Transcript Momentum_and_Impulse_Powerpointm

Momentum and Impulse
Introduction to Momentum
• Momentum is “inertia in motion.”
• Momentum is represented by “p”.
• Momentum is the product of the mass and
the velocity of an object.
p = mv
• Momentum is a vector quantity, meaning it
has both magnitude and direction. Its
direction is the same as its velocity.
• Momentum is measured in units of kg m/s
Introduction to Impulse
• Impulse is the product of the net force acting on a
body during the time which the force acts on it.
Units are N s.
Impulse = F(Δt)
• “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
• Impulse-Momentum Theorem – impulse is equal
to change in momentum.
𝐼𝑚𝑝𝑢𝑙𝑠𝑒 = Δ p
𝐹 𝑡 = 𝑚 Δv
F  t  mv f  mvi
Remember Newton’s
nd
2
Law?
Start with impulse – momentum
equation and divide both sides by t:
𝐹 𝑡 = 𝑚 Δv
𝐹𝑡
Δv
=m
𝑡
𝑡
F=ma
Look familiar???
Conservation of Momentum
• The total momentum of a system of objects
must remain constant, unless outside forces
act upon the system.
• In a closed isolated system, momentum
cannot be created nor destroyed.
• Momentum can be transferred from one
object to another, through an impulse (which
changes the individual momentums).
• 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. The objects
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.
• Separations or Explosions – the objects are at rest initially or
are all one object and then they separate or explode.
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
• mAvA+mBvB= (mA+mB) vf
𝑣𝐴
𝑣𝐵
𝑚𝐴
𝑚𝐵
vf
(𝑚𝐴 + 𝑚𝐵)
Elastic Collisions
Before
𝑣𝐴
• Remember: pinitial = pfinal
• mAvA+mBvB =mAvA’+mBvB’
𝑚𝐴
𝑚𝐵
After
• Usually mass remains the same
after the collision but this does
not always happen.
• ’ means after the collision
𝑣𝐴 ′
𝑚𝐴
𝑚𝐵
𝑣𝐵 ’
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 total momentum
of the system is zero. 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.
mbvb’ = - mrvr’
Why use an Airbag?
• The change in momentum and thus the
impulse stays the same whether or not you
have an airbag (same mass and change in
velocity).
• So if you increase the time over which the
force acts, the force of impact will decrease.
• time increases, so force decreases
Δp = F t
m Δv = F t
m Δv =
F
t
Why follow through on your golf swing?
• If you follow through, you are increasing the time
over which the force acts on the ball.
• For the same force, you would increase the impulse.
• Increasing the impulse would result in a greater
change in momentum.
• For the same mass, there would be a greater change in
velocity or acceleration. So the ball would go faster
and/or farther (if a tree or other obstacle doesn’t get in
its way!).
• Follow through increases the time which increases the
Δv or acceleration.
Ft=Δp
F t = m Δv
F
t = m Δv
Bug hitting windshield of bus
• The force of the bug on the bus is equal but opposite the
force of the bus on the bug - Newton’s 3rd Law.
𝐹𝑜𝑛 𝑏𝑢𝑠 = 𝐹𝑜𝑛 𝑏𝑢𝑔
• The time over which the force of the bug acts on the bus
and the time of the force of the bus acting on the bug is
the same as well.
• Since the force and time are the same, the impulse on
the bus and the impulse on the bug are the same.
𝐹𝑡𝑜𝑛 𝑏𝑢𝑠 = 𝐹𝑡𝑜𝑛 𝑏𝑢𝑔
𝐼𝑚𝑝𝑢𝑙𝑠𝑒𝑜𝑛 𝑏𝑢𝑠 = 𝐼𝑚𝑝𝑢𝑙𝑠𝑒𝑜𝑛 𝑏𝑢𝑔
Continued on the next page
Bug hitting windshield of bus con’t
• Although the momentums are very different, the
change in momentum of the bus and the change
in momentum of the bug are the same, since
their impulses were the same. (impulse = Δ p)
Δ p𝑏𝑢𝑠 =Δ p𝑏𝑢𝑔
• However the change in velocity or acceleration
of the bug will be much greater than that of the
bus because of the bug’s much smaller mass.
Δ p𝑏𝑢𝑠 =Δ p𝑏𝑢𝑔
𝐹𝑏𝑢𝑠 = 𝐹𝑏𝑢𝑔
m Δv (bus) = m Δv (bug)
m a (bus)= m a (bug)