Download 7-1 Momentum and Its Relation to Force

Chapter 7
Linear Momentum
Objectives
Students should be able to:
1. Define linear momentum and calculate it.
2. Distinguish between the unit of force and
momentum.
3. design an experiment in order to make
conclusions about the total momentum in a
system before and after a collision or
explosion.
Units of Chapter 7
•Momentum and Its Relation to Force
•Conservation of Momentum
•Collisions and Impulse
•Conservation of Energy and Momentum in
Collisions
•Elastic Collisions in One Dimension
Units of Chapter 7
•Inelastic Collisions
•Collisions in Two or Three Dimensions
•Center of Mass (CM)
•CM for the Human Body
•Center of Mass and Translational Motion
Let’s start with everyday
language
What do you say when a sports team
is on a roll?
They may not have the lead but they
may have ___________
MOMENTUM
A team that has momentum is hard to
stop.
Momentum Defined
p = mv
p = momentum
vector
m = mass
v = velocity vector
Momentum
• Momentum depends on the mass of an
object and the speed it is going.
– Momentum = mass x velocity
• Because velocity has direction then
momentum does, also.
Momentum of Objects
• Put the following in the order of most
momentum to least:
–
–
–
–
–
Mosquito
Automobile
Space Shuttle
Bullet
Freight Train
Questions
• Does a small object always have less
momentum than a large one?
• How can a bullet from a rifle knock over
an animal?
Which has more momentum?
• A truck or a roller skate rolling down a hill
with the same speed?
• A truck stopped at a light or a marble
rolling down the road?
• When could the roller skate and the truck
have the same momentum?
What is Momentum?
An object with a lot of momentum is also hard to
stop
Momentum = ρ = mv
Units: kg∙m/s
m=mass
v=velocity
Momentum is also a vector (it has direction)
Momentum
MASS
Momentum is _________
in
MOTION
________.
Momentum is a vector quantity.
Momentum is dependant on the
VELOCITY
mass and the ___________
of
an object.
Momentum Facts
• p = mv
• Momentum is a vector quantity!
• Velocity and momentum vectors point in the same direction.
• SI unit for momentum: kg·m/s (no special name).
• Momentum is a conserved quantity (this will be proven later).
• A net force is required to change a body’s momentum.
• Momentum is directly proportional to both mass and speed.
• Something big and slow could have the same momentum as
something small and fast.
Momentum Examples
10 kg
3 m/s
10 kg
30 kg · m
/s
Note: The momentum vector does not have to be
drawn 10 times longer than the velocity vector,
since only vectors of the same quantity can be
compared in this way.
26º
5g
p = 45 kg · m /s
at 26º N of E
Equivalent Momenta
Car: m = 1800 kg; v = 80 m /s
p = 1.44 ·105 kg · m /s
Bus: m = 9000 kg; v = 16 m /s
p = 1.44 ·105 kg · m /s
Train: m = 3.6·104 kg; v = 4 m /s
p = 1.44 ·105 kg · m /s
continued on next slide
Equivalent Momenta
(cont.)
The train, bus, and car all have different masses and
speeds, but their momenta are the same in magnitude. The
massive train has a slow speed; the low-mass car has a
great speed; and the bus has moderate mass and speed.
Note: We can only say that the magnitudes of their
momenta are equal since they’re aren’t moving in the
same direction.
The difficulty in bringing each vehicle to rest--in terms of a
combination of the force and time required--would be the
same, since they each have the same momentum.
7-1 Momentum and Its Relation to Force
Momentum is a vector symbolized by the
symbol p, and is defined as
(7-1)
The rate of change of momentum is equal to the
net force:
(7-2)
This can be shown using Newton’s second law.
Newton’s Law and Momentum
• Newton’s Second Law can be used to relate the
momentum of an object to the resultant force
acting on it




v (mv )
Fnet  ma  m

t
t
• The change in an object’s momentum divided
by the elapsed time equals the constant net
force acting on the object


p change in momentum

 Fnet
t
time interval
May 22, 2017
Problem
 A 1200 kg car drives west at 25 m/s for 3 hours.
What is the car’s momentum?
 Identify the variables:



1200 kg = m
25m/s, west = v
3 hours = t
p = mv
p = (1200kg)(25m/s) = 30000 kgm/s, west
Example 7-1: Force of a tennis serve.
For a top player, a tennis
ball may leave the racket on
the serve with a speed of 55
m/s (about 120 mi/h). If the
ball has a mass of 0.060 kg
and is in contact with the
racket for about 4 ms (4 x
10-3 s), estimate the average
force on the ball.
Copyright © 2009 Pearson Education, Inc.
Example 7-1: Force of a tennis serve.
For a top player, a tennis ball
may leave the racket on the
serve with a speed of 55 m/s
(about 120 mi/h). If the ball has a
mass of 0.060 kg and is in
contact with the racket for about
4 ms (4 x 10-3 s), estimate the
average force on the ball.
Would this force be large
enough to lift a 60-kg
person?
Copyright © 2009 Pearson Education, Inc.
Example 7-2: Washing a car: momentum
change and force.
Water leaves a hose at a rate of 1.5 kg/s with
a speed of 20 m/s and is aimed at the side of
a car, which stops it. (That is, we ignore any
splashing back.) What is the force exerted by
the water on the car?
Copyright © 2009 Pearson Education, Inc.
Homework
• Be ready with your procedure for next class.
• In two days, complete chapter 7 problems 1,
3, and 5.
Leading to Inquiry for Total
Momentum of a System Before
and After a Collision or explosion
 Each group will have a different type of
collision or explosion. Some will overlap
since we will focus on three types of
collisions/explosions.
Momentum – Elastic Collisions
 Elastic Collision – a collision in which the colliding bodies do not
stick together.
© 2001-2007 Shannon W. Helzer. All Rights Reserved.
Momentum – Inelastic Collisions
 Inelastic Collision – a collision in which the colliding bodies stick
together.
© 2001-2007 Shannon W. Helzer. All Rights Reserved.
Explosions
M
v1
m1
“before”
m2
v2
“after”
Momentum
 Identify the number and types of collisions in the animation below.
© 2001-2007 Shannon W. Helzer. All Rights Reserved.
Momentum
 Identify the number and types of collisions in the animation below.
© 2001-2007 Shannon W. Helzer. All Rights Reserved.
Momentum
 Identify the number and types of collisions in the animation below.
© 2001-2007 Shannon W. Helzer. All Rights Reserved.
Inquiry for Total Momentum Before
and After a Collision/Explosion
• PROBLEM
• Design an experiment to demonstrate the
effect of a collision/explosion on total
momentum of the objects before and after
using the same mass for each cart and then
for a second experiment change one of the
cart’s mass by adding mass.
Inquiry for Total Momentum Before
and After a Collision/Explosion
• Design an experiment to demonstrate the effect of a collision/explosion
on total momentum of the objects before and after using the same mass
for each cart and then for a second experiment change one of the cart’s
mass by adding mass to it.
• Make a prediction on the effect of some condition on the
total momentum before and after a collision.
• Materials
–
–
–
–
–
Dynamics cart with spring bumper or plunger
Meter stick
Stop watch
Masses
Large white boards
Inquiry for Total Momentum Before and
After a Collision/Explosion
• Your group will present using the whiteboards your
design and findings.
• Did anything unusual happen? Were there any special insights you gained
and want to make a note of? Were there any changes made to your
procedure? What new questions arose?
• Were any of the results NOT what you expected?
• Which of your pre-lab ideas have you decided are now incorrect? Why?
• Did the data support your original hypothesis?
• If not, what hypothesis does the data support?
Objectives: The student will be able
to:
Perform several investigations in order to make
conclusions about the total momentum in a system
before and after collisions or explosions.
Inquiry for Total Momentum Before
and After a Collision/Explosion
• Design an experiment to demonstrate the effect of a collision/explosion
on total momentum of the objects before and after using the same mass
for each cart and then for a second experiment change one of the cart’s
mass by adding mass to it.
• Make a prediction on the effect of some condition on the
total momentum before and after a collision.
• Materials
–
–
–
–
–
Dynamics cart with spring bumper or plunger
Meter stick
Stop watch
Masses
Large white boards
Inquiry for Total Momentum Before and
After a Collision/Explosion
• Your group will present using the whiteboards your
design and findings.
• Did anything unusual happen? Were there any special insights you gained
and want to make a note of? Were there any changes made to your
procedure? What new questions arose?
• Were any of the results NOT what you expected?
• Which of your pre-lab ideas have you decided are now incorrect? Why?
• Did the data support your original hypothesis?
• If not, what hypothesis does the data support?
Evaluation
•
Individually, you will make a claim about each investigation with supporting
evidence, and then explain how the conservation of momentum can be applied to
these investigations.
• What conclusion(s) did you reach due to the results of this experiment?
• What evidence supports your conclusion(s)?
• Are your results reliable? How did you compensate for sources of error in the
experiment?
• Can you test the predictions? If so, do results agree with your conclusion(s)?
• What new problems/questions does the experiment bring up?
RELATE
• What are some possible applications of your conclusions to the real world
situations?
• Do the results of your experiment fit any laws/theories of physics?
•
This will be due
.
Conclusions
• Based on the investigations, what conclusion
can you make about the momentum in a
system?
• Kahoot 7-1