Download Momentum and Impulse

Vectorman productions present:
A Nick enterprise:
Momentum and Impulse
Version: 1.29
this product is intended for the serious physics student, if you are not a serious physics
student,please use version 1.3, momentum and impulse
for dummies
Introduction to Momentum
• Momentum is the “quantity of motion.”
• Momentum is represented by “p”.
• Momentum is the product of the mass and
the velocity of an object or: p=mv
• Momentum is a vector quantity, meaning it
has both magnitude and direction.
• Measured in units of kg m/s
Introduction to Impulse
• Impulse is the product of the net force acting on a
given body during the time it acts. Units are N s.
• Impulse = F(Δt)
• Impulse = Change in Momentum
F  t  p
F  t  mv f  mvi
• “A large change in momentum occurs only when
there is a large impulse. A large impulse, however,
can result from either a large force acting over a
short time, or a smaller force acting over a longer
time.”
F*t=F*T
Remember Newton’s
nd
2
F  ma
v
F m
t
Ft  mv
Look .. familiar ?
Law?
Conservation of Momentum
• The total momentum of a system of objects
must remain constant unless outside forces
act upon the system.
• Momentum, like other physical quantities,
cannot be destroyed, merely redistributed.
• Momentum is distributed through impulse, or
the change in momentum (see how this all
fits together yet?)
• Most studies of the conservation of
momentum involve collisions.
Types of Collisions
• Perfectly (completely) Inelastic Collisions -collisions
where the objects stick together and move as one. The
mass after the collision is equal to the sum of the masses
and there is just one final velocity. Kinetic energy is not
conserved since a lot of kinetic energy is converted to heat
or other energies.
• Perfectly (completely) Elastic Collisions – collisions where
the objects bounce off of each other or separate. They then
return to their original shape. Kinetic energy is conserved.
• Many collisions are neither completely elastic or inelastic.
They separate after the collision but do not return to their
original shape, so heat is created and kinetic energy is lost.
• Separation or Explosion Collisions – the objects are at rest
initially or are all one object and then they separate.
Inelastic - Collisions that Stick
• For Collisions that Stick, the
after mass is the sum of all
the masses, and there is a
common or shared velocity.
• Remember:
pinitial = pfinal
• m1v1+m2v2= (m1+m2) vf
v1
v2
m1
m2
vf
(m1 + m2)
Elastic Collisions
Before
v1
• Remember: pinitial = pfinal
• m1v1+m2v2 =m1v1’+m2v2’
m1
m2
After
• Usually mass remains the
same after the collision but
this does not always happen.
• ’ means after the collision
v1’
m1
m2 v2’
Perfectly Elastic Collisions
• Momentum is conserved.
mAv A  mB vB  mAvA '  mB vB ' '
• Kinetic energy is also conserved.
1
1
1
1
2
2
2
mAv A  mB vB  mAv A '  mB vB '2
2
2
2
2
Separations/Explosions
• Sometimes objects start as one and separate
into two or more parts moving with
individual velocities.
– Example: A bullet is fired from a rifle. The
bullet leaves the rifle with a velocity of vb and
as a result the rifle has a recoil velocity of vr.
– Solution: Before the rifle is fired the
momentum of the system is zero. So…
0 = mbvb’ + mrvr’
– Note: for total momentum to remain zero, the
rifle’s momentum must be equal to but in the
opposite direction to the bullet’s momentum.
The Law of Momentum
Conservation
Momentum Conservation Principle
• For a collision occurring between object 1 and
object 2 in a closed, isolated system, the total
momentum of the two objects before the collision
is equal to the total momentum of the two objects
after the collision. That is, the momentum lost by
object 1 is equal to the momentum gained by
object 2.
A closed isolated system
is a set of objects
which encounter no
forces or influences other
than those they exert on
each other.
• Consider a collision between two objects - object
1 and object 2. For such a collision, the forces
acting between the two objects are equal in
magnitude and opposite in direction (Newton’s
Third Law)
• The forces act between the two objects for a
given amount of time.
• Regardless of how long the time is, it can be said
that the time that the force acts upon object 1 is
equal to the time that the force acts upon object 2.
• Since the forces between the two objects are
equal in magnitude and opposite in direction, and
since the times for which these forces act are
equal in magnitude, it follows that the impulses
experienced by the two objects are also equal in
magnitude and opposite in direction.
• Since each object experiences equal and
opposite impulses, it follows logically that
they must also experience equal and
opposite momentum changes.
• In a collision, the momentum change of
object 1 is equal and opposite to the
momentum change of object 2. That is, the
momentum lost by object 1 is equal to the
momentum gained by object 2.
Why use an Airbag?
• Since the change in momentum and thus the impulse stays
the same whether or not you have an airbag, the force with
which you hit will be decreased by increasing the time
over which the force acts.
Δp = F t
m (vf – vi) = F t
m (vf - vi ) =
F
t
Why follow through in your golf swing?
• By following through you are increasing the time that the club is
in contact with the ball. Thus you are increasing the impulse
(assuming force is the same) which results in a greater change in
momentum. That means a greater acceleration or change in
velocity so the ball will go faster and farther (if a tree or other
obstacle doesn’t get in its way!).
Ft=Δp
F t = m Δv
F
t = m Δv
• Consider a collision in football between a fullback
and a linebacker during a goal-line stand. The
fullback plunges across the goal line and collides
in midair with linebacker. The linebacker and
fullback hold each other and travel together after
the collision. The fullback possesses a momentum
of 100 kg*m/s, East before the collision and the
linebacker possesses a momentum of 120 kg*m/s,
West before the collision. The total momentum of
the system before the collision is 20 kg*m/s, West.
• Therefore, the total momentum of the system after
the collision must also be 20 kg*m/s, West. The
fullback and the linebacker move together as a
single unit after the collision with a combined
momentum of 20 kg*m/s. Momentum is conserved
in the collision.