Download 6 ppt Momentum and Collisions

Chapter 6
Momentum and Collisions
6.1 Momentum and Impulse
Linear Momentum
After a bowling ball strikes the pins, its speed and
direction change. So does the speed and direction of the
pins.
Newton’s laws can be used to calculate the motion of the
ball after it hits the pins.
The force and duration of a collision between objects
affects the motion of both.
Momentum is mass times velocity
The momentum of an object is simply its mass times its
velocity.
Momentum is represented by the symbol “p”.
Momentum is a vector quality. It is expressed as
kilograms times meters per second (kg . m/s)
The faster you move, the more
momentum you will have.
This is why it is harder to stop when you are moving
faster than when going slower.
An object that is heavier but traveling at the same speed
as another, will have more momentum.
Light objects traveling at great speeds can have a lot of
momentum like hailstones!
video
Practice A
Momentum
A 2250 kg pickup truck has a velocity of 25 m/s to the
east.
What is the momentum of the truck?
p = mv
Answer
5.6 x 104 kg . m/s to the east or
56,000
A change in momentum takes force and time
It takes more force to stop a ball that is moving quickly
than one that is moving slowly.
Think about catching a fast ball versus one that is
moving slowly.
Think about how much force is
needed to stop a train versus a car.
video
Practice B
Force and Impulse
A 1400 kg car moving eastward with a velocity of 15 m/s
collides with a utility pole and is brought to rest in 0.30 s.
Find the force exerted on the car during the collision.

Answer
7.0 x 104 N to the east or
70,000 N
Stopping times and distance depend on the
impulse-momentum theorem
Highway safety engineers use
the impulse-momentum
theorem to determine stopping
distances and safe following
distances for vehicles.
A truck hauling bricks can have
twice the mass of an empty
truck. Therefore, it will have
twice the momentum.
Having the same type of
brakes, the heavier truck will
take twice the distance to stop.
video
Practice C
Stopping Distance
A 2240 kg car traveling west slows down uniformly from
20.0 m/s to 5.00 m/s.
How long does it take the car to decelerate if the force
on the car is 8410 N to the east?
How far does the car travel during the deceleration?
Answer
4.00 s
Answer
-50.0 m
Force is reduced when the time interval of an
impact is increased
The impulse-momentum theorem
is used to design safety
equipment.
This equipment is able to reduce
the force exerted on the human
body during collisions.
The falling girl in this photo has the
same momentum whether she hits
the ground or the mat.
The mat however changes her
momentum over a longer period of
time.
When an egg falls on a hard
surface, it comes to rest in a short
period of time.
If it lands on a pillow, its
momentum is changed over a
longer period of time.
By applying a small force to the
egg over a longer period of time,
the change in momentum is still
the same, the results very
different.
Questions
1. The momentum of an object is simply its mass
velocity
times its _________.
2. An object that is heavier but traveling at the
same speed as another, will have more ________
momentum
force to stop a ball that is
3. It takes more ______
moving quickly than one that is moving slowly.
4. By applying a small force to a falling egg over a
time the change in momentum
longer period of ______,
is still the same, the results very different.
6.2 Conservation of Momentum
Momentum is Conserved
Now we will consider the momentum of two or more
objects interacting.
Below ball A is moving towards a stationary ball, B.
Once they collide, ball A becomes stationary and ball B
continues at the velocity A was at.
This collision caused all of ball A’s momentum to go to B.
Lets see
how this
looks with
numbers…
The total momentum of each ball remains constant.
This is known as the law of conservation of momentum.
The total momentum of all objects interacting with one
another remains constant regardless of the nature of the
forces between the objects.
Momentum is conserved in collisions
Total momentum is conserved in a system.
Any additional objects added will interact the same,
conserving the momentum.
At this point, however, frictional forces have been
disregarded.
Momentum is conserved for objects pushing away
from each other
Momentum is also conserved when two objects at rest
push away from each other.
They move in opposite directions with equal momentum.
video
Practice D
Conservation of Momentum
A 76 kg boater, initially at rest in a stationary 45 kg boat,
steps out of the boat and onto a dock.
If the boater moves out of the boat with a velocity of 2.5
m/s to the right what is the final velocity of the boat?
Because v1 and v2 are 0 m/s, we can cancel out…

Answer
4.2 m/s to the left
Newton’s third law leads to conservation of
momentum
Consider two bumper cars with velocities of v1i and v2i.
After they collide there velocities become v1f and v2f.
The impulse-momentum theorem FΔt = Δp describes
their change in momentum.
Newton’s third law tells us the force acting on these cars
is equal and opposite.
To simplify, if the momentum of one object increases
then the momentum of the other decreases.
How can this be if both are conserved?
Answer; this only occurs because the direction changes,
the magnitude stays the same it is only equal but
opposite.
Forces in real collisions are not constant during the
collision
In real collisions the forces may vary in time in a
complicated way.
During the collision, the forces are equal and opposite in
magnitude.
In solving impulse problems, we
use average force over time.
Questions
1. T / F Momentum is not conserved in collisions.
false
2. T / F Momentum is conserved for objects
pushing away from each other. true
3. If the momentum of one object increases then
decreases
the momentum of the other __________.
4. T / F Forces in real collisions are not constant
during the collision.
true
6.3 Elastic and Inelastic Collisions
Collisions
Total momentum remains constant in any type of
collision.
However, the total kinetic energy is generally not
conserved.
This is because some kinetic energy is converted to
internal energy when the objects deform.
video
Perfect inelastic collisions can be
analyzed in terms of momentum
When two football players, collide and move as one
mass, this is known as a perfectly inelastic collision.
Perfectly inelastic collisions are easy to analyze in terms
of momentum because they essentially become one
object afterwards.
Their final mass is equal to their combined mass.
Practice E
Perfect Inelastic Collisions
A 1850 kg luxury sedan stopped at a traffic light is struck
from the rear by a compact car with a mass of 975 kg.
The two cars become entangled as a result of the collision.
If the compact car was moving at a velocity of 22.0 m/s
before the collision, what is the velocity of the two after?
m1 = 1850
m2 = 975
v1 = 0 m/s

answer
7.59 m/s
v2 = 22.0 m/s
Kinetic energy is not conserved in inelastic collisions
Total kinetic energy is not conserved with an inelastic collision.
Some of the energy is lost to sound and to internal energy as
the objects deform.
Elastic collisions allow the objects to return to their original
shape. With inelastic they stay deformed.
Practice F
Kinetic Energy in Perfectly Inelastic
Collisions
Two clay balls collide head-on in a perfectly inelastic
collision.
The first ball has a mass of 0.500 kg and an initial
velocity of 4.00 m/s to the right.
The second has a mass of 0.250 kg and an initial
velocity of 3.00 m/s to the left.
What is the decrease in kinetic energy during the
collision?
m1 = 0.500 kg
m2 = 0.250 kg
v1 = to the right = 4.00 m/s
v2 = to the left = - 3.00 m/s

Unknown: ∆KE = KEf – KEi = ?
Since our collision is perfectly inelastic,
they will stay and travel together as one
object. We must solve for vf first.

Answer
1.67 m/s to the right
KEi = ½(0.500 kg)(4.00 m/s)2 + ½(0.250 kg)(-3.00)2 = 5.12 J
KEf = ½(0.500 kg + 0.250 kg)(1.67 m/s)2 = 1.05 J
KEf – KEi = 1.05 J – 5.12 J = -4.07 J
( - ) indicates energy lost
Elastic Collisions
In an elastic collision, two objects collide and then return
to their original shape.
No kinetic energy is lost in this process.
In the other collisions we have learned about,
momentum was the only thing that was conserved.
Elastic collisions are the only type that both are
conserved.
Video
Most collisions are neither elastic nor perfectly
inelastic
In real life there really is no such thing as perfectly elastic
or inelastic.
In most collisions, some of the kinetic energy is converted
to into sound, such as two billiard balls clicking as they hit.
So any collision that produces sound can not be perfectly
elastic.
Kinetic energy is conserved in elastic collisions
The two soccer balls below are colliding but at different
velocities.
During the collision, the impulse will be equal but the
momentum of each ball will change.
After the collision the slower ball will reverse direction
and then travel at the velocity of the faster ball.
In the case of a golf ball being hit, the ball accelerates
from a velocity of zero and the club is slowed due to the
impulse during contact.
The momentum is conserved.
Since this is an elastic collision, the kinetic energy is
conserved as well.
Summary
This table summarizes out three type of collisions
Practice G
Elastic Collisions
Two marbles are colliding as shown above.
What will the velocity and direction of the 0.030 kg
marble be after the collision?

Answer
0.090 m/s to the right
Questions
momentum remains constant in any type
1. Total __________
of collision.
2. T / F Total kinetic energy is conserved with an
inelastic collision. false
3. Elastic collisions allow the objects to return to
deformed
their original shape. With inelastic they stay _____
elastic is the
4. Of the three types of collisions, _______
only one where momentum and kinetic energy are
conserved.
Elastic or Inelastic?
Elastic or Inelastic?
Elastic or Inelastic?
Elastic or Inelastic?
Elastic or Inelastic?
End