Transcript Momentum!!!
Momentum!!!
Physics
Mr. Padilla
Mr. Padilla, what is momentum?
Momentum is the inertia of motion.
Newton’s 1st Law of Motion
A moving objects desire to remain moving.
Momentum is the mass of an object
multiplied by its velocity.
p = mv
Units: (kg)(m/s) = (kgm)/s
Can we do some examples?
Ted runs at a speed of
7.5m/s. If Ted has a
mass of 80kg, what is
his momentum?
What is the momentum
of a golf ball with a
mass of .01kg, rolls
down a hill at a speed
of 5m/s?
Can you think of a time
when Ted and the golf
ball will have the same
momentum?
p = mv
p = (80kg)(7.5m/s)
p = 600 kgm/s
p = mv
p = (.01kg)(5m/s)
p = .05 kgm/s
When velocity = 0
Sample Problem 6A
A 2250 kg pickup truck has a velocity of 25
m/s to the east. What is the momentum of
the truck?
How can we change momentum?
Momentum can change by changing the
objects mass or its velocity.
It is more common to change its velocity by
undergoing acceleration
Since force causes acceleration, applying
a force will cause a change in momentum.
How long the force is applied will
determine how much the momentum is
changed.
Impulse
Impulse is force applied over time.
Impulse (Δp) = Ft
Impulse is also equal to the change in
momentum.
Ft = Δ(mv)
Δp = mvf - mvi
Units = Ft = Ns
Ns = kgm/s
Impulse –Momentum Theorem
FΔt = Δp
FΔt = mvf - mvi
Examples of impulse.
If you were in an out of control car, would
you rather stop by hitting a brick wall or a
large hay stack?
The hay stack is the smart answer.
Both will apply the same change in
momentum, impulse, but the wall will do it
over a shorter time, and so will exert more
force. Ft is the same for both.
Sample Problem 6B
A 1400 kg car moving westward with a
velocity of 15 m/s collides with a utility pole
and is brought to a rest in 0.30 s. Find the
magnitude of the force exerted on the car
during the collision.
Bouncing
Which would change velocity more,
bringing a fast moving object to a stop or
sending it back in the opposite direction?
For the same reasons, momentum is
changed more if an object bounces.
This means there is also a greater impulse
exerted.
Example 1
300kg of water rushes Δ(mv) = Ft
down a hill at 15m/s,
(300kg)(15m/s) = F(5s)
it hits a dam and is
4500Ns = F(5s)
900N = F
brought to a stop.
How much force must
the dam exert to stop
it in 5s?
Example 2
If, in the last example,
the water was turned
and moved back the
way it came at 10m/s,
what would be the
impulse?
What would be the
force exerted?
Impulse = Δ(mv)
(300kg)(15m/s) (300kg)(-10m/s)
4500Ns - -3000Ns
7500Ns
Impulse = Ft
7500Ns = F(5s)
1500N = F
Sample Problem 6C
A 2250 kg car traveling to the 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 8450 N to the
east? How far does the car travel during
the deceleration?
Conservation
If no net force or net impulse acts on a
system, the momentum of that system
cannot change.
When momentum, or any quantity does
not change, we say it is conserved.
Law of Conservation of Momentum
In the absence of an external force, the
momentum of a system remains unchanged.
Momentum in a System
When a cannon fires a cannon-ball, the cannon
exerts a force on the cannon-ball and the
cannon-ball exerts an equal and opposite force
on the cannon according to Newton’s 3rd Law.
Before the firing, the system is at rest, so the
momentum is zero.
After it is fired, the net momentum, or total
momentum is still zero.
Look at it with calculations…
Total initial momentum = total final
momentum
p1i + p2i = p1f + p2f
(m1v1)i + (m2v2)i = (m1v1)f + (m2v2)f
When is Momentum Conserved?
If a system undergoes changes, where all
forces are internal, the net momentum
before and after the event are the same.
Examples:
Cars colliding
Stars exploding
Sample Problem 6D
A 76 kg boater, initially at rest in a
stationary 45 kg boat, steps out of the boat
and onto the 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?
Homework, Hooray!!!
Practice Problems
6A-D (odds only)
And Now…
Collisions !!!!!!!!
Collisions
When ever 2 objects collide and there are
no external forces the net momentum of
both objects before the collision equals the
net momentum after the collision.
net momentum
before
net momentum
mv mv
i
f
after
Types of Collisions
3 kinds
Elastic – Objects collide without being
permanently deformed and with out
generating heat.
Objects bounce perfectly in elastic collisions
Perfectly Inelastic – Colliding objects get
tangled and coupled together.
Inelastic – objects deform during collisions,
but move separately after collision
Perfectly Inelastic
Elastic
2 objects collide and
Kinetic energy is
move off as one
conserved in perfectly
mass.
elastic collisions
(m1v1)i + (m2v2)i =
pi =pf
and
(m1+m2)vf
KEi = KEf
KE is NOT constant in
inelastic collisions
Some KE is converted
to sound and internal
energy
Sample Problem 6E
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 to the north before
the collision, what is the velocity of the
entangled mass after the collision?
Most collisions involve some external
force.
Most external forces are negligible
during a collision.
Perfectly elastic collisions are not
common in the everyday world.
Heat is usually generated by any collision.
They only occur regularly on the microscopic
level
Sample Problem 6F
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 mass
of the second ball is 0.250 kg, and it has
an initial velocity of 3.00 m/s to the left.
What is the final velocity of the composite
ball of clay after the collision? What is the
decrease in kinetic energy during the
collision?
Elastic Collisions
Remember:
Kinetic energy is conserved in elastic collisions
(m1v1)i + (m2v2)i = (m1v1)f + (m2v2)f
or
( ½ m1v12)i + ( ½ m2v22)i = ( ½ m1v12)f + ( ½ m2v22)f
Sample Problem 6G
A 0.015 kg marble moving to the right at
0.225 m/s makes an elastic head-on
collision with a 0.030 kg shooter marble
moving to the left at 0.180 m/s. After the
collision, the smaller marble moves to the
left at 0.315 m/s. Assume that neither
rotates before or after the collision and
that both marbles are moving on a
frictionless surface. What is the velocity of
the 0.030 kg marble after the collision?