and the law of momentum
conservation
applies
to the
slides with
the ball across
the ice.
baseball-catcher's mitt collision. Fill in the before- and after9.
A 10-kg
medicine
at the
a velocity
of 15
50-kg
skater who is at rest on ice. The
Consider
skater and
them/s
ballto
asatwo
separate
collision
table
below. ball is thrown
skater catches the ball and subsequently
slides
with
the
ball
across
the ice. Consider the skater
parts of an isolated system. (no external forces).
and the ball as two separateFill
parts
of
an
isolated
system.
(No
external
forces).
in the before- and after-collision table below.
Momentum Before
Momentum After
Momentum
A) Fill in the before- and after-collision table below.
Collision
Collision
Change
Momentum Before
Momentum After
Momentum
Baseball
Collision
Collision
Change
Ball
Catcher's Mitt
Skater
Total
Total
Determine
baseball/
immediately
after thePSYW
collision. PSYW
Determine the
the velocity
velocity of
of the
medicine
ballcatcher's
and the mitt
skater
after the collision.
B) Determine the velocity of medicine ball and the skater after the collision.
4.
2. with
A large
A 4800-kg truck traveling
a fish with a mass of 1-kg is in motion at
45head-on
cm/ s when it encounters a smaller fish
velocity of + 4.0 m/ s collides
(m=
0.25a kg) that is at rest. The large fish
with a 1200-kg car traveling
with
velocity
of
-12
m/
s.
The
truck
swallows
thevelocity
smallerof
fish
andm/s
continues
in head-on with a 1200-kg car
10. A 4800-kg truck travelingand
withcar
a
+4.0
collides
entangle
and
move
together
after
the
motion
at
a
reduced
speed.
Fill
in
the
beforetraveling with a velocity of -12 m/s. The truck and car entangle and move together after the
collision. Fill in the before-and
andafter-collision
aftertable below.
collision.
collision table below.
A) Fill in the before- and after- collision table below.
Momentum
Momentum Before
Before
Collision
Collision
Momentum
Momentum After
After
Collision
Collision
Momentum
Momentum
Change
Change
Truck
Large
Fish
Small Fish
Car
Total
Total
Determine the velocity of the large and the small fish after the collision. PSYW
Determine the velocity of the truck and car immediately after the collision. PSYW
B) Determine the velocity of the truck and car immediately after the collision.
© The Physics Classroom, 2009
Page 11
Momentum and Collisions
Name:
Momentum Problem-Solving
Read from Lesson 2 of the Momentum and Collisions chapter at The Physics Classroom:
http://www.physicsclassroom.com/Class/momentum/u4l2d.html
Unit III-A: Impulse and Momentum
http://www.physicsclassroom.com/Class/momentum/u4l2e.html
Worksheet 2
MOP Connection:
Momentum and Collisions: sublevels 8 and 9
1. Determine the post-collision velocities of the following objects or combination of objects.
1. Determine the post-collision velocities of the following objects or combination of objects.
a.
b.
c.
d.
e.
f.
© The Physics Classroom, 2009
Page 13
2. A 0.10-kg billiard ball moving at 1.5 m/s strikes a second billiard ball of the same mass moving in
the opposite direction at 0.4 m/s. The second billiard ball rebounds and travels at 0.70 cm/s after
the head-on collision. Determine the post-collision velocity of the first billiard ball.
3. A 225-kg bumper car (and its occupant) is moving north at 1 m/s when it hits a 200-kg car
(occupant mass included) moving north at 0.30 m/s. The 200-kg car is moving north at 0.7 m/s after
the head-on collision. Determine the post-collision velocity of the 225-kg car.
4. In a freight yard, a train is being put together from freight cars. An empty freight car, coasting at
10 m/s, strikes a loaded car that is stationary, and the cars couple together. Each of the cars has a
mass of 3000 kg when empty, and the loaded car contains 12,000 kg of canned soda (a year’s
supply for the Physics class). With what speed does the combination of the two cars start to move?
5. A ball of mass 3.0 kg, moving at 2 m/s eastward, strikes head-on a ball of mass 1.0 kg that is
moving at 2 m/s westward. The balls stick together after the impact. What are the magnitude and
direction of the velocity of the combined mass after the collision?
Unit III-A: Impulse and Momentum
Worksheet 3
1. Two pop cans are at rest on a stand. A firecracker is placed between the cans and lit. The
firecracker explodes and exerts equal and opposite forces on the two cans. Assuming the system
of two cans to be isolated, the post-explosion momentum of the system ____.
A) is dependent upon the mass and velocities of the two cans
B) is dependent upon the velocities of the two cans (but not their mass)
C) is typically a very large value
D) can be a positive, negative or zero value
E) is definitely zero
2. Two ice dancers are at rest on the ice, facing each other with their hands together. They push off
on each other in order to set each other in motion. The subsequent momentum change (magnitude
only) of the two skaters will be ____.
A) greatest for the skater who is pushed upon with the greatest force
B) greatest for the skater who pushes with the greatest force
C) the same for each skater
D) greatest for the skater with the most mass
E) greatest for the skater with the least mass
3. Kim holds a 2.0 kg air rifle loosely and fires a bullet of mass 1.0 g. The muzzle velocity of the
bullet is 150 m/s.
A) What is the recoil speed of the rifle?
B) If the girl now holds the rifle tightly against her body, the recoil speed is less. Explain why.
Calculate the new recoil speed assuming the girl has a mass of 48 kg.
4. Arty the astronaut, whose mass is 80 kg, carries an empty oxygen tank with a mass of 10 kg. He
throws the tank away from himself with a speed of 2.0 m/s. With what velocity does he start to
move off into space?
5. Two girls with masses of 50.0 kg and 70.0 kg are at rest on frictionless in-line skates. The larger
girl pushes the smaller girl so that the latter rolls away at a speed of 10.0 m/s. What is the effect of
the action on the larger girl? What is the change in momentum of each girl?
6. A raft of mass 180 kg carries two swimmers of mass 50 kg and 80 kg. The raft is initially floating
at rest. The two swimmers simultaneously dive off opposite ends of the raft, each with a horizontal
velocity of 3 m/s. With what velocity and in what direction does the raft start to move?
7. Jamal is rolling along on his 4.0 kg skateboard with a constant speed of 3.0 m/s when he
jumps off the back and continues forward with a velocity of 2.0 m/s relative to the ground. This
causes the skateboard to go flying forward with a speed of 15.5 m/s relative to the ground.
What is Jamal’s mass?
8. A 1.5-kg cannon is mounted on top of a 2.0-kg cart and loaded with a 50-gram ball. The cannon,
cart, and ball are moving forward with a speed of 3 m/s. The cannon is ignited and launches the
ball forward with a speed of 75 m/s. Determine the post-explosion velocity of the cannon and cart.
Unit III-A: Impulse and Momentum
Worksheet 4
1. Two carts are moving toward each other at 10 m/s.
A) If the cars have the same mass and stick together on impact, what is their combined velocity?
B) If cart A has a mass that is twice that of cart B and they stick together on impact, what is their
combined velocity?
2. One way of measuring the muzzle velocity of a bullet is to fire it horizontally into a massive block
of wood placed on a cart. Assuming no friction, we then measure the velocity with which the wood
containing the bullet and cart begin to move. In one experiment the bullet had a mass of 50 g and
the wood and its cart had a mass of 10 kg. After the shot, the cart, wood, and bullet moved at a
constant speed, traveling 0.80 m in 0.40 s. From this data determine the original speed of the
bullet.
3. A 10-gram bullet, traveling at 200 m/s, strikes a wooden block resting on a frictionless surface.
The block’s mass is 1 kg. If the bullet imbeds in the block, how fast will they move off together?
4. Two balls rest on a tabletop. The first has a mass of 2 kg while the second has a mass of 3 kg.
Someone rolls the first ball across the table at 5 m/s. It collides with the second ball and completely
stops. What is the speed of the second ball?
5. A man is stuck on a nearly frictionless frozen pond, unable to stand or move. He has a
backpack with him that has a mass of 40 kg and his mass is 100 kg. If he throws the backpack
north at 5 m/s, determine the man’s velocity (magnitude and direction!).
6. A 2.0 kg melon is balanced on a bald man’s head. His son shoots a 50.0 g arrow at it with a
speed of 30.0 m/s. The arrow passes through the melon and emerges with a speed of 18.0 m/s.
Find the speed of the melon as it flies off the man’s head.
7. Antonio, the 72 kg bullfighter, runs toward an angry bull at a speed of 4.0 m/s. The 550 kg bull
charges toward Antonio at 12 m/s and Antonio must jump on the bull’s back at the last minute to
avoid being run over. What is the new velocity of Antonio and the bull as they move across the
arena?
4.
When a boxer recognizes that he/ she will be hit by an
opposing fist, he/ she rides the punch. Use physics to explain
why.
5.
Mountain climbers use nylon safety ropes due to their tendency to stretch considerably under stress.
Use physics to explain why.
Unit III-A: Impulse and Momentum
Worksheet 5
Consider the diagram at the right for the first
Consider the diagram at the right for
three questions.
depictsThe
Before
the The
next diagram
three questions.
and After velocities
ofdepicts
an 800-kg
carand
in two
diagram
Before
After
different collisions
with of
a an
wall.
In case
A,two
the
velocities
800-kg
car in
collisions
wall.
car rebounds different
upon collision.
In with
caseaB,
the In
car
case A, theup
carand
rebounds
hits the wall, crumples
stops.upon
Assume
collision.
In each
case B,collision
the car hits
the
that the collision
time for
is the
wall, crumples up and stops. Assume that the collision time for each collision is the same.
same.
6.
In which case does the car experience the greatest momentum change?
a. Case A
b. Case B
c. Both the same
d. Insufficient information
1. In which case does the car experience the greatest momentum change?
A) Case A
B) 7.
Case
C)theBoth
the same the greatestD)impulse?
Insufficient information
InBwhich case does
car experience
a. Case A
b. Case B
c. Both the same
d. Insufficient information
2. In which case does the car experience the greatest impulse?
The
thesame
800-kg car in case
has a magnitude
of ___ N•s.
A) Case A
B) 8.
Case
B impulse encountered
C) Bothbythe
D)AInsufficient
information
a. 0
b. 800
c. 3200
d. 4000
7200
NotA
enough
3. The impulse encountered bye.the
800-kg car in f.case
has a information
magnitude to
of determine.
___ N•s.
A) 0
B) 800
C) 3200
9. Evaluate
the potential
hazard to a passenger involved
D) 4000
E) 7200
F) Not enough
information
to determine.
in a head-on collision in which the two cars stick
together compared to when they rebound upon
4. A(n) _________________ causes and is equal to a change
in momentum.
impact.
Explain.
A) force
B) impact
C) impulse
D) collision
5. Insert these words into the four blanks of the sentence: mass, momentum, acceleration, time,
impact, weight, impulse, and force. (Not every word will be used.)
In a collision, 10.
an object
experiences
__________________
forthat
a certain
amount
of with a wall.
The diagram
below a(n)
depicts
the changes in velocityacting
of a ball
undergoes
a collision
Indicate which case (A or B) has the greatest change in velocity, greatest acceleration, greatest
____________________
and which is known as a(n) _______________ ; it serves to change the
momentum change, and greatest impulse. Support each answer.
_____________________ of the object.
6. Discuss the following in terms of impulse and momentum:
A) Why are paddedGreatest
dashboards
safer Explanation:
in automobiles?
! v? _____
Greatest a? _____ Explanation:
Greatest ! p? _____ Explanation:
B) Why are nylon ropes,
which
Greatest
F! t?stretch
_____ considerably
Explanation: under stress favored by mountain climbers?
C) Why is it preferred that railroad cars be loosely coupled with slack between cars?
© The Physics Classroom, 2009
7. Two cars of equal mass are traveling down Austin Highway with equal velocities. They both
Page 4
Using the F•t = m•! v Equation to Analyze Impulses and Momentum Changes:
3. Two cars of equal mass are traveling down Lake Avenue with equal velocities. They both come to a
come to
a stop
different
lengths
time.
dot diagrams
car are
shown below.
stop
over over
different
lengths
of time.ofThe
dotThe
diagrams
for each for
car each
are shown
below.
WhichWhich
car (Acar
or (A
B) or
experiences
the the
greatest
acceleration?
Explain.
B) experiences
greatest
acceleration? ______
______ Explain.
Which car (A or B) experiences the greatest change in momentum? ______ Explain.
Which car (A or B) experiences the greatest change in momentum? ______ Explain.
Which car (A or B) experiences the greatest impulse? ______ Explain.
Which car (A or B) experiences the greatest impulse? ______ Explain.
Which car (A or B) experiences the greatest force? ______ Explain.
Which car (A or B) experiences the greatest force? ______ Explain.
© The Physics Classroom, 2009
Page 3
8. If a Hummer and a VW Beetle traveling at equal speeds have a head-on collision,
A) Which vehicle will experience the greatest force of impact? Justify your answer.
B) Which will experience the greatest change in momentum? Justify your answer.
C) Which will experience the greatest acceleration? Justify your answer.
9. Consider the interaction between a large cannon and the cannonball that it fires. During the
explosion, which object experiences the greatest ...
A) force (F)?
Cannon
Cannonball
Both the same
B) time duration (t) of the force?
Cannon
Cannonball
Both the same
C) impulse (F•t)?
Cannon
Cannonball
Both the same
D) momentum change (m•Δv)?
Cannon
Cannonball
Both the same
E) velocity change (Δv)?
Cannon
Cannonball
Both the same
F) acceleration (a)?
Cannon
Cannonball
Both the same
10. Calculate
the_________________
impulse experienced
appropriate
units on your answer.)
9. A(n)
causes by
and....
is .equal(Show
to a change
in momentum.
a. ... a 65.8-kg
halfback
encountering
a
force
of
1025
N
for
0.350
seconds.
a. force
b. impact
c. impulse
d. collision
Momentum
and
Collisions
Momentum
Collisions
10. and
Calculate
the impulse experienced by .... .
(Show appropriate units on your answer.)
a. ... a 65.8-kg halfback encountering a force of 1025 N for 0.350 seconds.
9.
9.
A(n)
causes
andisisequal
equaltoto
change
in
momentum.
b. ..._________________
a 0.168-kg tenniscauses
ball encountering
aa aforce
ofin126
N that changes its
A(n)
_________________
and
change
momentum.
a.
b. impact
impact
impulse
collision
a. force
force
b.
c.c.impulse
d. d.
collision
velocity by 61.8 m/ s.
Unit III-A: Impulse and Momentum
Worksheet 6
... impulse
a 0.168-kg
tennis ballby
encountering
a force
of 126 Nunits
that
changes
its answer.)
velocity by 61.8 m/ s.
10.
the
impulse
experienced
by....
..... . (Show
(Show
appropriate
units
your
10. Calculate
Calculateb.the
experienced
appropriate
onon
your
answer.)
a.
65.8-kg halfback
halfbackencountering
encounteringa aforce
forceofof1025
1025
for
0.350
seconds.
a. ... a 65.8-kg
NN
for
0.350
seconds.
11. Determine
the impulse
(I), momentum
(! p), momentum
andvalues.
other values.
Determine
the impulse
(I), momentum
changechange
(Δp), momentum
(p) and(p)
other
b.
...
a
0.168-kg
tennis
ball
encountering
a
force
of
126
N
that
changes
its
velocity
by
b.
0.168-kg
tennis
encountering
a2.
force
of
126
Nmedicine
61.8
m/
s.on
11.
Determine
theball
impulse
(I), momentum
change
(!that
p), changes
momentum
(p)
and
other
values.
1. A 7-ball
collides
with
the
8-ball.
A moving
ballitsisvelocity
caught
by
a61.8
girl
ice on
skates
A 7-ball
collides
with
the
8-ball.
A moving
medicine
ball
is by
caught
bym/
a s.girl
ice skates.
.
A 7-ball collides with the 8-ball.
A moving medicine ball is caught by a girl on ice skates.
11.
the impulse
impulse(I),
(I),momentum
momentumchange
change(!(!p),
p),
momentum
and
other
values.
11. Determine
Determine the
momentum
(p)(p)
and
other
values.
A
collides with
withthe
the8-ball.
8-ball.
A 7-ball collides
moving
medicine
ball
is caught
a girl
skates.
AAmoving
medicine
ball
is caught
by by
a girl
on on
ice ice
skates.
A car is at rest when it experiences a forward propulsion force to set it in motion. It then experiences
A car isaatsecond
rest when
it experiences
a forward
propulsion
forceFinally,
to set itbrakes
in motion.
It then experiences
forward
propulsionaforce
to speed
it up evenforce
more.
to Ita then
stop.
3. A car is at rest
when
it experiences
forward
propulsion
to set it init motion.
a second forward propulsion force to speed it up even more. Finally, it brakes to a stop.
experiences
a second forward propulsion force to speed it up even more. Finally, it brakes to a stop.
A car is at rest when it experiences a forward propulsion force to set it in motion. It then experiences
A car is at rest when it experiences a forward propulsion force to set it in motion. It then experiences
more.
it brakes
to atostop.
aa second forward
forward propulsion
propulsionforce
forcetotospeed
speedititup
upeven
even
more.Finally,
Finally,
it brakes
a stop.
A tennis ball is at rest when it experiences a forward force to set it in motion. It then strikes a wall
where it encounters a force that slows it down and finally turns it around and sends it backwards.
4. A tennis
ballball
is at
rest
when
aforward
forward
force
toit set
itmotion.
in motion.
Itstrikes
then
A tennis
tennis
is
rest
when
ititexperiences
experiences
force
toto
setset
in
motion.
It then
astrikes
wall
A
ball
is at
at
rest
whenit
experiencesa aforward
force
it in
It then
strikes
a walla wall
where
it
encounters
a
force
that
slows
it
down
and
finally
turns
it
around
and
sends
it
backwards.
where where
it
encounters
a
force
that
slows
it
down
and
finally
turns
it
around
and
sends
it
backwards.
it encounters
a force
that it
slows
it down and
finally turns
around
sends it backwards.
A tennis
ball is at rest
when
experiences
a forward
forceit to
set it and
in motion.
It then strikes a wall
where it encounters a force that slows it down and finally turns it around and sends it backwards.
© The
The Physics
Physics
2009
© The Classroom,
Physics Classroom,
2009
©
Classroom,
2009
Page
2 2Page 2
Page
5. Discuss the advisability of attempting to jump from a rowboat to a dock that seems just within
jumping distance. Justify your answer.
© The Physics Classroom, 2009
6. In a series of physics demos, students of varying mass are placed on large massless carts and
Page 2
deliver impulses to each other's carts, thus changing their momenta. In some cases, the carts are
loaded with equal mass; in other cases they are unequal. In some cases, the students push off
each other; in other cases, only one team does the pushing. These situations are depicted below.
A) In which cases do the carts encounter unequal impulses? ____________ Explain.
B) In which cases do the carts encounter unequal momentum changes? ____________ Explain.
C) In which cases do the carts encounter unequal velocity changes? ____________ Explain.
D) Why is it difficult for a firefighter to hold a hose that ejects large amounts of high-speed water?
7. Calculate the impulse experienced by
A) a 65.8-kg halfback encountering a force of 1025 N for 0.350 seconds.
B) a 0.168-kg tennis ball encountering a force of 126 N that changes its velocity by 61.8 m/s.
9. While being thrown, a net force of 132 N acts on a baseball (mass = 140 g) for a period of 4.5 x
10-2 seconds.
A) What is the magnitude of the change in momentum of the ball?
B) If the initial speed of the baseball in question 8 is v0= 0 m/s, what will its speed be when it leaves
the pitchers hand?
C) When the batter hits the ball, a net force of 1120 N, opposite to the direction of the ball’s initial
motion, acts on the ball for 9.0 x 10-3 seconds during the hit. What is the final velocity of the ball?
Unit III-A: Impulse and Momentum
Worksheet 7
1. A golf ball that weighs 0.45 N is dropped from a height of 1 m. Assume that the golf ball does not
dissipate any energy when it hits the floor.
A) In the margin, construct a motion map for the golf ball from the time it is dropped until it reaches
its highest point of rebound.
B) Determine the time required for the ball to reach the floor.
C) What will the instantaneous momentum of the golf ball be immediately before it strikes the floor?
D) What will be the change in momentum, (p) from the instant before the ball collides with the
floor until the instant after it rebounds from the floor? (Illustrate with a vector diagram.)
E) Suppose that the golf ball was in contact with the floor for 4.0 x 10 -4 seconds. What was the
average force on the ball while it was in contact with the floor?
2. A car with a mass of 1000 kg is at rest at a stoplight. When the light turns green, it experiences a
net force of 2000 N for 10 s.
A) What is the value of the acceleration that the car experiences?
B) What is the value of the change in velocity that the car experiences?
C) What is the value of the impulse on the car?
D) What is the value of the change in momentum that the car experiences? What is the final
velocity of the car at the end of 10 seconds?
3. The same car from question 2 continues at that speed for a while, then brakes are applied to the
car, causing it to come to rest in 4 s.
A) What is the value of the change in momentum that the car experiences as it comes to rest?
B) What is the value of the impulse on the car? What is the value of the force (average) that
causes the car to stop?
C) What is the acceleration of the car as it stops?
4. A force of 800 N causes an 80-kg fullback to change his velocity by 10 m/s. Determine the
impulse experienced by the fullback.
5. A 0.80-kg soccer ball experiences an impulse of 25 N•s. Determine the momentum change of
the soccer ball.
6. A 0.10-kg hockey puck decreases its speed from 40 m/s to 0 m/s in 0.025 s. Determine the force
that it experiences.
7. A 50 kg cart is moving across a frictionless floor at 2.0 m/s. A 70 kg boy, riding in the cart, jumps
off so that he hits the floor with zero velocity.
A) What impulse did the boy give to the cart?
B) What was the velocity of the cart after the boy jumped?
Unit III-A: Impulse and Momentum
Extra Credit Worksheet
1. Read: In working with propulsion due to a fluid, it is very helpful to rearrange the impulsemomentum theorem from: Fnet ∆t =∆(m v) to Fnet = (∆m/∆t) ∆v, where ∆m/∆t is called the mass flow
rate, i.e. the number of kilograms of propelled fluid per second, ∆v is the change in velocity of the
fluid, and Fnet is the net force on the fluid, which is equal to the thrust force on the propeller or
rocket. You’ll have to remember what you learned in chemistry and geometry to find mass flow rate!
2. A motorboat’s propeller has a diameter of 20 cm.
A) When the boat is cruising at 10 m/s, determine the mass flow rate through the propeller region.
Imagine that the propeller simply accelerates the cylinder of water it passes through. (Water’s
density is 1000 kg/m3)
B) Find the water exhaust velocity needed to produce 1200 N of thrust on the boat.
3. An airplane’s propeller has a diameter of 1.8 m.
A) When the plane is cruising at 60 m/s, determine the mass flow rate through the propeller region.
Imagine that the propeller simply accelerates the cylinder of air it passes through. (Air’s density is
1.16 kg/m3)
B) When the incoming air is accelerated from 60 m/s to an exhaust velocity of 150 m/s, find the
thrust on the plane.
4. The space shuttle’s main engines spray out 736,000 kg of water vapor at 4500 m/s by chemically
combining hydrogen and oxygen for 460 seconds. Find the average thrust force provided by the
main engines.
5. A 0.36 kg soda bottle rocket holds 1.5 kg of water as it sits upon the launch pad. The rocket
expels all of the water in 0.7 seconds producing a rocket burnout velocity of 33 m/s. (The burnout
velocity is the rocket’s velocity once thrust ceases.)
A) Draw a force diagram for the 0.7 s thrust phase of the launch.
B) Determine the mass flow rate for the rocket.
C) Determine the rocket’s average acceleration for the 0.7 s thrust phase of the launch. When is
the instantaneous acceleration of the rocket the greatest and the least?
D) Determine the average net force on the rocket.
E) Determine the exhaust velocity of the water ejected from the rocket.
Unit III-A: Impulse and Momentum
Review Worksheet
Name:
Review Questions Momentum and Collisions
1. A moving car has momentum. If it moves twice as fast, what happens to its momentum?
Momentum Conservation as a Guide to Thinking
2. Two cars, one twice as massive as the other, move down a hill at the same speed. Compare
Read from Lesson 2 of the Momentum and Collisions chapter at The Physics Classroom:
momentum of the lighter car to the momentum of the heavier car.
http://www.physicsclassroom.com/Class/momentum/u4l2dd.html
MOP Connection:
Momentum and Collisions: sublevel 10
3. How does the momentum
a fired cannonball
compare
to the
momentum
of the
recoiling
cannon?
Momentum
and Collisions
1. The of
following
diagrams depict
inelastic
collisions
between
objects
of different
mass. ForNam
eac
determine the post-collision velocity (v') of the two coupled objects. Express v' in terms of v.
4. Consider the interaction between a large bus traveling at highway speed on
a nice summer
day
Momentum
Conservation
as a G
and the momentum of an unlucky bug that suddenly changes as it splatters onto the front window.
Read
During the collision, which object experiences the greatest
...from Lesson 2 of the Momentum and Collisions chapte
a.
b.
http://www.physicsclassroom.com/Class/
A) force (F)?
Bus
Bug
Both the same
B) time duration (t) of the force?
Bus
Bug
Both the same
MOP Connection:
Momentum and Collisions: sublevel
C)
impulse
(F•t)?
Bus
Bug
Both the same
Momentum and Collisions
Name:
D) momentum change (m•Δv)?
Bus
Bug
Both the same
1. The following diagrams depict inelastic collisions betwe
E) velocity change (Δv)?
Bus
Bug
Both the same
determine the post-collision
velocity (v') of the two coupl
F) acceleration
(a)?
Bus
Bug
Both the same
Momentum Conservation as a Guide to Thinking
Read from Lesson
2 of the
Momentum
and
Collisions
chapter
at The
Classroom:
5. What
is the
difference
between
totally
elastic
andPhysics
totally inelastic
collisions? Circle all that apply.
d.
Totally
elastic
p
is
conserved.
The
objects
bounce.
The
objects stick together.
http://www.physicsclassroom.com/Class/momentum/u4l2dd.html
a.
c.
Totally inelastic
MOP Connection:
1.
p is conserved.
The objects bounce. The objects stick together.
b.
Momentum and Collisions: sublevel 10
Practice Problems
The following
depict
inelastic collisions
between objects
of(v')
different
For eachobjects.
case,
6. Fordiagrams
each case,
determine
the post-collision
velocity
of themass.
two coupled
Express v' in
determine the post-collision velocity (v') of the two coupled objects. Express v' in terms of v.
terms of v.
a.
e.
b.
c.
f.
d.
7. Car companies test the safety of their cars by putting them through a crash test to observe the
integrity of the passenger compartment. If a 1000 kg car is sent toward a cement wall with a speed
of 14 m/s and the impact brings it to a stop in 8.00 x 10-2 seconds, with what average force is it
brought to rest?
c.
g.
d.
e.
h.
f.
8. If 270 million people in the United States jumped up in the air simultaneously, pushing off Earth
with an average force of 800 N each for a time of 0.10 seconds, what would happen to the 5.98 x
1024 kg Earth? Show your calculations to justify your answer.
9. In Sharkey’s Billiard Academy, Maurice notices that the cue ball is lined up for a perfect head-on
e.
i.
f.
g.
j.
h.
collision with the 8-ball. Each ball has a mass of 0.80 kg and the cue ball comes to a complete
stop upon making contact with the 8-ball. Suppose Maurice hits the cue ball by exerting a force of
180 N for 5.0 x 10-3 s, and suppose it does knock head-on into the 8-ball. Calculate the resulting
velocity of the 8-ball.
10. Bernie rolls a 7.0 kg bowling ball down the alley for the league championship. One pin is still
standing, and Bernie hits it head-on with a velocity of 9.0 m/s. The 2.0 kg pin acquires a forward
velocity of 14 m/s. What is the new velocity of the bowling ball?
11. Running at 2.0 m/s, Bruce, the 45.0 kg quarterback, collides with Biff, the 90.0 kg tackle, who
is traveling at 7.0 m/s in the other direction. Upon collision, Biff continues to travel forward at 1.0
m/s. How fast is Bruce knocked backwards?
12. A firecracker is initially at rest when it is set on fire and explodes. One part of the firecracker,
has a mass of 5 g and goes flying Westward with a velocity of 25 m/s. The other part has a
mass of 3 g and goes flying Eastward. What is the velocity of the second part of the firecracker?
13. A 620 kg moose stands in the middle of the railroad tracks, frozen by the lights of an oncoming 10,000 kg train that is traveling at 10.0 m/s. The engineer sees the moose, but is unable
to stop the train in time and the moose rides down the track sitting on the cowcatcher. What is
the new combined velocity of the train and the moose?