Transcript Unit Eight Momentum

Momentum and Collisions
Preview
Section 1 Momentum and Impulse
Section 2 Conservation of Momentum
Section 3 Elastic and Inelastic Collisions
Section 4 Extra Questions
Section 1
Momentum and Collisions
Section 1
What do you think?
• Imagine an automobile collision in which an
older model car from the 1960s collides with a
car at rest while traveling at 15 mph. Now
imagine the same collision with a 2007 model
car. In both cases, the car and passengers are
stopped abruptly.
• List the features in the newer car that are designed to
protect the passenger and the features designed to
minimize damage to the car.
• How are these features similar?
Momentum and Collisions
Section 1
What do you think?
• What are some common uses of the term
momentum?
• Write a sentence or two using the term momentum.
• Do any of the examples provided reference the
velocity of an object?
• Do any of the examples reference the mass of
an object?
Momentum and Collisions
Section 1
Momentum
• Momentum (p) is proportional to both mass and velocity.
• A vector quantity
• SI Units: kg • m/s
Momentum and Collisions
Section 1
Momentum and Newton’s 2nd Law
• Prove that the two equations shown below are
equivalent.
F = ma
and
F = p/t
• Newton actually wrote his 2nd Law as F = p/t.
– Force depends on how rapidly the momentum
changes.
Momentum and Collisions
Section 1
Impulse and Momentum
• The quantity Ft is called impulse.
– SI units: N•m or kg•m/s
• Impulse equals change in momentum.
– Another version of Newton’s 2nd Law
– Changes in momentum depend on both the force and the
amount of time over which the force is applied.
Momentum and Collisions
Impulse-Momentum Theorem
Click below to watch the Visual Concept.
Visual Concept
Section 1
Momentum and Collisions
Changing momentum
• Greater changes in
momentum(p) require
more force (F) or more
time (t) .
• A loaded truck requires
more time to stop.
– Greater p for truck with
more mass
– Same stopping force
Section 1
Momentum and Collisions
Section 1
Classroom Practice Problems
• A 1350 kg car has a velocity of 22.0 m/s to the
north. When braking rapidly, it stops in 4.50 s.
– What was the momentum of the car before braking?
– What is the magnitude of the force required to stop
the car?
• Answers:
– 2.97 x 104 kg • m/s to the north
– 6.60 x 103 N
Momentum and Collisions
Section 1
Stopping Time
Ft = p = mv
• When stopping, p is the same for rapid or gradual
stops.
• Increasing the time (t) decreases the force (F).
– What examples demonstrate this relationship?
• Air bags, padded dashboards, trampolines, etc
• Decreasing the time (t) increases the force (F).
– What examples demonstrate this relationship?
• Hammers and baseball bats are made of hard material to reduce
the time of impact.
Momentum and Collisions
Section 1
Classroom Practice Problems
• A 65 kg passenger in a car travels at a speed of
8.0 m/s. If the passenger is stopped by an airbag
in 0.75 s, how much force is required?
– Answer: 6.9 x 102 N
• If the car does not have an air bag and the
passenger is instead stopped in 0.026 s when
he strikes the dashboard, by what factor does
the force increase?
– Answer: F = 2.0 x 104 N so it is 29 times greater
Momentum and Collisions
Section 1
Now what do you think?
• Imagine an automobile collision in which an
older model car from the 1960s collides with a
car at rest while traveling at 15 mph. Now
imagine the same collision with a 2007 model
car. In both cases, the car and passengers are
stopped abruptly.
– List the features in the newer car that are designed to
protect the passenger and the features designed to
minimize damage to the car.
– How are these features similar?
Momentum and Collisions
Section 1
Now what do you think?
• How is momentum defined?
• How is Newton’s 2nd Law written using
momentum?
• What is impulse?
• What is the relationship between impulse and
momentum?
Momentum and Collisions
Section 2
What do you think?
• Two skaters have equal mass and are at
rest. They are pushing away from each
other as shown.
• Compare the forces on the two girls.
• Compare their velocities after the push.
• How would your answers change if the
girl on the right had a greater mass than
her friend?
• How would your answers change if the
girl on the right was moving toward her
friend before they started pushing apart?
Momentum and Collisions
Section 2
Momentum During Collisions
• When the bumper cars collide,
F1 = -F2 so
F1t = -F2t,
and therefore
p1 = -p2 .
• The change in momentum for one object is equal and
opposite to the change in momentum for the other object.
• Total momentum is neither gained not lost during
collisions.
Momentum and Collisions
Section 2
Conservation of Momentum
• Total momentum remains constant during collisions.
• The momentum lost by one object equals the momentum
gained by the other object.
• Conservation of momentum simplifies problem solving.
Momentum and Collisions
Conservation of Momentum
Click below to watch the Visual Concept.
Visual Concept
Section 2
Momentum and Collisions
Section 2
Classroom Practice Problems
• A 62.0 kg astronaut on a spacewalk tosses a
0.145 kg baseball at 26.0 m/s out into space.
With what speed does the astronaut recoil?
– Step 1: Find the initial momentum of both astronaut
and baseball.
• Answer: zero because vi = 0 for both
– Step 2: Since pi = 0, then pf, astronaut= -pf, baseball
– Step 3: Substitute and solve for vf,astronaut
• Answer: -0.0608 m/s or -6.08 cm/s
• Does a pitcher recoil backward like the astronaut
when throwing the ball? Explain.
Momentum and Collisions
Section 2
Classroom Practice Problem
• Gerard is a quarterback and Tyler is a defensive
lineman. Gerard’s mass is 75.0 kg and he is at
rest. Tyler has a mass of 112 kg, and he is
moving at 8.25 m/s when he tackles Gerard by
holding on while they fly through the air. With
what speed will the two players move together
after the collision?
• Answer: 4.94 m/s
Momentum and Collisions
Section 2
Now what do you think?
• Two skaters have equal mass and are at
rest. They are pushing away from each
other as shown.
• Compare the forces on the two girls.
• Compare their velocities after the push.
• How would your answers change if the
girl on the right had a greater mass than
her friend?
• How would your answers change if the
girl on the right was moving toward her
friend before they started pushing apart?
Momentum and Collisions
Section 3
What do you think?
• Collisions are sometimes
described as elastic or
inelastic. To the right is a
list of colliding objects.
Rank them from most
elastic to most inelastic.
• What factors did you
consider when ranking
these collisions?
1.
2.
3.
4.
5.
A baseball and a bat
A baseball and a glove
Two football players
Two billiard balls
Two balls of modeling
clay
6. Two hard rubber toy
balls
7. An automobile collision
Momentum and Collisions
Perfectly Inelastic Collisions
• Two objects collide and stick together.
– Two football players
– A meteorite striking the earth
• Momentum is conserved.
• Masses combine.
Section 3
Momentum and Collisions
Section 3
Classroom Practice Problems
• An 2.0 x 105 kg train car moving east at 21 m/s
collides with a 4.0 x 105 kg fully-loaded train car
initially at rest. The two cars stick together. Find
the velocity of the two cars after the collision.
– Answer: 7.0 m/s to the east
• Now calculate the kinetic energy of the two cars
before and after the collision. Was kinetic energy
conserved?
– Answer: KEbefore= 4.4 x 107 J, KEafter= 1.5 x 107 J
• KE is not conserved. It is less after the collision.
Momentum and Collisions
Section 3
Inelastic Collisions
• Kinetic energy is less after the collision.
– It is converted into other forms of energy.
• Internal energy - the temperature is increased.
• Sound energy - the air is forced to vibrate.
• Some kinetic energy may remain after the
collision, or it may all be lost.
Momentum and Collisions
Section 3
Elastic Collisions
• Objects collide and return to their original shape.
• Kinetic energy remains the same after the collision.
• Perfectly elastic collisions satisfy both conservation laws
shown below.
Momentum and Collisions
Section 3
Elastic Collisions
• Two billiard balls collide
head on, as shown. Which
of the following possible
final velocities satisfies the
law of conservation of
momentum?
– vf,A = 2.0 m/s, vf,B = 2.0 m/s
– vf,A = 0 m/s, vf,B = 4.0 m/s
– vf,A = 1.5 m/s, vf,B = 2.5 m/s
• Answer: all three
m = 0.35 kg
m = 0.35 kg
v = 4.0 m/s
v = 0 m/s
Momentum and Collisions
Section 3
Elastic Collisions
• Two billiard balls collide
head on, as shown. Which
of the following possible
final velocities satisfies the
law of conservation of
kinetic energy?
– vf,A = 2.0 m/s, vf,B = 2.0 m/s
– vf,A = 0 m/s, vf,B = 4.0 m/s
– vf,A = 1.5 m/s, vf,B = 2.5 m/s
• Answer: only vf,A = 0 m/s,
vf,B = 4.0 m/s
m = 0.35 kg
m = 0.35 kg
v = 4.0 m/s
v = 0 m/s
Momentum and Collisions
Types of Collisions
Click below to watch the Visual Concept.
Visual Concept
Section 3
Momentum and Collisions
Types of Collisions
Section 3
Momentum and Collisions
Section 3
Now what do you think?
• To the right is a list of
colliding objects. Rank
them from most elastic to
most inelastic.
• What factors did you
consider when ranking
these collisions?
1.
2.
3.
4.
5.
A baseball and a bat
A baseball and a glove
Two football players
Two billiard balls
Two balls of modeling
clay
6. Two hard rubber toy
balls
7. An automobile collision
Momentum and Collisions
Preview
• Multiple Choice
• Short Response
• Extended Response
Section 3
Momentum and Collisions
Section 3
Multiple Choice, continued
2. The vector below represents the momentum of a car
traveling along a road.
The car strikes another car, which is at rest, and the
result is an inelastic collision. Which of the following
vectors represents the momentum of the first car
after the collision?
F.
G.
H.
J.
Momentum and Collisions
Section 3
Multiple Choice, continued
3. What is the momentum of a 0.148 kg baseball
thrown with a velocity of 35 m/s toward home
plate?
A. 5.1 kg • m/s toward home plate
B. 5.1 kg • m/s away from home plate
C. 5.2 kg • m/s toward home plate
D. 5.2 kg • m/s away from home plate
Momentum and Collisions
Section 3
Multiple Choice, continued
Use the passage below to answer questions 4–5.
After being struck by a bowling ball, a 1.5 kg bowling
pin slides to the right at 3.0 m/s and collides head-on
with another 1.5 kg bowling pin initially at rest.
4. What is the final velocity of the second pin if the first
pin moves to the right at 0.5 m/s after the collision?
F. 2.5 m/s to the left
G. 2.5 m/s to the right
H. 3.0 m/s to the left
J. 3.0 m/s to the right
Momentum and Collisions
Section 3
Multiple Choice, continued
Use the passage below to answer questions 4–5.
After being struck by a bowling ball, a 1.5 kg bowling
pin slides to the right at 3.0 m/s and collides head-on
with another 1.5 kg bowling pin initially at rest.
5. What is the final velocity of the second pin if the first
pin stops moving when it hits the second pin?
A. 2.5 m/s to the left
B. 2.5 m/s to the right
C. 3.0 m/s to the left
D. 3.0 m/s to the right
Momentum and Collisions
Section 3
Multiple Choice, continued
6. For a given change in momentum, if the net
force that is applied to an object increases,
what happens to the time interval over which
the force is applied?
F. The time interval increases.
G. The time interval decreases.
H. The time interval stays the same.
J. It is impossible to determine the answer
from the given information.
Momentum and Collisions
Section 3
Multiple Choice, continued
8. Two shuffleboard disks of equal mass, one of which
is orange and one of which is yellow, are involved in
an elastic collision. The yellow disk is initially at rest
and is struck by the orange disk, which is moving
initially to the right at 5.00 m/s. After the collision, the
orange disk is at rest. What is the velocity of the
yellow disk after the collision? Think energy!
F. zero
G. 5.00 m/s to the left
H. 2.50 m/s to the right
J. 5.00 m/s to the right
Momentum and Collisions
Section 3
Multiple Choice, continued
Use the information below to answer questions 9–10.
A 0.400 kg bead slides on a straight frictionless wire and moves
with a velocity of 3.50 cm/s to the right, as shown below. The
bead collides elastically with a larger 0.600 kg bead that is
initially at rest. After the collision, the smaller bead moves to the
left with a velocity of 0.70 cm/s.
9. What is the large bead’s velocity after the collision?
A. 1.68 cm/s to the right
B. 1.87 cm/s to the right
C. 2.80 cm/s to the right
D. 3.97 cm/s to the right
Momentum and Collisions
Section 3
Multiple Choice, continued
Use the information below to answer questions 9–10.
A 0.400 kg bead slides on a straight frictionless wire and moves
with a velocity of 3.50 cm/s to the right, as shown below. The
bead collides elastically with a larger 0.600 kg bead that is
initially at rest. After the collision, the smaller bead moves to the
left with a velocity of 0.70 cm/s.
10. What is the total kinetic energy of the system after the collision?
F. 1.40  10–4 J
G. 2.45  10–4 J
H. 4.70  10 –4 J
J. 4.90  10 –4 J
Momentum and Collisions
Section 3
Short Response
11. Is momentum conserved when two objects
with zero initial momentum push away from each
other?
Momentum and Collisions
Section 3
Short Response, continued
An 8.0 g bullet is fired into a 2.5 kg pendulum
bob, which is initially at rest and becomes
embedded in the bob. The pendulum then
rises a vertical distance of 6.0 cm.
13. What was the initial speed of the bullet? Show
your work.
Momentum and Collisions
Section 3
Short Response, continued
Base your answers to questions 13–14 on the
information below.
An 8.0 g bullet is fired into a 2.5 kg pendulum
bob, which is initially at rest and becomes
embedded in the bob. The pendulum then
rises a vertical distance of 6.0 cm.
14. What will be the kinetic energy of the pendulum
when the pendulum swings back to its lowest
point? Show your work.
Momentum and Collisions
Section 3
Extended Response
15. An engineer working on a space mission
claims that if momentum concerns are taken into
account, a spaceship will need far less fuel for
the return trip than for the first half of the
mission.Write a paragraph to explain and
support this hypothesis.