Download Unit 9 Summary

Unit 9:
Momentum & Impulse
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1.
Momentum
Define momentum and distinguish between momentum and velocity.
momentum = (mass)(velocity)
2.
Impulse
Define impulse; distinguish between impulse and force.
Determine the impulse acting on an object
via a F vs t graph
given the change in momentum.
Determine the force acting on an object, given its change in momentum.
3. Conservation of Momentum
Show that the system momentum before a collision is equal to the system momentum after
the collision.
system momentum = constant
Show that the total system momentum after an explosion remains zero.
Distinguish between elastic and inelastic collisions (∆Ek1 ≠ ∆Ek2)
Use conservation principles to solve momentum problems involving elastic and inelastic
collisions for initial velocity, final velocity or mass, given the other values.
Momentum & Impulse
The final unit in our study of classical physics
mechanics brings together many models from
previous units. In this unit we will connect:
• Constant velocity model
• Uniform acceleration model
• Newton’s 1st, 2nd, & 3rd Laws of Motion
• Conservation of energy model
Momentum & Impulse
Our previous work examined the relationship of
the motion of an object and the energy it
stores in motion. This relationship was
described by:
• the mass of the object
• the velocity of the object
Energy kinetic: Ek= ½ mv2
Momentum & Impulse
Therefore, two objects with the same mass could
store different amounts of energy if the velocities
were different.
Likewise, two objects with the same velocity could
store different amounts of energy if the masses
were different.
As we consider our new model, we will further
examine the relationship of mass and velocity in
connection with Newton’s Laws.
Momentum & Impulse
Newton’s 1st Law holds that an object in motion will
continue moving in the same manner (no velocity
change) unless acted on by an unbalanced force.
(Fnet=0N : constant velocity or Fnet≠0N : uniform
acceleration)
Newton’s 2nd Law describes this change in motion by
quantifying the relationship between net force (Fnet)
and the mass of the object. (acceleration= Fnet/mass)
Newton’s 3rd Law holds that two objects interacting with
each other must exert equal magnitude, but opposite
direction forces on each other.
(FAB=-FBA)
Momentum & Impulse
Rearranging Newton’s 2nd Law we get:
Fnet= m(a)
Using the definition of acceleration (Δv/Δt) we get:
Fnet= m (Δv/Δt)
Multiplying both sides by Δt simplifies to
Fnet(Δt) = m (Δv)
This simplification allows the motion allows a comparison
of the mass and velocity of two objects that are
interacting with each other according to Newton’s 3rd
Law
Momentum & Impulse
Fnet AB(Δt) = mA (ΔvA)
Fnet BA(Δt) = mB (ΔvB)
According to Newton’s 3rd Law, FAB=-FBA.
Therefore, adding the first two relationships
results in the following:
Fnet AB(Δt)
= mA (ΔvA)
+Fnet BA(Δt)
= mB (ΔvB)
0
= mA (ΔvA) + mB (ΔvB)
0 = mA (ΔvA) + mB (ΔvB)
0 = mA (vfA- viA ) + mB (vfB- viB)
0 = mAvfA- mAviA + mBvfB- mBviB
mAviA + mBviB = mAvfA+ mBvfB
This new relationship holds that the sum of the
products of two objects mass and velocities
before interaction must equal the sum of the
products after the interaction.
Model Summary
Conservation of momentum relationship
mAviA + mBviB = mAvfA+ mBvfB
Impulse – Change in Momentum relationship
(impulse)
=
(change in momentum)
Fnet(Δt)
=
m (Δv)
Model Summary
Conservation of momentum relationship
mAviA + mBviB = mAvfA+ mBvfB
The conservation of momentum is unlike the
conservation of energy in that momentum is
directional. This allows a system with no
initial momentum to change into a system
with momentum provided the sum of the
momenta is zero.
Model Summary
Impulse – Change in Momentum relationship
(impulse)
=
Fnet(Δt)
=
(change in momentum)
m (Δv)
Using the Impulse-Momentum relationship, it is
possible to analyze a system to determine what
factor could be modified to either increase of
decrease force acting on an object. A common
application of this concept is found in safety
features engineered into automobiles.
Model Summary
Impulse – Change in Momentum relationship
(impulse)
=
(change in momentum)
Fnet(Δt)
=
m (Δv)
One representation used to compare changes to a system is the force versus time graph. The graph
below compares two scenarios where change in momentum is the same; however maximum force
is changed by increasing the time interval for the event. The areas under the curves represent the
impulse and for both situations, the areas would be equal. If the time interval is extended, then
the same change in momentum can occur using a smaller average force.
Force
Time
Resources
• Honors Text – pages 198-216
• CP Text – pages 58-64