Download chap 6 momentum

Momentum
Momentum and Collisions
This chapter is concerned with
inertia and motion.
Momentum helps us understand
collisions.
Momentum
Inertia in motion
mass => quantity of matter in
an object
inertia => an object's
resistance to change in motion
Momentum Defined
The quantity of motion,
momentum, as being directly
proportional to the object's
mass and velocity.
Momentum is a vector
quantity……. ……..because it is
a scalar (mass) of the vector
p = Mv
Momentum = mass X
velocity
Momentum Defined
 = mv
where  is
momentum with units
kgm/s
m is the mass with units kg
v is the velocity with units
m/s
Momentum Defined
Very Fast objects have
Greeeeat momentum
Very Massive Objects have
Greeeat momentum
Momentum
If Direction Not
Important………..
…….Momentum = mass x
speed
Therefore……..p = ms
A large truck has more momentum
than a car moving at the same
speed because it has a greater
mass.
Which is more difficult to slow
down? The car or the large truck?
Large Momentum Examples:
– Huge ship moving at a small velocity
P = mv
– High velocity bullet
P = mv
Impulse
In order to change the
momentum of an object you
must apply a force over some
time interval.
Impulse = Force  time interval
  p= F t
Impulse
Newton’s Second Law can read
SF = ma = m(v/t) = (mv)/(t) = (p/ t)
Rearranging,
Impulse = p = Ft
Impulse
When force is limited ...
– increase t (Follow through!)
– make it bounce (Pelton wheel)
Impulse and Momentum
Impulse = Change in Momentum

= Final (mv) - Initial (mv)
F t = mv
Make it Bounce
p1
p2 = -p1
p = p2 - p1 = -p1 - p1
= -2p1
Case 1: Increasing Momentum
– Apply a force for a long time.
– Examples:
• Follow through on a golf swing.
• Pushing a car.
F
t
Case 2: Decreasing Momentum
– Apply a force for a long time.
– Examples:
•
•
•
•
Air bags in cars.
Catching an egg.
Boxing, Figure 5.6
Soft collisions, Figure 5.3.
F
t
Case 3: Decreasing Momentum
– Apply a force for a short time.
– Examples:
• Boxing
• Karate
F
t
Minimize the Force
To minimize force …
–Increase t
• catching a ball
• Bungee jumping
If SF = 0, then impulse = p = zero,
or
Momentum is conserved
Conservation of Momentum
This means that the momentum
doesn’t change.
Recall that F t = (mv)
In this equation, F is the "external
force".
Internal forces cannot cause a
change in momentum.
Examples
Conservation of Momentum: If there
are no external forces, the total
momentum for a system remains
unchanged.
Example 1: a person sitting inside a
car pushing against the dashboard
Example 2: a bullet fired from a rifle
Example 3: a rocket is space
Conservation of Momentum
Conservation of Momentum
Conservation of Momentum
In any "closed system" the
total momentum does not
change.
Conservation of Momentum
……..(Total momentum)before event
= (Total momentum) after event
(mbvb + mrvr) before = (mbvb + mrvr)
Demonstrations
Rocket balloon
Cannon
Rocket Scooter
When can Momentum be Conserved?
Internal
forces cannot cause
a change in momentum of the
system.
For
conservation of
momentum, the external
forces must be zero.
Momentum and Collisions
Elastic Collisions
– objects rebound
– e.g. superball
Inelastic Collisions
– object stick together an usually
become distorted and generate heat
– e.g. clay ball
COLLISIONS
Collisions involve forces internal to
colliding bodies.
Inelastic collisions - conserve
momentum
Totally inelastic collisions - conserve
momentum and objects stick
together
Elastic collisions - conserve energy
and momentum
v = 10
v=0
M
M
Before Collision
p = Mv
v’ = 5
M
Mv = 2Mv’
v’ = ½ v
M
After Collision
p = 2Mv’
Conserve Energy and Momentum
Before Collision
Case 1:
Equal masses
Case 2:
M>M
Case 3:
M<M
Momentum = Mass x Velocity
p = mv
v
p = mv
Elastic and inelastic collision
V1
M
V2
M
Before Collision
V1’
M
M
After Collision
V2’
Types of Collisions
1. Elastic
2. Inelastic collisions
3. Completely Inelastic collisions
Elastic Collisions
Momentum…. is
conserved in
every collision
Kinetic Energy…..is
conserved……. …..No sound
or heat is produced
Elastic Collisions
Examples…..
Subatomic particles
repelling magnets
a “perfect”super ball
Elastic Collisions
M1v1o + m2 v2o = m1 v1f +m2v2f
Inelastic Collisions
Momentum…... is conserved
Kinetic Energy……. is not
conserved
lost in form of heat or sound
Contains almost all types of
collisions
Inelastic Collisions
M1v1o + m2 v2o = (m1+m2)vf
Perfectly Inelastic Collisions
More…. Kinetic energy is lost as
heat or sound
Colliding objects stick together
Example Problems...