Download momentum

Impulse
And
Momentum
Have you ever
wondered…
1. Why Neo uses
“follow through”
when he throws
his knives?
2. Why Neo bends
his knees upon
landing impact?
3. Why does it hurt
Neo less to fall
on a wood floor
than a cement
one?
Momentum is a cornerstone in physics concepts.
It refers to the quantity of motion that an object has.
Conceptually, think of momentum as “inertia in motion.”
1
Momentum is a vector quantity. The magnitude
which is the product of mass and velocity and
whose direction is that of the velocity vector.
2
Newton’s first law explains that objects in motion “want” to
stay in motion. But just how much do moving objects wish to
stay in motion?
Does a 1 kg skate moving at 10 m/s “want” to stay in motion
as much as a 10,000 kg truck moving at the same speed?
To answer, think about which one would be harder to stop.
Better yet, which one would you rather have approaching
you?
The amount of momentum which an object has
is dependent upon two variables: how much
stuff is moving and how fast the stuff is moving.
In other words:
The size of the momentum is equal to the mass
of the object multiplied by the size of the object's
velocity.
3
In physics, the symbol for the quantity momentum is the lower
case letter "p“. The formula for momentum is:
P = mv
p = momentum
m = mass
v=velocity.
The standard metric unit of momentum is the kg • m/s.
The equation illustrates that momentum is directly
proportional to an object's mass and directly proportional to
the object's velocity.
5, 6, 7
From the definition of momentum (p = mv), it
becomes obvious that an object has a large
momentum if either its mass or its velocity is large.
Both variables are of equal importance in
determining the momentum of an object.
mV or Mv
Objects at rest do not have
momentum - they do not have
any “mass in motion."
8.9
A sample momentum calculation.
Let’s say that the mass of an object is 2.0 kg
and that the velocity is 4.0 m/s. That is”
M = 2.0 kg
V = 4.0 m/s
p = mv
p = (2.0 kg)(4.0 m/s)
p = 8.0 kg•m/s
Consider a Mack truck and a roller skate moving
down the street at the same speed.
The considerably greater mass of the Mack truck
gives it a considerably greater momentum.
Question
Will the truck always have more momentum than the
roller skate?
NO!
If a truck is at rest it has no momentum.The momentum of
an object at rest is always 0.
A truck moving very slowly and a roller skate moving very
fast could have the same momentum.
Momentum is not velocity.
Sometimes the concept of momentum is confused
with the concept of velocity.
Momentum is made up of both mass and velocity.
One must take the mass and multiply it times the
velocity to get the momentum.
10
Momentum is a conserved quantity in physics.
This means that if you
have an object or several
objects in a system,
interacting with each other,
but not being influenced by
any forces from outside
of the system, then the
total momentum of the
system does not change
over time.
11
Law Of Conservation Of Momentum
In the absence of an external force, the momentum
of a system remains unchanged.
The momentum lost by an object in a closed system
will be gained by other objects so that the total
momentum will remain the same in the system.
12, 13
Closed System: No matter or energy is allowed to enter or leave the system.
The separate momenta of each object within the system may
change.
One object might change momentum, while another object
changes momentum in an opposite manner, picking up the
momentum that was lost by the first.
Conservation of Momentum
Momentum = 0 before the shot
And after the shot
Cannon’s
momentum
Shell’s momentum
(equal and
opposite)
Before collision:
1. The momentum of the cart is 60 kg*cm/s
2. The momentum of the dropped brick is 0 kg*cm/s
3. The total system momentum is 60 kg*cm/s.
After collision:
1. The momentum of the cart is 20.0 kg*cm/s
2. The momentum of the dropped brick is 40.0 kg*cm/s
3. The total system momentum is 60 kg*cm/s.
4. The momentum lost by the loaded cart (40 kg*cm/s) is gained by
the dropped brick.
Momentum is transferred from the stick to the
puck. The momentum lost by the stick is equal
to the momentum gained by the puck. The total
amount of momentum stays the same.
Many violent collisions, fights, and body checks occur during an
ice hockey game. That is why it is perfectly appropriate to
demonstrate the rules of momentum, impulse, and collisions using
examples from ice hockey.
What We Know:
1. If velocity changes, momentum changes, and
acceleration (either + or –) occurs
2. For acceleration to occur, a force has to be
applied.
3. If a given force is applied over a longer time, more
acceleration occurs.
A force applied over time will change the momentum of an
object:
Time passes as a force is applied
to an object. When this happens
we say that an impulse is applied
to the object.
IMPULSE is a measure of how
much force is applied for how much
time, and it’s equal to the change in
momentum.
Forces applied over time
periods create impulses.
14, 15
Impulse is the product of the force exerted to change the
momentum of an object and the time it took to do it.
I = FΔT
I = impulse
F = force in Newtons
T = Time over which the force is applied (usually
seconds)
Impulse is measured in N-s (pronounced "Newton seconds")
F
t or Ft
16, 17
Imagine that a force of 2.0 N is applied to an object for 3.0 s.
Here is how to calculate that impulse:
I = FΔT
I = (2.0N)(3.0s)
I = 6.0 N-s
.
An object experiences a force of 15.32 N for a time
period of 3.45 s. What is the impulse on the object?
I = FΔT
I = (15.32N)(3.45s)
I = 52.85 N-s
An object experiences an impulse of 39.50 N-s for a time
period of 16.11 s. What is the force on the object?
I = FΔT
F = 39.50 N-s / 16.11 s
F = 2.54 N
Impulse Changes Momentum
• 1) Apply 10 N for 10 minutes
• 2) Apply 10 N for 5 minutes
Which scenario produces more momentum change?
I = Ft
I = Ft
(10 N)(600 s)
(10 N)(300 s)
6000 N-s
3000 N-s
Impulse changes momentum.
A greater impulse
exerted on an object
A greater change in
momentum
OR
Impulse = Change in momentum
I =F∆t = (m∆v)
Impulse = Δ(mv)
Greek symbol “Delta”
Means “the change in…”
Impulse can be exerted on an object to either
INCREASE or DECREASE its momentum.
18
Impulse
The formula for impulse can also be written as
F∆t = (m∆v)
I = Impulse
F = Force Newtons
t = Time
seconds
m = Mass kilograms
v = Velocity m/s
Units: N-s (Newton seconds)
19
An object is moving with a velocity of 4.23 m/s, and it speeds up
to a velocity of 14.18 m/s in 11.23 s. If its mass is 7.31 kg, what
force acted upon it?
fΔt = mΔv
f = 72.72 kg•m/s / 11.23 s
f = 6.47 N
A small force acting for a long time can be as effective as a
huge force acting for a short time.
fT
or
Ft
1. To decrease momentum, reduce the force applied or
extend the time over which the force is applied.
2. To increase momentum, increase the force and shorten
20, 21
the time over which it is applied.
Air bags can save your life in an auto accident.
Air bags increase the time your body gets to stop during
a collision.
Another way to change momentum is to change the factors
that determine momentum; mass and velocity.
A second way to increase momentum, is by increasing
either the mass or velocity (or both) of an object.
A second way to decrease momentum is to decrease
either the mass or velocity (or both) of an object.
mV
vM
22, 23
Crash Cushion (or Crash Attenuators) are rubber devices that
protects the motorist from a blunt object such as concrete wall or
guard rail.
Inside of the cushions is a very high density foam. As the vehicle
hits the front of the system, the system collapses. This increases
the time over which the force of the car is applied, thus reducing
the force applied by the collision with a car..
To increase impulse, either the force or time interval must
be increased. In baseball, this is done by hitting harder or
following through with the swing.
To decrease impulse, either the
applied force is reduced or the
time of contact is shortened.
24, 25
For example,
A bat stays in contact with the ball for 1.6 s causing an
impulse of 13.44 N-s. The average force of the bat on
the ball is:
F = Impulse/time = (13.44 N.s)/(0.0016 s) = 8,400 N
Increase the time over which the an impulse is acts:
F = Impulse/time = (13.44 N.s)/(0.0032 s) = 4,200 N
If the time over which an impulse acts (ball
stays in contact with the bat), the force
applied will decrease.
1.
2.
Friction between wheels and track not enough to set
entire train in motion
But enough locomotive friction to set one car in
motion
•
Coupling tightens
Next car is in motion
Impulse vs. Impact
Slack between coupling in RR cars allows the required
impulse to be broken into a series of smaller impulses
so friction between locomotive wheels and track can
pull the entire train.
26
Bouncing
• Impulses are greater when bouncing takes place
• Ft = ∆(mv)
• Falling flower pot hits your head
• Falling flower pot hits your head and bounces off
• Momentum is reversed. Impulse to stop< impulse
to “throw it back again”
– 2(∆mv)
– Karate chop
– Pelton wheel
27
Bouncing
Think about a bouncing ball:
Before it hits the ground: At the moment it hits
Speed = v
the ground:
Momentum = mv
Speed = 0
Momentum = 0
Impulse needed to stop
the ball = mv
After it leaves the ground:
Speed = v
Momentum = mv
Impulse needed to
accelerate the ball
upwoard = mv
Total Impulse = 2mv
Important point: It only takes an impulse of mv to stop the
ball. It takes twice the impulse (2mv) to make it bounce)
28
If the time of impact is long, the force will be milder. If
the time is very short, the force is powerful. When
things bounce off an object after hitting them, it is
even more deadly in force magnitude.
Momentum Vectors
• Momentum is conserved even when interacting objects don’t
move in a straight line.
• We can use our previously learned vector techniques to
anlayze these problems.
29
Momentum Vectors
Momentum is a vector quantity. The momentum
of the wreck is equal to the vector sum of car
A and B before the collision.
Question
2 cars are involved in a collision. Which would be more
damaging - if the cars collide and bounce or collide and
crumple?
Collide and bounce. The momentum change is
larger and therefore there is a greater impulse
and greater force.
Question
What are two ways that crumple zones in cars minimize the
effect of force in a collision?
1. Crumpling increases the time over which the
momentum is changed, thus decreasing the force.
2. Crumpling means less likely to rebound, thus less
impulse.
Question
Why is falling on a floor with more give less
dangerous than falling on a floor with less give?
The floor with more give allows a greater time for
the impulse that reduces the momentum of the
fall. A greater time for changing momentum
means less force.
Impulse: A one inch punch!
Momentum and impulse in action.
A lot of momentum, impulse and
a whole bunch of other fun stuff.
The
End
Resources:
The Phsics Classroom
YouTube
National Transportation Safety Board
Conceptual Physics: Paul Hewitt
The Matrix website
The Matrix Revolution website