CHAPTER 6
Momentum
Momentum (p)
• Momentum = mass x velocity
• Momentum is a measure of inertia in motion
– how much motion an object has
•
p = mv
• A really slow moving truck (
m ) and an
v
v
extremely fast roller skate (m ) can have
the same momentum.
• Units for momentum are kg*m/s
Example Questions
• A 100 kg cart is moving with a velocity of 5
m/s, what is its momentum?
• 500 kg*m/s
• A 2 kg bowling ball is rolling with a speed
of 5 m/s, what is its momentum?
• 10 kg*m/s
Change in Momentum (Δp)
• A change in ‘p’ can only be caused by a
change in v (Δv)  Δp = mΔv
– Change in mass, WILL NOT change ‘p’
Δp Examples
• A 100 kg car increases its speed from 5
m/s to 15 m/s, what is its change in
momentum?
• Δp =mΔv = (100kg) (15m/s – 5m/s)
• = (100kg)(10m/s) = 1000 kg*m/s
Δp examples
• A 2 kg bowling ball slows down from 8 m/s
to 3 m/s, what is its change in momentum?
• Δp=mΔv = (2kg) (3m/s – 8m/s)
• = (2kg)(-5m/s) = -10 kg*m/s
What causes a Δp?
• Δp is only caused by a change in velocity (Δv)
• Δv means acceleration (a)
• Aaand Acceleration is caused by a Net Force
(Fnet)
• Sooo
Fnet causes Δp
Impulse & Momentum
• Applying a net Force for some time to an
object creates an acceleration which
changes the momentum
• Impulse = Force x time (Ft)
• (Ft) = Impulse = Δp = mΔv
Impulse – Momentum Theorem
• Impulse (Ft) = Change in Momentum (Δp)
• Ft = mΔv
• The impulse (Ft) is equal to the change in
momentum
MOMENTUM
• An object at rest has no momentum, why?
• Because anything times zero is zero
– If v= 0 then p=0
FORCE
• To INCREASE MOMENTUM,
apply the greatest force possible for as long
as possible.
• Examples :
• pulling a sling shot
•
•
•
drawing an arrow in a bow all the way back
a long cannon for maximum range
hitting a golf ball or a baseball
. (follow through is important for these !)
TIME
• https://www.youtube.com/watch?v=As3Nz
DQknVc
MOMENTUM
• Decreasing Momentum
• Which would it be more safe to hit in a car ?
mv
t
F
mv
F
• Knowing the physics helps us understand why
t
hitting a soft object is better than hitting a hard one.
MOMENTUM
• In each case, the momentum is decreased by the same
amount --- Δp
is same for both
is same for both, sooo impulse (Ft)
• Hitting the haystack extends the impact time
• The longer impact time reduces the force of impact and
decreases the deceleration.
• Whenever it is desired to decrease the force of impact,
extend the time of impact !
DECREASING Impact Force
• If the time of impact is increased by 100 times (say from .01
sec to 1 sec), then the force of impact is reduced by 100
times (say to something survivable).
•
•
•
•
EXAMPLES :
Padded dashboards on cars
Airbags in cars
or
safety nets in circuses
Moving your hand backward as you catch a fast-moving ball
with your bare hand
or
a boxer moving with a punch.
• Flexing your knees when jumping from a higher place to the
ground.
or
elastic cords for bungee jumping
• Using wrestling mats instead of hardwood floors.
• Dropping a glass dish onto a carpet instead of a sidewalk.
EXAMPLES OF DECREASING
MOMENTUM
F = change in
t
momentum
t = change in
F
momentum
• Increased impact time reduces force of impact
Ft = Δmv applies here.
• Bungee Jumping …
mv = the momentum gained before the cord
begins to stretch that we wish to change.
Ft = the impulse the cord supplies to
reduce the momentum to zero.
Because the rubber cord stretches for
a long time the average force on the
jumper is small.
Questions :
• When a dish falls, will the impulse be less if
it lands on a carpet than if it lands on a hard
ceramic tile floor ?
• The impulse would be the same for either surface because
there is the same momentum change for each. It is the
force that is less for the impulse on the carpet because of
the greater time of momentum change. There is a
difference between impulse and impact.
• If a boxer is able to increase the impact time
by 5 times by “riding” with a punch, by how
much will the force of impact be reduced?
• Since the time of impact increases by 5 times, the force of
impact will be reduced by 5 times.
Bouncing
• IMPULSES ARE GREATER WHEN AN OBJECT
BOUNCES, b/c greater Δp when v goes from + to than from + to 0
• The impulse required to bring an object to a stop and
then to throw it back upward again is greater than
the impulse required to merely bring the object to a
stop.
• When a martial artist breaks boards,
• does their hand bounce?
• Is impulse or momentum greater ?
• Example :
• The Pelton Wheel.
The Law of Conservation of Momentum
• Unless there is an external force acting on a
system, the momentum of the system remains
unchanged.
• If there are no outside forces, total momentum of
a system remains constant
• This means that, when all of the forces are internal
(for EXAMPLE: the nucleus of an atom undergoing
.
radioactive decay,
.
cars colliding, or
.
stars exploding
the net momentum of the system before and after the
event is the same.
Difference between internal &
external forces…
• The force or impulse on the object must come
from outside the object. (we talked about this with
Newton’s 3rd Law )
• EXAMPLES: The air in a basketball,
sitting in a car and pushing on the dashboard
or sitting in a boat and blowing on the sail
don’t create movement.
• Internal forces like these are balanced and cancel
each other.
• If no outside force is present, no change in
momentum is possible.
QUESTIONS
• 1. Newton’s second law states that if no net force is
exerted on a system, no acceleration occurs. Does
that also mean that no change in momentum
occurs?
• No acceleration means that no change occurs in
velocity and therefore no change in momentum.
• 2. Newton’s 3rd law states that the forces exerted on
a cannon and cannonball are equal and opposite.
Does it follow that the impulse exerted on the
cannon and cannonball are also equal and opposite?
• Since the time interval and forces are equal and
opposite, the impulses (F x t) are also equal and
opposite.
The Law of Conservation of
Momentum
• No change in momentum occurs unless outside
force acts
•
•
•
•
•
•
Initial total momentum = Final Total Momentum
For a collision between 2 objects...
Ʃpbefore = Ʃpafter
Ʃmvbefore = Ʃmvafter
P1i + p2i = p1f + p2f
Or m1v1i + m2v2i = m1v1f + m2v2f
COLLISIONS
• ELASTIC COLLISIONS
Momentum transfer from one
Object to another .
Is a Newton’s cradle like the one
Pictured here, an example of an
elastic or inelastic collision?
• INELASTIC COLLISIONS
Problem Solving #1
(write this down)
• A 6 kg fish swimming at 1 m/sec swallows a 2 kg fish
that is at rest. Find the velocity of the fish immediately
after “lunch”.
• System is both fish, so …..
•
net momentum initial = net momentum final
• (6 kg)(1 m/sec) + (2 kg)(0 m/sec) = (6 kg + 2 kg)(vf)
•
6 kg.m/sec = (8 kg)(vf)
•
vafter = 6 kg.m/sec / 8 kg
•
8 kg
vf =
•
vf = ¾ m/s
Problem Solving #2
• Now the 6 kg fish swimming at 1 m/sec swallows a 2 kg
fish that is swimming towards it at 2 m/sec. Find the
velocity of the fish immediately after “lunch”.
• System is both fish, so….
•
net momentum initial = net momentumfinal
•
(net mv)i = (net mv)f
• (6 kg)(1 m/s) + (2 kg)(-2 m/s) = (6 kg + 2 kg)(vafter)
• 6 kg.m/sec + -4 kg.m/sec = (8 kg)(vafter)
•
vafter = 2 kg.m/sec / 8 kg
•
8 kg
vafter =
•
vafter = ¼ m/sec
Problem Solving #3 & #4
• Now the 6 kg fish swimming at 1 m/sec swallows a 2
kg fish that is swimming towards it at 3 m/sec.
•
(net mv)i = (net mv)f
• (6 kg)(1 m/sec) + (2 kg)(-3 m/sec) = (6 kg + 2 kg)(vf)
• 6 kg.m/sec + -6 kg.m/sec = (8 kg)(vf)
•
vafter = 0 m/sec
• Now the 6 kg fish swimming at 1 m/sec swallows a 2
kg fish that is swimming towards it at 4 m/sec.
•
(net mv)i = (net mv)f
• (6 kg)(1 m/sec) + (2 kg)(-4 m/sec) = (6 kg + 2 kg)(vf)
• 6 kg.m/sec + -8 kg.m/sec = (8 kg)(vf)
•
vf = -.25 m/sec
MOMENTUM VECTORS
• Momentum can be analyzed by using vectors
• The momentum of a car accident is equal to the
vector sum of the momentum of each car A & B
before the collision.
A
B
MOMENTUM VECTORS (Continued)
• When a firecracker bursts, the vector sum of the momenta
of its fragments add up to the momentum of the firecracker
just before it exploded.
• The same goes for subatomic elementary particles. The
tracks they leave help to determine their relative mass and
type.
CHAPTER #8 - MOMENTUM
• Finish