Transcript Chapter 9 - Cloudfront.net

CHAPTER 9
Momentum
and Its
Conservation
WHAT’S THE RELATIONSHIP BETWEEN FORCE
AND VELOCITY?

What happens when the
baseball is struck by the bat?
_______________tells us that the
forces on the bat and ball are
equal.
 _______________tells us that
both bat and ball will
experience an acceleration
proportional to their masses.
 But what is the relationship
between the velocities of the
ball and the bat and the forces
they experience?

“THE BIG MO”: MOMENTUM
p  mv
 The
________________ p of an object of
mass m moving with a velocity v is
defined as the __________ of the ______
and the __________.


SI Units are kg m/s (Dimensions = ML/T)
Vector quantity, the direction of the momentum
is the same as the velocity’s.
MORE ABOUT MO

Momentum components:

px = m vx and py = m vy
Applies to two-dimensional motion.
 Again the direction of momentum and velocity are the
same.


Momentum is related to ________________.
We can derive an equation that relates KE and
momentum.
 More on kinetic energy in chapter 10.

CHANGING THE BIG MO
 How
does an object change its acceleration?
 How
would an object change its momentum?

In order to change the momentum of an object, a
_______________ must be applied.
IMPULSE
 The
_________of change of momentum of
an object is equal to the __________acting
on it.
p m(vf  vi )

 Fnet
t
t


Just like with acceleration, when the
__________is zero, no change occurs to
momentum.
Gives an alternative statement of Newton’s
second law.
IMPULSE

When a single, constant force acts on the
object, there is an ____________ delivered to the
object.
I  Ft
I
is defined as the impulse.
 ____________________, the direction is the same as
the direction of the __________.
 The impulse is also described using the letter J.
 Impulse is useful for describing ______________ that
do not last a long time. (More on this later.)

IMPULSE-MOMENTUM
THEOREM

The theorem states that the ___________ acting
on the object is equal to the ___________________
of the object.
I  Ft  p  mvf  mvi
This theorem holds for _________ and ____________
forces.
 If the force is not constant, use the average force
applied.

SAMPLE PROBLEM
Rico strikes a 0.058 kg golf ball with a force of
272 N and gives it a velocity of 62.0 m/s. How
long was Rico’s club in contact with the ball?
AVERAGE FORCE IN IMPULSE

The ______________can be thought of as the constant
force that would give the same impulse to the object in
the time interval as the actual time-varying force
gives in the interval.
Fav t  p
AVERAGE FORCE AND COLLISIONS
IMPULSE AND COLLISIONS

Impulse is most useful in describing _________ of
_______________.


The impulse-momentum theorem allows us to study
the effects that the ________________of a collision has
on the _________ felt by the ____________.
For example, why is it important for boxers to wear
boxing gloves?
CHANGING IMPULSE AND COLLISIONS
_____________ the contact time increases the
___________ but reduces the _________ during the
collision.
 Increasing force increases the impulse as well.

IMPULSE APPLIED TO AUTO
COLLISIONS

The most important factor is the ___________or
the time it takes the person to come to a rest.
Increasing the collision time is the key factor.
 This will reduce the chance of dying in a car crash.

WAYS TO INCREASE THE TIME
Crumple zones
Seat
belts
Air
bags
TYPICAL COLLISION VALUES
 For
a 75 kg person traveling at 27 m/s and
coming to stop in 0.010 s.
F = -2.0 x 105 N
 a = 280 g

 Almost
certainly fatal:
F = 90 kN fractures bone.
 a = 150 g for 4 ms causes spinal cord damage
(causes the nerves to enter the base of the brain)

COLLISIONS
 ______________
is conserved in any _________.
 ______________is not always conserved.

Some KE is converted to other forms of energy (i.e.
internal energy, sound energy, etc.) or is used to do
the work needed to deform an object.
 Two


broad categories of collisions:
Elastic collisions
Inelastic collisions: Perfectly inelastic and
inelastic
 Elastic
and perfectly inelastic collisions
represent ideal cases of collisions.
 Most real world cases fit somewhere between
these two extremes.
CONSERVATION OF MOMENTUM
 Momentum
in an
isolated system in which
a collision occurs is
conserved.
A collision may be the
result of _______________
between two objects.
 “Contact” may also arise
from the ______________
interactions of the
electrons in the surface
atoms of the bodies.
 An isolated system will
have no external forces
acting on the objects.

CONSERVATION OF MOMENTUM

The principle of conservation of momentum states
when no external forces act on a system consisting
of two objects that collide with each other, the total
momentum of the system remains constant in time.

F
Specifically, the total momentum before the collision
will equal the total momentum after the collision.
FORCES IN A COLLISION
 The
force with
which object 1
acts on object 2 is
equal and
opposite to the
force with which
object 2 acts on
object 1.
 Impulses are also
equal and
opposite.
CONSERVATION OF
MOMENTUM FORMULA
 Mathematically:
m1v1i  m2v2i  m1v1f  m2v2f




Momentum is conserved for the system of
objects.
The system includes _____________________
interacting with each other.
Assumes only internal forces are acting during
the collision.
Can be generalized to any number of objects.
SAMPLE PROBLEM
A 1875 kg car going 23 m/s rear-ends a 1025 kg
compact car going 17 m/s on ice in the same
direction. The two cars stick together. How fast
do the two cars move together immediately after
the collision?
RECOIL AND PROPULSION IN
SPACE
Xe atoms are expelled from the ion engine.
 vatoms = 30km/h; Fatoms = 0.092 N
 Advantage: runs for a very long time

GLANCING COLLISIONS
 For
a general collision of two objects in
three-dimensional space, the conservation
of momentum principle implies that the
total momentum of the system in each
direction is conserved.

m1v1ix  m2 v 2ix  m1v1f x  m2 v 2f x and
m1v1iy  m2 v 2iy  m1v1f y  m2 v 2f y


Use subscripts for identifying the object, initial
and final velocities, and components.
We will examine collisions in two-dimensions.
GLANCING COLLISIONS
The “after” velocities have x and y components.
 Momentum is conserved in the x direction and in
the y direction.
 Apply conservation of momentum separately to
each direction.

SAMPLE PROBLEM
A 1,500 kg car traveling
east with a speed of 25.0 m/s
collides at an intersection
with a 2,500 kg van
traveling north at a speed of
20.0 m/s as shown in the
figure. Find the direction
and magnitude of the
velocity of the wreckage
after the collision, assuming
that the vehicles undergo a
perfectly inelastic collision
and assuming that friction
between the vehicles and
the road can be neglected.
THE
END
CHAPTER 9
Momentum
and Its
Conservation